AUTOMATED PREDICTION OF FLARING BEHAVIOR BASED...

AUTOMATED PREDICTION OF FLARING BEHAVIOR BASED ON

COMPLEXITY MEASURES FROM SOLAR MAGNETOGRAMS

BY

AMANI M. AL-GHRAIBAH, B.S.B.M.E.

A thesis submitted to the Graduate School

in partial ful�llment of the requirements

for the degree

Master of Science

Major Subject: Electrical Engineering

New Mexico State University

Las Cruces, New Mexico

December 2012

�An Automated Predection of Flaring Behavior Based on Complexity Measures

From Solar Magnetograms,� a thesis prepared by Amani Al-Ghraibah in partial

ful�llment of the requirements for the degree, Master of Engineering, has been

approved and accepted by the following:

Linda LaceyDean of the Graduate School

Laura BoucheronChair of the Examining Committee

Date

Committee in charge:

Dr. Laura Boucheron, Chair

Dr. Phillip Deleon

Dr. James McAteer

ii

DEDICATION

I dedicate my dissertation work to my family and many friends. A special feeling of

gratitude to my loving parents, Muneer and Hanan AL-Ghraibah whose words of

encouragement and push for tenacity ring in my ears. My sister Zain, my brothers

Mohammad and Omar who all gave me an incorporeal support. A special feeling

of gratitude to my loving husband: Mohammad Omari, intelligent friend who has

never left my side. Also, I dedicate this work to my little son Karam who always

bring happiness to me after a long day of work. I also dedicate this dissertation

to my many friends who have supported me throughout the process. I will always

appreciate all they have done.

iii

ACKNOWLEDGMENTS

In the name of Allah the most merciful and most gracious, �rst and foremost all

praise and thanks to Allah (God) for giving me strength, patience, and providing

me the knowledge to �nalize this work.

I would like to thank my committee members who were more than generous

with their expertise and precious time. A special thanks to Dr. Laura Boucheron,

my adviser for her countless hours of re�ecting, reading, encouraging, and most

of all patience throughout the entire process. Thank you Dr. Phillip Deleon and

Dr. James McAteer for agreeing to serve on my committee. I would like to ac-

knowledge and thank electrical and computer engineering department for allowing

me to conduct my research. Special thanks goes to the members of astronomy

department and NMSU solar and stellar research group for their support and help

over the last two years.

Finally, I am gratefully acknowledge the New Mexico State University Interdis-

ciplinary Research Grant and NASA-EPSCOR for their funding support during

my work. Also, I would like to thank Dr. Laura Boucheron, Dr. Jason Jackiewiz

and Dr. Bernard McNamara for the great award that they gave it to me.

iv

VITA

October 9, 1985 Born in Irbid, Jordan

2003-2008 B.S.B.M.E., Jordan University of Science and Technology,Irbid, Jordan

2008-2009 Teaching Assistant, Biomedical Engineering Department,Jordan University of Science and Technology.

2010-2012 Graduate Research Assistant,Electrical and Computer Engineering Department,New Mexico State University, Las Cruces, New Mexico.

PUBLICATIONS [or Papers Presented]

1. Fields, Flares, And Forecasts. L. Boucheron, Amani Al-Ghraibah, J. McA-

teer, H. Cao, J. Jackiewicz, B. McNamara, D. Voelz, B. Calabro, K. DeGrave,

M. Kirk, A. Madadi, A. Petsov, G. Taylor. Solar Physics Division Meeting,

2011.�poster�.

2. Automated Classi�cation of Flaring Behavior in Solar Active Regions: Pre-

liminary Results. Amani Al-Ghraibah, Laura E. Boucheron and R. T. James

McAteer. American Astronomical Society 219th Meeting, 2012.�poster�.

3. Automated Predection of Flaring Behavior Based on Complexity Measures

From Solar Magnetograms. Amani Al-Ghraibah, Laura E. Boucheron and R. T.

James McAteer. Solar Information Processing Workshop, 2012.�poster�.

4. Automated Prediction of Flaring Behavior Based on Complexity Measures

from Solar Magnetograms, Amani Al-Ghraibah, Laura E. Boucheron, and R. T.

James McAteer. Solar Physics, 2012. �Submitted�

v

FIELD OF STUDY

Major Field: Digital Signal Processing and Pattern Recognition

vi

ABSTRACT

Automated Prediction of Flaring Behavior Based on Complexity Measures From

Solar Magnetograms

BY

AMANI AL-GHRAIBAH, B.S.B.M.E.

MASTER OF SCIENCE

New Mexico State University

Las Cruces, New Mexico, 2012

Dr. Laura E. Boucheron, Chair

Solar active events are the source of many energetic and geo-e�ective events

such as solar �ares and coronal mass ejections. Understanding how these complex

source regions evolve and produce these events is of fundamental importance, not

only to solar physics but also to the demands of space weather forecasting. Here,

we present work using physical properties of magnetic region complexity for an

automated classi�cation of future �are activity. First, we extract features related

to physical properties of active region magnetic �elds including fractal-, gradient-,

vii

neutral line-, emerging �ux-, and wavelet-based techniques. Second, we use au-

tomated classi�ers to predict whether an active region will �are in the following

k hours, where k will vary. Third, we apply feature selection to extract the most

signi�cant features for �are prediction and improve the classi�cation speed and ac-

curacy. This work gives a preliminary assessment of the use of feature extraction,

feature selection, and classi�cation for �are prediction as well as to lend insight

into the physical characteristics of active regions that are most discriminatory for

such a prediction task.

viii

CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 The Sun and Solar Activity . . . . . . . . . . . . . . . . . . . . . 1

1.2 Relation of Photospheric Magnetic Field to Solar Activity . . . . 5

1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2 IMAGE ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Gradient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Neutral line Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Fractal Dimension Analysis . . . . . . . . . . . . . . . . . . . . . 23

2.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 Emerging Flux Region Analysis . . . . . . . . . . . . . . . . . . . 29

ix

2.5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . 30

2.6 Wavelet Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.6.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.6.2 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . 34

3 CLASSIFICATION, FEATURE SELECTION AND PERFORMANCE

MEASURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.1 Fisher Linear Discriminant Analysis (FLDA) . . . . . . . . . . . . 39

3.2 Relevance Vector Machine (RVM) . . . . . . . . . . . . . . . . . . 40

3.3 Feature Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . 46

4 EXPERIMENTS AND RESULTS . . . . . . . . . . . . . . . . . . 49

4.1 Experiment setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 Classi�cation using Fisher Linear Discriminant Analysis . . . . . . 51

4.2.1 Classi�cation Using All Features . . . . . . . . . . . . . . . 51

4.2.2 Classi�cation Using Feature Subsets . . . . . . . . . . . . . 52

4.3 Classi�cation using Relevance Vector Machine . . . . . . . . . . . 57

4.3.1 Classi�cation Using All Features . . . . . . . . . . . . . . . 57

4.3.2 Classi�cation Using Feature Subsets . . . . . . . . . . . . . 58

4.4 Classi�cation after Feature Selection . . . . . . . . . . . . . . . . 62

4.4.1 FLDA Classi�cation on Optimal Subset . . . . . . . . . . 63

x

4.4.2 RVM Classi�cation on Optimal Subset . . . . . . . . . . . 65

4.4.3 Determination of an Appropriate Number of Optimal Features 66

5 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6 FUTURE WORK . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

A MATLAB CODE . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

A.1 Gradient Analysis Code . . . . . . . . . . . . . . . . . . . . . . . 77

A.2 Neutral line Detection Code . . . . . . . . . . . . . . . . . . . . . 79

A.3 Fractal Dimension Code . . . . . . . . . . . . . . . . . . . . . . . 83

A.4 Emerging Flux Region Code . . . . . . . . . . . . . . . . . . . . . 86

A.5 Wavelet Analysis Code . . . . . . . . . . . . . . . . . . . . . . . . 89

A.6 Feature Selection Code . . . . . . . . . . . . . . . . . . . . . . . . 91

A.7 Fisher Linear Discriminant Analysis Classi�cation Code . . . . . . 94

A.8 Relevance Vector Machine (RVM) Classi�cation Code . . . . . . . 99

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

xi

LIST OF TABLES

1 Features extracted from gradient analysis. . . . . . . . . . . . . . 13

2 Features extracted from neutral line analysis . . . . . . . . . . . . 22

3 Features extracted after EFR analysis . . . . . . . . . . . . . . . . 32

4 Features extracted from wavelet analysis. . . . . . . . . . . . . . . 37

5 Flaring forcasting contingency table . . . . . . . . . . . . . . . . . 47

6 The top 16 ranked features at 14 hours timescale. . . . . . . . . . 64

xii

LIST OF FIGURES

1 Magnetogram image. . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Magnetogram active region image and the resultant magnitude gra-

dient image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 Standard deviation feature and active region's �are times. . . . . 14

4 Noisy zero-Gauss contour before being weighted by the gradient

image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Visualizations of the gradient-weighted NL for a simple bipolar re-

gion and a multipolar region . . . . . . . . . . . . . . . . . . . . . 18

6 Thresholded GWNL images for the bipolar and multipolar ARs

considered in Figure 5. . . . . . . . . . . . . . . . . . . . . . . . . 20

7 Values of gradient-weighted length of the NL and the active region's

�are times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

8 Examples of dilated neutral line image with two di�erent structur-

ing element radii. . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

9 Example log-log plot of dilated area versus structuring element ra-

dius (points) along with the least-squares �tted line. . . . . . . . . 27

10 Three example NL images and their respective NL FD. . . . . . . 27

xiii

11 Fractal dimension values and the active region's �are times for one

active region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

12 Two magnetogram images taken on 10/29/2003 and their resultant

di�erence image. . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

13 Thresholded di�erence image and its binary mask. . . . . . . . . . 32

14 Maximum values of the di�erence images in one active region and

known �are times. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

15 The original magnetogram image and its three highpass detail im-

ages after one level of wavelet decomposition. . . . . . . . . . . . 36

16 Energy values at 5 levels of wavelet decomposition for the image

shown in Figure 15(a). . . . . . . . . . . . . . . . . . . . . . . . . 37

17 Energy values at level 2 for one active region and known �are times. 38

18 Illustration of FLDA classi�cation for a two class case. . . . . . . 41

19 Illustration of RVM classi�cation for a two class case. . . . . . . . 43

20 FLDA classi�cation results using a combination of all features. . . 51

21 FLDA classi�cation results using gradient features listed in Table 1. 54

22 FLDA classi�cation results using neutral line features listed in Ta-

ble 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

23 FLDA classi�cation results using the fractal dimension feature. . . 55

24 FLDA classi�cation results using emerging �ux region features listed

in Table 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

xiv

25 FLDA classi�cation results using wavelet features listed in Table 4. 56

26 RVM classi�cation results using a combination of all features. . . 57

27 RVM classi�cation results using gradient features listed in Table 1. 59

28 RVM classi�cation results using neutral line features listed in Table 2. 60

29 RVM classi�cation results using fractal dimension feature. . . . . 60

30 RVM classi�cation results using emerging �ux region features listed

in Table 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

31 RVM classi�cation results using wavelet features listed in Table 4. 61

32 Histogram of features selected at 14 hours timescale ranked from

least frequent at 1 to most frequent at 35. . . . . . . . . . . . . . 63

33 FLDA classi�cation results using 6 top-ranked features. . . . . . . 65

34 RVM classi�cation results using 6 top-ranked features. . . . . . . 66



37 TSS values at 14 hour before �are case using di�erent features subsets. 69

xv

1 INTRODUCTION

1.1 The Sun and Solar Activity

The sun is the closest star to the earth. It is the source of heat which sustains

life to earth and controls our climate and weather. The sun is an intensely hot,

self-luminous body of gases at the center of the solar system. Its gravitational

attraction maintains the planets, comets, and other bodies of the solar system in

their orbits.

The sun has many di�erent layers that describe its structure, including the

core, radiation zone, convection zone, photosphere, chromosphere, and corona.

The core is the innermost layer of the sun and it is a source for all the sun's energy.

Once the energy is produced in the core of the sun, it has to travel from the solar

center to the outer regions. From that the radiation zone provides an e�cient

means of transferring energy near the core and the temperature in the radiation

zone is cooler than the core. In the convective zone, the energy is transferred much

faster than it is in the radiative zone. This is because it is transferred through

the process of convection. Hotter gas coming from the radiative zone expands and

rises through the convective zone. It can do this because the convective zone is

cooler than the radiative zone and therefore less dense. As the gas rises, it cools

1

and begins to sink again. As it falls down to the top of the radiative zone, it heats

up and starts to rise. This process repeats, creating convection currents and the

visual e�ect of boiling on the Sun's surface which is called granulation [47].

As we look down into the atmosphere at the surface of the Sun the view

becomes more and more opaque. The point where it appears to become completely

opaque is called the photosphere. Thus, the photosphere may be thought of

as the imaginary surface from which the solar light that we see appears to be

emitted. The diameter quoted for the Sun usually refers to the diameter of the

photosphere. The Photosphere emits most of the Sun's light that reaches earth

directly. Temperatures range from about 18,000 F (10,000 C) at the bottom

to 8,000 F (4,000 C) at the top; its density is about 1/1,000 that of air at the

surface of Earth. The Photosphere has a granular structure and sunspots are

photospheric phenomena. The layer that sits just above the photosphere is called

the chromosphere and it is the extended gases from photosphere. Opposite of the

photosphere, the temperature of this layer increases with increasing height, its

temperature at the top of photosphere is only about 4,400 K, while at the top of

the chromosphere, some 2,000 km higher, it reaches 25,000 K. One of the features

of the chromosphere is the chromospheric network. It outlines the supergranules

and is present there because of the magnetic �eld bunches in the supergranules.

The network makes a web pattern of magnetic �eld lines on the Sun.

The outermost layer of the sun is the corona. Visible for the human eyes only

2

during eclipses, it is a low density cloud of plasma with higher transparency than

the inner layers. The corona is hotter than some of the inner layers. Its average

temperature is 1 million K (2 million F) but in some places it can reach 3 million

K (5 million F) [47].

The sun is not a quiet star, but one that exhibits sudden releases of energy.

Solar activity refers to any natural phenomena occurring on or in the sun, such as:

sunspots and the solar cycle, solar �ares, solar wind, and coronal mass ejections.

Sunspots are dark, planet-sized regions that appear on the surface of the sun. The

average number of spots that can be seen on the face of the sun is not always the

same, but goes up and down in a cycle called the sunspot cycle, which has an

average period of about eleven years. Sunspots are caused by the sun's magnetic

�eld welling up to the photosphere. The powerful magnetic �elds around sunspots

produce active regions on the sun, which often lead to solar �ares and Coronal

Mass Ejections (CMEs). The solar activity of �ares and CMEs are called �solar

storms�.

Solar �ares are among the most energetic events in the solar system and have

intrigued generations of physicists. These events in�uence a panorama of physical

systems, from the surface of the Sun, through the solar system and onto Earth,

where they can cause adverse space weather conditions. Flares occur in active

regions in outer solar atmosphere (corona). Active regions (ARs) are volumes of

the Sun with complex, twisted magnetic �eld con�gurations. The energy released

3

by solar �ares (up to ≈ 1032 erg) is thought to come from the energy stored in the

magnetic �eld being suddenly converted into other forms, accelerating particles

to near-relativistic speeds and creating temperatures in excess of 10,000,000 K.

Turbulent motions on the surface of the Sun (the photosphere) twist and wind up

the magnetic �eld in the corona. A complex photosphere causes a complex corona,

and a complex corona has more stored energy, hence will produce more, larger,

solar �ares. However, the precise conditions required to create these enormously

energetic events are as yet unknown and so accurate space weather forecasts re-

main elusive.

At the surface of the Earth we are well protected from the e�ects of solar �ares

and other solar activity by the Earth's magnetic �eld and atmosphere. The most

dangerous emissions from �ares are energetic charged particles (primarily high-

energy protons) and electromagnetic radiation (primarily x-rays). Coronal mass

ejections are more likely to have a signi�cant e�ect on our activities than �ares

because they carry more material into a larger volume of interplanetary space.

While a �are alone produces high-energy particles near the Sun, some of which

escape into interplanetary space, a CME drives a shock wave which can contin-

uously produce energetic particles as it propagates through interplanetary space.

When a CME reaches the Earth, its impact disturbs the Earth's magnetosphere,

setting o� a geomagnetic storm. A CME typically takes 3 to 5 days to reach

the Earth after it leaves the Sun. Observing the ejection of CMEs from the Sun

4

provides an early warning of geomagnetic storms.

1.2 Relation of Photospheric Magnetic Field to Solar Activity

Many studies have been made of coronal activity and their concomitant photo-

spheric �eld distributions [1�3,8, 9, 13�16,20,24�26,28,29, 32,37�39,43�45,55,59,

65,69�72,74]. A consistent, causal relationship between photospheric �eld condi-

tions and activity is unknown (e.g., see conclusions in [25,37,39,43]). Nevertheless,

there is optimism that photospheric measures may yield some insight into immi-

nent eruptive behavior (e.g., [1, 2, 13,20,24,32,38,55,69]).

Many of the previously mentioned studies rely on measures from vector mag-

netograms [15, 16, 25, 37�39, 74], which provide both longitudinal (line-of-site)

and transverse components, but is not yet readily available for large datasets.

This thesis will look at a large set of parameters, unlike the few (≤ 7) studied

in [1�3,8,9,13�16,20,24�26,28,29,32,43�45,55,59,65,69�72,74]. Furthermore, we

study a large data sample unlike [1�3,8,14�16,24�26,32,37,38,65,74] who utilize

< 100 active regions, and we explicitly include control data (i.e., regions that do

not �are) unlike [1�3, 24�26, 45, 55, 65, 74]. Our work will also utilize standard

pattern recognition and classi�cation techniques to determine (classify) whether

a region is expected to �are; this is in contrast to many previous studies that

rely merely on correlations or observations of parameters in relation to �aring

activity [1�3,8, 9, 24�26,29,32,37,44,45,55,65,74].

5

To the best of our knowledge, there are no studies that use both line-of-sight

magnetograms and a large dataset. In this thesis, we will analyze a large set of line-

of-sight (LOS) Michelson Doppler Imager (MDI) magnetograms [58] and extract

a large set of features to describe active region complexity and other features

of postulated importance for �are prediction. We hope this work will provide

a similar reference for LOS magnetograms as the comprehensive work on vector

magnetograms [39]. Of particular interest in this work is the characterization of

local structure of active region �elds�critical in many theories of activity�that can

be lost in some global measures. The general categories of features we consider

are:

1. Field gradient, indicative of pressure build-up in the photosphere

2. Neutral lines, related to energy release locations

3. Fractal dimension, which relates to the active region complexity

4. Emerging �ux regions, which can act as energy release triggers

5. Wavelet analysis, which allows separation of the �eld into its component

lengthscales

These measurements will allow us to more completely characterize �eld distri-

butions in active regions. Furthermore, we will consider these features in an

automated classi�cation framework whereby we will predict a �are occurrence for

6

a given time window using a combination of the features. Additionally, we use

feature selection to determine the optimal features for describing the complexity

of an active region. This will allow for an improvement in both the computational

e�ciency and accuracy of the classi�cation algorithms.

1.3 Outline

We present details of the complexity features we use in Chapter 2, including a

physical motivation for each of the features and the speci�cs of extracting those

features. We brie�y review the automated classi�cation methods in Chapter 3, and

present results using the proposed features for classi�cation of �are activity and

discuss discriminatory features in Chapter 4. In Chapter 5 we provide discussion

and conclusions, and future work in Chapter 6.

7

2 IMAGE ANALYSIS

In this chapter we describe the dataset used for this work and provide background

and technical description related to each of the �ve main categories used for feature

extraction.

2.1 Dataset

Magnetogram images are not a �picture� of the Sun which you might see with your

eyes. Rather, it's an image taken by an instrument which can detect the strength

and location of the magnetic �elds on the sun. In a magnetogram image, grey

areas indicate that there is low magnetic �eld, while black and white areas indicate

regions where there is a strong positive (white) or negative (black) magnetic �eld

[33]. Figure 1 shows an example of one magnetogram image; its size is 152x152

pixels and is not a �xed size for all of the magnetogram images. Our dataset

contains approximately 2000 di�erent active regions (ARs), where each active

region is saved in one directory. Each of these directories has tens to hundreds of

subsequent magnetogram images showing the development of that active region

on the solar surface.

For our work, magnetogram images are considered only if the center of the AR

is within 650 arcseconds of the disk center (the full disk radius is 950 arcseconds)

to avoid projection e�ects and disk edge artifacts. To do that, the distance from

8

Figure 1: Magnetogram image.

the disk center to the center of the active region is calculated and it is called

the radius. Then, we ignore the image if the resulting radius is greater than 650

arcseconds. This condition is applied to each magnetogram image in our data

before the feature extraction process is started.

2.2 Gradient Analysis

2.2.1 Background

The evolution of magnetic �elds in solar active regions can be described by the

magnetic induction equation

∂B

∂t= ∇× (v ×B) +

1

Rm

∇2B (1)

where Rm is the magnetic Reynolds number, and v and B are the vector velocity

and magnetic �elds, respectively. The magnetic Reynolds number varies from 106

to 1010 in the photosphere (e.g., [48]), meaning that the �rst term on the right hand

9

side of Equation (1) dominates on the solar surface. That is, the magnetic �eld is

frozen into the plasma, and is advected by bulk plasma motions. It is because the

�eld is frozen into the plasma in the photosphere that large transverse gradients

are observed across the neutral line (the line separating positive and negative

polarities) of large δ spots [49] [74]. Here, converging photospheric �ows sweep

opposite polarity �elds towards the neutral line of the δ. Over a period of hours,

the continued concentration of opposite polarities in a relatively small area leads

to strong transverse gradients [19].

In general, the spatial gradient provides a measurement of �eld conditions at

localized positions within the region. Photospheric �eld gradients have long been

reported to be associated with �aring activity and have been reported by many

authors for individual single events (e.g., [74]). From a theoretical perspective,

several models predict the existence of increased gradients in the �eld for a few

hours prior to activity [4] [51].

Other researchers have used gradient analysis for �are prediction. Wang et

al [65] concentrated his study on the analysis of the magnetic gradient along �aring

neutral lines where he found that the onset of each solar �are is followed by an

obvious change in the magnetic gradient. Zhang [73] de�ned the nonpotentiality

of solar active regions depending on the shear and gradient of the magnetic �eld

because they are important and re�ect the strength of the electric current in the

active regions. The magnetic gradient was used by Prasad [50] to di�erentiate the

10

stressed magnetic �elds in active regions. Leka and Barnes ( [37], [38], [39]) used

the �rst four moments of the spatial gradient magnitude in their discriminatory

analysis for �aring and non-�aring regions. Yu et al [69] used the maximum

horizontal gradient as one of three parameters in their multiresolution short-term

solar �are prediction.

2.2.2 Data Processing

From the perspective of image processing, the spatial gradient is the �rst derivative

of the image. This processing will highlight small specks and edges that may not

be as visible in the original image. For an image f(x, y), the gradient of f at

coordinates (x, y) is de�ned as the two-dimensional column vector [21]

vf =

[Gx

Gy

]=

[df/dxdf/dy

]= (

df

dx)i+ (

df

dy)j (2)

where Gx and Gy are the spatial gradients in the x and y directions, respectively,

and i and j are unit vectors in the x and y directions, respectively. The magnitude

of this vector is given by:

|vf | =√G2x +G2

y (3)

To approximate the �rst derivative for the discretely-indexed image f , we use

the two Sobel �lters

hx =

−1 0 1−2 0 2−1 0 1

(4)

11

(a) Original magnetogram image. (b) Magnitude gradient image.

Figure 2: Magnetogram active region image and the resultant magnitude gradient

image. In the later image, we note that the high gradient regions (red colors)

correspond to regions where the polarity at the magnetic �eld changes over a

small spatial scale.

and

hy =

1 2 10 0 0−1 −2 −1

(5)

The image is �ltered (convolved) with each Sobel �lter, yielding Gx = hx ∗ f and

Gy = hy ∗ f where ∗ is the 2-dimensional convolution operator.

Figure 2 shows an example of one magnetogram image and the magnitude

gradient result of that image. From Figure 2 (b) we can note that regions with

the largest gradient (red colors) correspond to regions where the polarity of the

magnetic �elds changes over a small spatial scale.

The gradient magnitude is computed for each magnetogram image in our

dataset. To condense this gradient information into single descriptors for each

12

Table 1: Features extracted from gradient analysis.

Gradient Features

Standard deviation Mean

Minimum Maximum

Median Skewness

kurtosis

image, we compute the mean, standard deviation, maximum, minimum, median,

skewness, and kurtosis for each image. In total, 7 features are extracted for the

gradient analysis as summarized in Table 1.

To see a qualitative relation between these features and the active region's

�are times, feature values were plotted with respect to time (number of images in

one active region). Figure 3 shows an example of a plot of the standard deviation

feature for one active region which includes 120 magnetogram images. Each black

point in the �gure is a known time for a �are in this active region and the blue

curve are values of the standard deviation of each gradient image; we can conclude

that the standard deviation could be a good indication of solar �ares as the curve

goes up just prior to active region �aring.

13

Figure 3: Standard deviation feature values (blue line) and the active region's

�are times (black points). We can conclude that the standard deviation could be

a good indication of solar �are as the curve goes up just prior to active region

�aring.

14

2.3 Neutral line Analysis

2.3.1 Background

The neutral line (NL) is de�ned as the line separating opposite polarities. Parker [48]

and Roumeliotis et al [54] recently showed that energy can be stored in the corona

when sunspots of opposite polarity are pushed together, thereby forming an ex-

tended current sheet above the NL. This current sheet steadily lengthens until

it is disrupted by an instability, which results in a large-scale release of energy.

The connection between NLs, current sheets, and reconnection was �rst recog-

nized by Dungey [12], who showed that magnetic �elds with an X-type �are class

topology tend to form above NLs, which can then result in spontaneous current

sheet formation. More recently, the tether-cutting model described in [46] and

the break-out model of [4] have shown that gradual shearing motion both across

and along the NL, can result in the formation of unstable arcade structures in the

solar corona, which can then erupt. It is clear that the behavior of the magnetic

�eld in the proximity of the NL, and the morphology and evolution of the NL

itself, are essential to understanding and predicting solar �ares and CMEs.

Recently, from a sample of 5 active regions that produced great �ares, Wang [65]

reported that great �ares occurred speci�cally in the NLs with maximum gradi-

ent. Mason et al [43] and Yu et al [69] both use the primary inversion line length

as one of four parameters in a study of automated �are forecasting, while Jing et

15

al [32] use the length of the strong-gradient NL to study the relationship with �are

productivity. Falconer et al [13] use the weighted length of the strong-gradient

NL to forecast major �ares, and other eruptive solar events.


First, the magnetogram images are smoothed using a 10x10 pixel averaging �lter

to remove much of the statistical noise which would otherwise limit the e�ec-

tiveness of subsequent steps. Second, contours at the zero Gauss level of the

smoothed image are overlaid on the original magnetogram image. Pixels along

this zero-Gauss contour are used to create a neutral line (NL) mask where the pix-

els along the NL are set to a value of 1 and other pixels are set to 0. Third, since

the zero-Gauss contours will �ag all pixels at the zero-Gauss level, including those

with very small gradient (i.e., not at the NL of the AR), we mask the gradient

image as described in Section 2.2 with the NL mask. This highlights regions of

the NL for which there is a large spatial gradient, indicating a transition between

large positive and large negative �ux. Figure 4 illustrates all of the zero-Gauss

contours for both a bipolar and multipolar region, while Figure 5 show two dif-

ferent visualizations of this gradient-weighted neutral line (GWNL) for the same

bipolar and multipolar ARs.

16

(a) Bipolar region. (b) Multipolar region.

Figure 4: Noisy zero-Gauss contour before being weighted by the gradient image.

Note the presence of many small zero-Gauss contours even in the quiet sun.

17

(a) Magnetogram image overlaid with NL

for a simple bipolar region.

(b) Gradient-weighted NL visualized as a

scaled image for a simple bipolar region.

(c) Magnetogram image overlaid with NL

for a multipolar region.

(d) Gradient-weighted NL visualized as a

scaled image for a multipolar region.

Figure 5: Visualizations of the gradient-weighted NL for a simple bipolar region

in (a) and (b) and a multipolar region in (c) and (d). In the visualization of (a)

and (c), the magnetogram image is overlaid with the NL. Larger yellow markers

indicate the presence of a stronger gradient at that spatial location along the

NL. The visualization of (b) and (d) shows the gradient-weighted NL as a scaled

image, where black colors indicate a higher gradient. These regions correspond to

the same regions illustrated in Figure 4.

.18

Falconer et al [16] distinguishes between purely bipolar active regions with a

single main neutral line and a complex active region with a mix of opposite-polarity

magnetic �ux resulting in no unambiguous main neutral line, called multipolar

active regions. In this work, we make no distinction between the primary NL and

the NL as it exists separating the mixed opposite polarity regions.

The NL is detected for each image in our dataset. We de�ne a total of 13

features related to the neutral lines. The �rst three features are de�ned as follows:

• Length of the NL: The GWNL is thresholded at 20% of the maximum value

to yield a strong-gradient binary NL mask. The length of this NL is deter-

mined as the sum of the pixels.

• Number of fragments of the NL: Using the same thresholded GWNL, the

number of fragments is de�ned as the number of 8-connected components

in the binary NL mask image.

• GWNL length: The gradient-weighted length of the NL, computed by sum-

ming the pixels in the GWNL image.

As illustration, Figure 6 shows the thresholded GWNL for each of the active

regions shown in Figure 5.

Additionally, ten more features are extracted based on the NL boundary cur-

vature and NL bending energy. For the extraction of these features, we compute

the orientation angle of each NL pixel in the thresholded image by considering

19

(a) Thresholded bipolar NL. (b) Thresholded multipolar NL.

Figure 6: Thresholded GWNL images for the bipolar and multipolar ARs consid-

ered in Figure 5.

the inverse tangent of the slope between the current pixel and adjacent pixel [53]:

θn = arctan

(y(n+ 1)− y(n)

x(n+ 1)− x(n)

), n = 1, . . . , N (6)

where x and y are the x- and y-coordinates of the N NL pixels, and by de�nition

x(N + 1) = x(1) and y(N + 1) = y(1). The curvature angles are computed

separately for each NL segment, and the mean, standard deviation, maximum,

minimum, and median is computed for the distribution of all curvature angles for

all NL segments.

The bending energy is analogous to the physical energy required to bend a

rod and is computed as the sum of the di�erence between subsequent boundary

points [53]:N∑n=1

(θn+1 − θn) (7)

This measure is computed separately for each NL segmented and the mean, stan-

20

Figure 7: Values of gradient-weighted length of the NL (blue line) and the active

region's �are times (black points). We can conclude that this feature could be a

good indication of solar �are as the curve goes up during and just prior to active

region �aring

dard deviation, maximum, minimum, and median is computed for the distribution

of bending energy. Table 2 summarizes the 13 features extracted from the neutral

line analysis. Figure 7 is an example of one of the features extracted in this section

which is the gradient-weighted length of the NL with the �are times in one active

region. Each black point in the �gure is a known time for a �are in this active

region and the blue curve are values of the gradient-weighted length of the NL of

each NL image; we can conclude that this feature could be a good indication of

solar �are as the curve goes up during and just prior to active region �aring.

21

Table 2: Features extracted from neutral line analysis

Neutral Line Features

NL length Number of NL fragments

NL Gradient NL Curvature Minimum

NL Curvature Std NL Curvature Maximum

NL Curvature Mean NL Curvature Median

NL Bending Energy Std NL Bending Energy Mean

NL Bending Energy Min NL Bending Energy Max

NL Bending Energy Median

22

2.4 Fractal Dimension Analysis

2.4.1 Background

In the absence of di�usion, and assuming that surface magnetic �elds are largely

vertical [60] and that �ows are largely horizontal, Tao et al [62] showed that the

advection of magnetic �ux tubes by random motions results in a spatial distribu-

tion of �ux which is clearly fractal. The complex nature of the surface magnetic

�elds has been studied by Lawrence and co-workers [34] [36] [7] [35], who �nd that

line-of-sight �elds scale in a self-similar and fractal manner. Prompted by these

and other �ndings,Schrijver et al [56] were able to demonstrate that the geom-

etry of �ux concentrations on the solar surface is well described by percolation

theory [57] [67], which naturally results in fractal dimensions consistent with ob-

servational values. Most recently,Vlahos et al [64] describe a 2D percolation model

for the formation and evolution of active regions, in which �ux tubes emerge from

the convective zone, and are subject to random surface motions. The magnetic

patterns formed on the solar surface form well-de�ned fractals which can evolve

towards a Self-Organized-Criticality (SOC). Further, the distribution of energies

in these models is consistent with those observed on the Sun.

Fractal dimension, D, is one of the important characteristics of fractals. D

is a statistical quantity indicating the complexity of the fractal in the sense of

its space �lling characteristics as one looks at �ner and �ner scales [41]. D can

23

also be used to measure the degree of boundary fragmentation or irregularity over

multiple scales [42].

There are many de�nitions of fractal dimensions that can be invoked to mea-

sure the fractal dimension D of a signal including the Hausdor� Dimension (DH),

Minkowski-Bouligand dimension (DM), box counting dimension (DB), and en-

tropy dimension (DE).

The commonly-used box counting method measures the fractal dimension by

partitioning the plane with a grid of squares of side ε and counting the number

N(ε) of squares that intersect the signal. The box counting dimesion DB is de�ned

as [42]:

DB = limε→0

log ε2N(ε)

log(ε)(8)

where ε2N(ε) is the box cover area. For the Minkowski-Bouligand dimension, a

curve is dilated using disks of di�erent radii ε and the union of these disks centered

at all points of the curveX creates a `Minkowski cover.' The Minkowski-Bouligand

dimension DM is de�ned by:

DM = limε→0

(2− logA(ε)

log(ε)) (9)

where A is the area of the dilated set at each scale ε and ε is the radius of the

structuring element used in the dilation step [42].

Based on the work of Maragos et al [42], in which it is concluded that DM is

closely related to DH (which is how Mandelbrot de�ned fractal dimension) and

24

able to quantify the fractal aspects of a signal while being simpler to compute, we

use the Minkowski-Bouligand dimension DM in subsequent work.


We begin with creation of the structuring element used in the morphological

operations. Generally, the structuring element is a matrix consisting of 0's and 1's

that can have any arbitrary shape and size. In this work, the disk shape (circle)

is used as a structuring element with radius ε chosen to be in the interval [1,10]

pixels.

This variable sized structuring element is used to dilate the binary NL image

(as described in Section 2.3). Dilation is a morphological operation that grows

or thickens objects in a binary image [22]. In essence, the value of the output

pixel (the pixel for which the structuring element is centered) is the maximum

value of all the pixels in the structuring element's neighborhood [22]. Dilation is

repeated with ten structuring elements of increasing radii to yield ten di�erent

dilated images. Figure 8 shows an example of one neutral line binary image after

dilation with a structuring element of radius r = 3 and r = 4.

Next, the area of each dilated image is determined by counting the number

of pixels with a value of 1. The relationship between these areas and the radius

of the structuring elements is shown in Figure 9, plotted in log-log per Equation

(9). From Equation (9), we can conclude that the fractal dimension is equal to 2

25

(a) Dilated image with radius r = 3 (b) Dilated image with radius r = 4

Figure 8: Examples of dilated neutral line image with two di�erent structuring

element radii.

minus the slope of the line �tted for the log-log plot shown in Figure 9.

Three examples of simple, complex, and no neutral line images are shown in

Figure 10 along with the resultant fractal dimension (FD). We note that the image

with no neutral line has the least FD value, while the complex neutral line has

the highest FD value. It thus appears that the FD of the NL varies with the

complexity of the NL and may be an important feature to distinguish regions

with complex magnetic con�gurations. Figure 11 shows the FD values for one

active region and the related �are times shown as black points. From that �gure

the FD values are becoming larger prior to a �are, so we can expect a �are at a

time when FD value is high.

26

Figure 9: Example log-log plot of dilated area versus structuring element radius

(points) along with the least-squares �tted line.

(a) Image with no NL, FD = 1.05 (b) Simple NL, FD = 1.49

(c) Complex NL, FD = 1.604

Figure 10: Three example NL images and their respective NL FD.

27

Figure 11: Fractal dimension values (blue line) and active region's �are times

(black points) for one active region. Note that FD values are becoming larger

prior to a �are, so we can expect a �are at a time when FD value is high.

28

2.5 Emerging Flux Region Analysis

2.5.1 Background

Magnetic �ux emergence is the origin of sunspots and active regions, and is of-

ten associated with solar activities like solar �ares and coronal mass ejections

(CMEs) [30]. In the initial phase of �ux emergence, the two opposite magnetic

polarities move apart at a relatively large speed (∼ 5 km/s) and then slow. New

�ux emerges continuously in the central part between the main polarities. The

newly emerged magnetic polarities separate and reach the already emerged main

polarities with high velocities.

Feynman et al [17] found that �lament eruptions are usually triggered by

Emerging Flux Regions (EFRs), while Tang et al [61] found that major �ares

tend to be associated with new �ux emergence. From a theoretical perspective,

the emerging �ux model of Heyvaerts et al [27] was among the �rst to address this

problem. In their model, a �are develops in three phases: (a) The pre�are heating

phase during which the emerging �ux reconnects with the overlying �eld. (b) The

impulsive phase is initiated by the onset of turbulence in the current sheet, which

accelerated particles to form microwave burst. (c) The main phase is characterized

by rapid annihilation of magnetic �eld in the current sheet. Moreover, CMEs,

which may be associated with �lament eruptions and/or �ares, could also be

triggered by EFRs as reported by Green et al [23]. EFRs can have immediate

29

e�ect on the stability of active regions and �laments and understanding EFRs is

very important to study and predict solar activities and space weather [30].


Every two subsequent images (in one active region) are subtracted to yield a

di�erence image. EFRs are identi�ed as areas in the di�erence image showing

large deviations (> 3σ) above the mean di�erence level. Figure 12 shows two

subsequent images and the di�erence between them while Figure 13 (a) shows the

masked 3σ regions (while all others have been set to zero) and Figure 13 (b) shows

a binary mask of the 3σ regions.

It should be noted that subsequent images may di�er in size by one pixel in each

dimension. To alleviate problems computing di�erence images for di�erently sized

images, a �xed image size is selected to be the new size for all the magnetogram

images, so some of them are interpolated and some are downsampled. Then nine

features are extracted as follows and as summarized in Table 3:

• EFR sum: the sum of the di�erence image (the EFR image).

• EFR absolute sum: the sum of the absolute value of the di�erence image.

• EFR gradient: the sum of the gradient image masked by the binary 3σ

image.

• EFR area 3 sigma: area of the 3σ region.

30

(a) Magnetogram image taken at 12:51. (b) Magnetogram image taken at 14:27.

(c) Di�erence image.

Figure 12: Two magnetogram images taken on 10/29/2003 and their resultant

di�erence image.

• EFR mean, EFR standard deviation, EFR median, EFR minimum, and

EFR maximum features: statistics of the EFR image.

Figure 14 shows an example of one of the statistical features plotted versus

time for one active region. We notice that some of the �ares (the black points on

the curve) take place when the maximum value of the di�erence image at that

time is large. This result may give a hint about the importance of the statistical

31

(a) Masked image by 3σ. (b) Binary image showing the 3σ region.

Figure 13: Thresholded di�erence image and its binary mask.

Table 3: Features extracted after EFR analysis

EFR Features

EFR Sum EFR Absolute sum

EFR Gradient EFR Area 3 sigma

EFR Std EFR Mean

EFR Minimum EFR Maximum

EFR Median

features (for example the maximum value of the di�erence image) as it has a

relation increasing or decreasing with the time of �aring.

32

Figure 14: Maximum values of the di�erence images in one active region and

known �are times in black dots. We notice that some of the �ares take place

when the maximum value of the di�erence image at that time is large.

33

2.6 Wavelet Analysis

2.6.1 Background

A wavelet analysis will provide an indispensable complement to the fractal analysis

discussed in Section 2.4. Measuring the fractal dimension of an active region

magnetic �eld is an essentially global investigation of the scaling properties of the

magnetic �eld. A wavelet analysis of magnetograms can discriminate spatially

localized scale features such as the emergence/submergence of �ux tubes. The

wavelet transform which maps scale content - the power in a particular location -

will be essential for determining the relative in�uence of local magnetic features

against the global properties of the active region �eld. Local magnetic features are

fundamental to many �are theories and so such a study forms a complementary

counterpart to a fractal analysis in developing our understanding of active region

physics.


If an image has both large and small objects which are present simultaneously

then it can be advantageous to study them at several resolutions. A simple struc-

ture for representing images at more than one resolution is the �image pyramid�.

An image pyramid is a collection of decreasing resolution images arranged in the

shape of a pyramid. Related to the concept of an image pyramid is the wavelet

34

transform. The wavelet transform utilizes basis function with compact time (spa-

tial) support (i.e., �nite in time/space). This is in contrast to the commonly used

Fourier transform whose basis functions, complex exponentials, are not compact

in time (space). Thus, the wavelet transform allows for both time (space) and

frequency resolution, although there is a tradeo� between the resolutions achiev-

able simultaneously. A variety of di�erent basis functions can be de�ned, each of

which has di�erent properties in time (space) and frequency. In this work, we use

the Haar wavelet [22] and a �ve-level decomposition.

Using the Haar transform, we can determine the resultant �lter coe�cients,

yielding a low resolution image (lowpass image) and three highpass detail images

(horizontal, vertical, and diagonal details) for each level of decomposition. Sub-

sequent levels of decomposition begin with the lowpass image from the previous

level.

Figure 15 shows an original magnetogram image and its three highpass details

images where each is half the original image size. These three highpass detail im-

ages are used to determine the energies of each level of decomposition by summing

the absolute values of the wavelet coe�cients (the highpass images). Five energy

values (features) are extracted for each image in the active region. Figure 16 shows

the resultant energy values at each level for the same image as shown in Figure 15

where the energy values are normalized for image area. Table 4 summarizes the

wavelet features. To get a qualitative relation between energy values and �aring

35

(a) Original magnetogram image. (b) Horizontal detail image.

(c) Vertical detail image. (d) Diagonal detail image.

Figure 15: The original magnetogram image and its three highpass detail images

after one level of wavelet decomposition.

at one active region, we include Figure 17 which shows the energy values of level

2 for one active region and the black points refer to known �are times. From the

�gure, we conclude that the wavelet energy takes larger values prior to �ares in

the active region.

36

Figure 16: Energy values at 5 levels of wavelet decomposition for the image shown

in Figure 15(a).

Table 4: Features extracted from wavelet analysis.

Wavelet Features

Wavelet Energy L1 Wavelet Energy L2

Wavelet Energy L3 Wavelet Energy L4

Wavelet Energy L5

37

Figure 17: Energy values at level 2 for one active region and known �are times

shown in black points. We can conclude that the wavelet energy takes larger

values prior to �ares in the active region.

38

3 CLASSIFICATION, FEATURE SELECTION AND PERFORMANCE

MEASURES

In this chapter, we provide a brief overview of the two classi�cation methods used

in this work and explain the feature selection method used to select the optimal

features. Also, we will describe the skill score measures that we use to quantify

forcast performance for the classi�cation methods.

3.1 Fisher Linear Discriminant Analysis (FLDA)

Linear discriminant analysis is one of the methods used in statistics and pattern

recognition to �nd a linear combination of features which characterizes two or

more classes of objects or events. A discriminant is a function that takes an input

vector X and assigns it to one of K classes, denoted Ck. In the two class case, the

linear discriminant is a function obtained by taking a linear function of the input

vector so that

y(X) = wTX + wo (10)

where w is called a weight vector, and wo is a bias. Thus, we are projecting the

D-dimensional input vector X to one dimension and basing the classi�cation on

threshold wo [5].

In general, the projection onto one dimension leads to a considerable loss of

information. However, by adjusting the components of the weight vector w, we

39

can select a projection that maximize the class separation. If we have N1 points

of class C1 and N2 points of class C2, then the D-dimensional mean vectors of the

two classes are given by [5]:

m1 =1

N1

∑n∈C1

Xn, m2 =1

N2

∑n∈C2

Xn (11)

where Xn is the n-th component of the input vector X. The idea proposed by

Fisher [18] is to maximize a function that will give a large separation between

the projected class means wTm1 and wTm2 and also give a small variance within

each projected class, thereby minimizing the class overlap.

Figure 18, adapted from [5], represents the decision boundary found by FLDA

analysis between two classes. To put this generic description in the context of

solar phenomena, the �red x� class may represent �are-productive active regions

and the �blue x� class may be non-�aring regions, while the x- and y-axes are

features such as those listed in Tables 1 through 4.

3.2 Relevance Vector Machine (RVM)

The Relevance Vector Machine (RVM) is a Bayesian sparse kernel technique for

regression and classi�cation. The RVM classi�cation method basically depends

on �nding a kernel function K(xn, xm) for all possible pairs xn and xm of training

points, which can be computationally infeasible during training and can lead to

excessive computation times when making predictions for new data points. In the

40

Figure 18: Illustration of FLDA classi�cation for a two class case. Figure adapted

from [5].

kernel-based algorithms that have sparse solutions, the predictions for new inputs

depends only on the kernel function evaluated at a subset of the training data

points [5].

As mentioned by Tipping [63], in supervised learning a set of input vectors Xn

along with corresponding targets tn as n = 1, 2....N are given. The tn might be

discrete class labels in the case of classi�cation and might be real continuous values

in regression. From this training set we wish to learn a model of the dependency

of the targets on the inputs with the objectives of making accurate predictions of

t for previously unseen values of x. Typically, predictions are based upon some

function y(x) de�ned over the input space, and �learning� is the process of inferring

this function. A �exible and popular set of candidates for y(x) is that of the form:

y(x;w) =M∑i=1

wiφi(x) = wTφ(x) (12)

41

where the output is a linearly-weighted sum of M , generally nonlinear and �xed,

basis functions φ(x) = (φ1(x), φ2(x), ..., φM(x))T . Tipping [63] presents details

about the Bayesian probabilistic framework for learning general models of the

form in Equation 12. The key of that approach is that as well as o�ering good

generalization performance, the inferred predictors are �sparse� in that they con-

tain few non-zero wi parameters. The majority of parameters are automatically

set to zero during the learning process, giving a procedure that is extremely ef-

fective at discerning those basis functions which are �relevant� for making good

predictions. �Relevance vector machines� (RVMs) and �support vector machines�

(SVMs) are two speci�c types of sparse learning.

As an illustration of RVMs and their underlying predictive distributions, con-

sider Figure 19 as taken from [5]. This example considers the use of an RVM

for a classi�cation problem (set of discrete labels t). In Figure 19(a), data drawn

from two di�erent classes are shown as red and blue x's. Consider the x-axis and

y-axis to represent two features that have been measured from each of the data

points; thus, Figure 19(a) is a scatter plot of feature values. The black bound-

ary in Figure 19 represents the decision boundary determined by the RVM. The

unique strength of the RVM, however, is illustrated in Figure 19(b) where the

predictive distribution is represented as a colormap where the more red a region

is in the feature plane, the higher the probability that a data point occupying

that location is a member of the class represented by the red x's. Similarly, the

42

(a) Two-class dataset (red x's and blue

x's) with RVM classi�cation decision

boundary (black curve). From [5].

.

(b) Predictive distribution of the RVM

classi�er where more red regions indi-

cate higher probability of belonging to

the `red x' class and more blue regions

indicate higher probability of belonging

to the `blue x' class. From [5].

Figure 19: Illustration of RVM classi�cation for a two class case. (a) scatter

plot of feature values for two classes (b) predictive distribution represented as a

colormap. Figures taken from [5].

more blue a location in the feature plane, the higher the probability that a data

point occupying that location is member of the class represented by the blue x's.

Figure 19 represents the decision boundary found by RVM classi�cation. As we

mentioned for Figure 18 the �red x� class may represent �are-productive active

regions and the �blue x� class may be non-�aring regions, while the x- and y-axes

are features such as those listed in Tables 1 through 4.

43

3.3 Feature Selection

Feature selection is a process that selects the relevant and important features

from a large set of features. Pudil et al [52] de�ne the feature selection as a

search problem that detects an optimal feature subset based on some selected

measure. Liu et al [40] represent that feature selection is one of the important and

frequently used techniques in data preprocessing for data mining. Also it has many

advantages in reducing the number of features, removes irrelevant, redundant, or

noisy data, and can speed up data mining algorithms and improve predictive

accuracy.

We can de�ne four basic steps in a typical feature selection method [10], [40]:

(1) a subset generation procedure, (2) an evaluation function, (3) a stopping

criterion, (4) a validation procedure. Subset generation is a search procedure

that produces candidate feature subsets for evaluation based on a certain search

strategy; this step can start with no features, with all features or with a random

subset of features. Next each candidate subset is evaluated and compared with

the previous best one according to a certain evaluation criterion. If the new subset

turns out to be better, it will replace the previous best subset. The previous two

steps are repeated until a given stopping criterion is satis�ed. Finally, the selected

subset needs to be validated by prior knowledge or evaluation on a test dataset.

In the feature selection methods used by Pudil et al [52], the best feature

44

set is constructed by adding to and/or removing from the current feature set, a

small number of features at a time until the required feature set Xd of cardinality

d is obtained. There are two ways to select the starting subset. The �rst one

begins with an empty set X0 which will be successively built up and is known

as the �bottom up� or �sequential forward selection� (SFS) method. The second

way is to start with the complete set of features Y and is called �top down� or

�sequential backward selection� (SBS) method. Both of these methods su�er from

the �nesting e�ect� which means that in the case of the �top down� search the

discarded features cannot be re-selected while in the case of the �bottom up�

search the features once selected cannot be later discarded, so these methods are

suboptimal.

Pudil et al [52] present �oating search methods of feature selection which

overcome the nesting problem. Floating means to let the values ��oat�, keep them

�exibly changing so as to approximate the optimal solution much as possible.

Then the resulting dimensionality in respective stages of the algorithm is not

changing monotonically but is ��oating� up and down. These feature selection

methods are denoted by �sequential forward �oating selection� (SFFS) method

and the opposite direction called �sequential backward �oating selection� (SBFS)

method.

The SFFS method is basically a bottom up search procedure which applies

the basic SFS procedure starting from the current feature set followed by a series

45

of successive conditional exclusions of the worst feature in the newly updated set

assuming a further improvement can be made to the previous set [52]. The SBFS

method is a top down search procedure which excludes features using the basis

SBS method starting from the current feature set followed by a series of successive

conditional inclusions of the most signi�cant feature from the available features

if an improvement can be made to the previous set. These methods still cannot

guarantee optimally of the selected feature subset, but they have been shown to

perform very well compared to other feature selection methods, and much more

computationally e�cient [31]. In our work, we use the SFFS as a feature selection

method.

3.4 Performance Measures

Table 5 shows the contigency table (confusion matrix) where TP is the true posi-

tive (correct �are forcast), FN false negative (incorrect no-�are forcast), FP false

positive (incorrect �are forcast), and TN true negative (correct no-�are forcast) [6].

These quanti�ed measures will be used to compare the performance of �are pre-

diction using the classi�cation methods discusssed in Sections 3.1 and 3.2. In

particular, we will consider the accuracy of classifying �aring regions (TP) and

accuracy of classifying non-�aring regions (TN).

Since �ares are relatively rare events, the classi�cation of �are activity relies

on an unbalanced dataset, where the number of examples of non-�ares largely

46

Table 5: Flaring forcasting contingency table

Observed Forcasted

Flare No �are

Flare TP FN

No �are FP TN

outweighs the number of examples of �ares. We will return to this issue in chap-

ter 4. As an example of the unbalanced data, for a 4 hour timescale, 6.5% of the

total dataset belong to �are regions and 93.5% of the total dataset belong to no

�are regions.

The use of skill scores attempts to alleviate some of the issues of unbalanced

data through di�erent combinations of the contingency table entries. Many dif-

ferent skill scores exist to quantify forcast performance, but the Heidke skill score

(HSS) and the Hanssen & Kuipers discrimenant known as the True skill score

(TSS) are the most widely used in �are forcasting [6]. HSS and TSS are both

mathmetical relations depending on the �are forecast contingency table [6], [68].

HSS is de�ned as:

HSS =2[(TP × TN)− (FN × FP )]

(TP + FN)(FN + TN) + (TP + FP )(FP + TN)(13)

and TSS is given by:

TSS =TP

TP + FN− FP

FP + TN(14)

47

Only TSS is unbiased when confronted with varying observed event/no-event sam-

ple ratios. TSS is preferred to use with the unbalanced dataset as it is not sensitive

to the active region sample ratio [6].

48

4 EXPERIMENTS AND RESULTS

We will use both FLDA and RVM classi�ers to predict whether a given AR will

�are in the following k hours. We will �rst describe the experimental setup com-

mon to both methods, followed by results and discussion for each classi�cation

method, presented across timescales. Then, in the last section, the optimal fea-

tures chosen by feature selection from the original 35 features and the accuracy

of classi�cation using a group of the optimal features will be compared with the

previous FLDA and RVM results.

4.1 Experiment setup

Our goal is to classify an active region to class C1 if it will �are in the subsequent

k hours and to class C2 if it will not �are in the subsequent k hours. From

the image analysis discussion in Chapter 2, we end with one feature matrix for

each active region. These feature matrices are concatenated into one matrix for

all active regions to be the input data matrix to the classi�cation process. The

input feature matrix X is de�ned by: X = {X1, X2, .., XN} where N is the total

number of active regions. Xi is the feature matrix of the i-th active region with a

dimensionality 35 × ni where ni is the number of images for the i-th AR. These

35 features encompass the gradient, fractal dimension, neutral line, emerging �ux

region, and wavelet features as discussed in Chapter 2.

49

In addition to this feature matrix, training of the classi�ers requires a label

vector. Each element in the label vector indicates whether the AR represented by

that image will �are in the next k hours (`1') or not (`0'). Flares are de�ned per

the GOES catalog which de�nes �ares according to their total x-ray �ux [66].

The classi�cation process follows two steps: training and testing. We randomly

choose 1000 active regions to train and �nd weight vector w. The remaining 1000

active regions are used in testing, where weight vector w is used to predict classes

for each data point in X, representing an active region image.

Since a large majority of regions will not �are within the time window consid-

ered, classi�cation methods can naively optimize their criterion by classifying all

regions as class C2 (no �are). One method to alleviate this issue of unbalanced

datasets is to arti�cially balance the dataset by subsampling one or both classes

to be evenly represented. By cross validation across many randomly balanced

datasets, we can get a better idea of accuracy. In this work, we use a 10-fold

cross-validation with 100 samples (subsampled from the 1000 training ARs) for

�aring and non-�aring populations.

The classi�cation process is repeated for di�erent timescales from 2 to 24 hours

prior to a �are in a steps of 2 hours (i.e 2,4,6,....,24). It should be noted that by

�time before a �are� we are refering to the classi�cation of whether a �are will

occur in the subsequent k hours.

50

4.2 Classi�cation using Fisher Linear Discriminant Analysis

4.2.1 Classi�cation Using All Features

(a) Accuracy of �aring and non-�aring

ARs.

(b) Skill score (HSS and TSS) values.

Figure 20: FLDA classi�cation results using a combination of all features.

Figure 20 (a) shows the �aring and non-�aring accuracies for classi�cation

of a randomly selected 1000 active regions using the Fisher linear discriminant

analysis discussed in Section 3.1. These accuracies are computed for a range of

timescales from 2 to 24 hours. Figure 20 (b) shows the skill score measures at each

timescale. From these �gures, we conclude that the FLDA classi�cation method

gives higher accuracies in predicting �aring active regions than non-�aring active

regions. TSS and HSS values seem to be stable but have low values in the range

between 0.003 to 0.2. The best published TSS values are >0.4 [6].

As a conclusion of FLDA classi�cation using all features, we notice that there

is no obvious trend in accuracy performance versus timescales and potentially a

51

slight increase in TSS for larger timescales.

4.2.2 Classi�cation Using Feature Subsets

Up to this point, we have considered the use of all features described previously

in Section 2 and listed in Tables 1 through 4. We can separate the features and

classify using a subset of features, for example the 7 gradient features as shown

in Figure 21. In a similar manner, classi�cation using other feature subsets as

discussed in Section 2 are shown in Figures 22-25. Our goal here is to determine

which subsets have better accuracy and to postulate the physical relation between

features and active region �aring.

From Figure 21 (a), we �nd that gradient features are more accurate at classi-

fying no �are activity. Possibly a lack of large gradient is indicative of no imminent

�ares, but a large gradient is not necessarily indicative of future �aring. Figure 21

(b) shows that TSS preformance is worse at < 10 hours but after that it has val-

ues within range of best published values [6]. This is surprising since it indicates

better predictions at > 10 hours and at other times it has a good TSS values while

classifying all regions as non-�aring as seen at 22 hours case. This is not clear

why it happens since we have a 10-fold cross validation.

NL features have more consistent accuracy for �aring and non-�aring regions

as shown in Figure 22 (a). A better skill scores is noted at longer timescales of

prediction in Figure 22 (b).

52

The fractal dimension feature can predict �aring activity more accuratly than

non-�aring activity as shown in Figure 23 (a), while it has small skill score values

as in Figure 23 (b). Again and as noted for the gradient features case, TSS has a

better value when classi�cation predict all regions as �aring as at 22 hours in the

timescale.

Figure 24 (a) shows the EFR classi�cation results; we can see that the EFR

features tend to result in classi�ers that naively classify all regions as either �aring

or not �aring. This may indicate that EFR features, at least by themselves, are

not good indicators of future �are activity. Because of that, the skill scores have

relatively low values.

From Figure 25 (a), we conclude that wavelet features have more consistent

and higher accuracies for �aring and non-�aring regions and it has a good TSS and

HSS values after 6 hours of the timescale, which is within the published range [6]

as in Figure 25 (b).

We conclude that NL and wavelet features have the best performance in pre-

dicting future �are activity. As future work for this part, we will relate the per-

formance of the feature subsets back to the physical process, in collaboration with

solar physicists. Also, we will try to explain the general trend for some feature

subsets where the skill scores increases with increasing timescales.

53


ARs.


Figure 21: FLDA classi�cation results using gradient features listed in Table 1.


ARs.


Figure 22: FLDA classi�cation results using neutral line features listed in Table 2.

54


ARs.


Figure 23: FLDA classi�cation results using the fractal dimension feature.


ARs.


Figure 24: FLDA classi�cation results using emerging �ux region features listed

in Table 3.

55


ARs.


Figure 25: FLDA classi�cation results using wavelet features listed in Table 4.

56

4.3 Classi�cation using Relevance Vector Machine

4.3.1 Classi�cation Using All Features

Figure 26 (a) shows the �aring and non�aring accuracies for classi�cation of 1000

randomly chosen active regions with respect to di�erent timescales using the rel-

evance vector machine analysis discussed in Section 3.2. Figure 26 (b) shows the

skill score measures at each timescale. We note more consistency of the �aring

and non-�aring accuracies over the range of 2 to 22 hours as compared to that of

the FLDA (Figure 20). In addition to consistency, the accuracies of �aring and

non-�aring prediction are close to each other and have higher values (between

0.6 to 0.8) than seen with FLDA. TSS and HSS values have values in the range

between 0.1 and 0.4 which is good and acceptable.


ARs.


Figure 26: RVM classi�cation results using a combination of all features.

57

4.3.2 Classi�cation Using Feature Subsets

Similar to the feature subset analysis for FLDA we can separate the features and

classify using a subset of features using the RVM classi�er. Classi�cation using

feature subsets as discussed in Section 2 are shown Figures 27-31. As we mentioned

before, the aim from this step is to determine which subsets have better accuracy

and to �nd the physical relation between features and active region �aring.

From Figure 27 (a), we note that gradient is a little more accurate in no-�aring

prediction than �aring. Both accuracies and skill scores results are not consistent

and classify all regions as no �are with high TSS vlaues at some timescales like

16-20 hours. That could be avoided if we use more cross validation than 10 for

future analysis.

Classi�cation using NL features is shown in Figure 28 (a). NL features have

consistent accuracies for no-�aring regions and higher than �aring. Also, it is very

close to FLDA classi�cation in Figure 22 (a). TSS and HSS trends increase with

increasing timescales (Figure 28 (b)) and close to FLDA skill scores (Figure 22

(b)).

Figure 29 shows RVM classi�cation using the fractal dimension feature. We

can see that FD always classi�es regions as non-�aring regions and skill scores

values are very small and close to zero. This result may indicate that FD is not

good in future �are prediction, or that is not good to use the FD feature alone to

58

predict �ares.

EFR �aring and non-�aring accuracies are shown in Figure 30 (a), EFR is

better for no-�aring prediction. Also, we note more consistency in �aring and

non-�aring accuracies than FLDA classi�cation (Figure 24 (a)). Skill scores have

low values but consistent (Figure 30 (b)).

From Figure 31 (a) we conclude that wavelet features have good prediction of

non-�aring regions while the �aring accuracies is not bad. Skill scores in Figure 31

(b) increase with larger timescales with a good and acceptable values. For future

work, we will relate the performance of the feature subsets back to the physical

process to explain the general trend for some feature subsets where the skill scores

increases with increasing timescales.


ARs.


Figure 27: RVM classi�cation results using gradient features listed in Table 1.

59


ARs.


Figure 28: RVM classi�cation results using neutral line features listed in Table 2.


ARs.


Figure 29: RVM classi�cation results using fractal dimension feature.

60


ARs.


Figure 30: RVM classi�cation results using emerging �ux region features listed in

Table 3.


ARs.


Figure 31: RVM classi�cation results using wavelet features listed in Table 4.

61

4.4 Classi�cation after Feature Selection

In the previous section, we found that some of the 5 feature subsets yielded better

accuracies and skill score performance. That choice of 5 subsets was arbitrary

according to the underlying algorithms. In this section, we seek to obtain a

feature subset that is optimal for the classi�cation task.

We choose the �sequential forward �oating selecting� (SFFS) method with

Fisherc criterion type to select the optimal feature set from the original features

discussed in Section 2 using the implementation found in the PRTools Matlab

package [11]. Since we are faced with an unbalanced dataset, and we use cross-

validation, the question is how to use feature selection in such a framework. Each

cross validation run will result in a di�erent optimal feature subset, but we hope

that there will be some consistency amongst the features selected over the dif-

ferent validations. Thus we must carefully de�ne what we mean by an �optimal�

feature subset under these conditions. While it has been shown that SFFS closely

approximates the optimal feature subset [6], by somehow combining multiple op-

timal feature sets, we cannot gurantee any sort of global optimality. However,

we will choose a subset of features which is expected to perform better than the

entire feature set, and refer to this subset as optimal. To choose optimal features,

we follow the process outlined below.

We randomly choose 1000 active regions to train using 500 samples from each

62

Figure 32: Histogram of features selected at 14 hours timescale ranked from least

frequent at 1 to most frequent at 35.

class in order to balance the data. This process is repeated 100 times to make

sure of our selection (100-fold cross validation), then the histogram of all features

is plotted which shows how many times each feature is selected as an optimal

feature. This process is repeated for all the timescales [2,24] hours, Figure 32

shows an example of this feature histogram at 14 hours timescale. Table 6 also

presents the names of the top 16 ranked features (labeled with 20 to 35 on the

x-axis of Figure 32). For example �NL Gradient� is selected 88 times from the 100

cross validations and �NL no Fragments� and �Gradient Std� are both selected 79

times and so on.

4.4.1 FLDA Classi�cation on Optimal Subset

The same classi�cation process as in Section 4.2 is used but the subset of optimal

features is used instead of all the features. The accuracy of �aring and non-�aring

63

Table 6: The top 16 ranked features at 14 hours timescale.

Top 16 ranked features from the histogram in Fig 32

35. NL Gradient 27. EFR Gradient

34. NL no Fragments 26. NL Curvature Max

33. Gradient Std 25. NL Curvature Min

32. Skewness 24. EFR Median

31. Gradient Median 23. EFR Mean

30. kurtosis 22. EFR AbsSum

29. NL Bendingenergy Median 21. EFR Std

28. Fractal dimension 20. EFR Sum

active regions while classifying using the top 6 ranked features at each timescale

are shown in Figure 33(a) while the skill score measures are shown in Figure 33(b).

We notice that the overall accuracies are larger than the accuracies when we use

all features as in Figure 20(a).

There are many ways to choose the number of optimal feature uses in the

feature subset, here we try di�erent subsets and we �nd that classi�cation using

the top 6 ranked features gives clear and good improvement in the �aring and non-

�aring accuracies. The feature selection process improves the prediction accuracies

of the FLDA classi�cation method in both �aring and non-�aring cases. However,

HSS and TSS measures are not as consistent and still maintain low values.

64


ARs.


Figure 33: FLDA classi�cation results using 6 top-ranked features.

4.4.2 RVM Classi�cation on Optimal Subset

The same classi�cation process as in Section 4.3 is used but using a new subset

with optimal features. The accuracy of �aring and non-�aring active regions are

shown in Figure 34(a) while the skill score measures are shown in Figure 34(b).

The feature selection process improves RVM classi�cation speed as we have fewer

features (i.e, the feature matrix X is smaller in size). The time to classify the

same number of active regions takes now one minute as opposed to 2-3 minutes.

However, the accuracies for RVM and FLDA classi�cation appear more consistent

across timescales when we used all features (see Figures 20 and 26).

65


ARs.


Figure 34: RVM classi�cation results using 6 top-ranked features.

4.4.3 Determination of an Appropriate Number of Optimal Features

To get more information about the accuracy and skill score values after choosing

an optimal feature subset for classi�cation, we include another example of RVM

classi�cation using the top 10 and 3 optimal features as shown in Figures 35

and 36. We note from Figure 35 that RVM consistency is absent as the accuracies

go up and down over the timescale. Nevertheless, TSS and HSS values looks good

and stable.

Figure 36 shows the classi�cation results of using the 3 top-ranked features.

We choose 3 features because at di�erent timescales, we noticed that the top 3

ranked features are mostly the same: �Gradient Std�, �NL no Fragments� and �NL

Gradient�. It is interesting to see the feature (�Gradient Std�) as one of the top

ranked features, because Figure 3 shows how this feature is related to future �ares

66


ARs.



for one active region. And as expected, it gives a good indication about future

�are prediction. Figure 36 (a) shows more consistency in �aring and non-�aring

accuracies than Figure 35 (a) especially between 6 and 20 hours timescales. The

TSS and HSS values also have good trends between 6 and 20 hours timescales as

shown in Figure 36 (b).

To get a close look at skill score improvement versus number of optimal features

selected, TSS values are calculated at one timescale (e.g., at 14 hours before

a �are) for di�erent size subsets, begining with the most optimal, and adding

features in decreasing rank until all 35 features are being used. We begin with the

3 top-ranked features (�Gradient Std�, �NL no Fragments� and �NL Gradient�),

as these features are the top 3 optimal features at di�erent timescales. Figure 37

illustrates the TSS values versus number of features used in classi�cation for the

RVM classi�er for a timescale of 14 hours. It is noticable that the maximum value

67


ARs.



of TSS is when we classify the active regions using a feature set with only the top

3 optimal features. The overall trend in TSS in Figure 37 decreases as the size of

the feature subset increases. The trend is not strictly monotonic, most likely due

to the use of an optimal subset chosen over several cross-validation runs.

From Sections 4.2 and 4.3 and by comparing Figures 20 and 26, we conclude

that the RVM classi�cation method has a more accurate and consistent perfor-

mance than FLDA classi�cation. The RVM method can predict both �aring and

non-�aring active regions at each time before �are cases much better than the

FLDA method. TSS and HSS values result for RVM classi�cation have higher

values (between 0.1 and 0.4) than FLDA. An advantage for FLDA that it is faster

and takes a few seconds whereas the RVM process takes a few minutes.

68

Figure 37: TSS values at 14 hour before �are case using di�erent features subsets.

69

5 CONCLUSION

In this work, a large magnetogram dataset were used to extract 35 di�erent

features that describe the physical properties of active region magnetic �elds using

5 di�erent analysis: 1. gradient analysis: which is an indicative of pressure build-

up in the photosphere, 2. neutral line: the line seperate opposit polarities at the

magnetic �eld which is related to energy release locations, 3. fractal dimension:

which relates to the active region complexity, 4. emerging �ux region: which can

act as energy release triggers, and 5. wavelet analysis: which allows separation of

the �eld into its component length scales.

Next, we used the extracted features to classify active regions as a �aring or

non-�aring regions in the coming k hours. Two classi�cation methods have been

used and the accuracies of �aring and non-�aring ARs along with the skill score

measures were found and compared. We found that the Relevance Vector Machine

(RVM) method of classi�cation was better in �aring and non-�aring prediction

than the Fisher Linear Discrimenant (FLDA) method. Also, skill score values

result for RVM classi�cation have higher and more consistent values than FLDA.

An advantage for FLDA that it is faster and takes few second whereas RVM takes

few minutes.

As a conclusion of the classi�cation using all features, for FLDA classi�cation

method, we noticed that there is no obvious trend in accuracy performance versus

70

timescales and TSS had slight increase for larger timescales. But, for RVM classi-

�cation method, we note more consistency of the �aring and non-�aring accuracies

over the range of 2 to 22 hours as compared to that of the FLDA. In addition to

consistency, the accuracies were close to each other and have higher values than

seen with FLDA. Also, TSS and HSS values were good and acceptable.

On the other hand, some features had a good relation with future �are ac-

tivities and gives a high �aring and non-�aring accuracies while others are not.

FLDA classi�cation using gradient features subset was more accurate at classify-

ing no �are activity. Possibly a lack of large gradient is indicative of no imminent

�ares, but a large gradient is not necessarily indicative of future �aring. Using

the EFR features subset result with a classi�er that naively classify all regions as

either �aring or not �aring, which may indicate that the EFR features are not

good indicator of future �are activity. However, the NL and the wavelet features

have the best performance in predicting future �are activity.

After RVM classi�cation using features subset, we noticed that both gradient

and NL features had consistent accuracies for no-�aring prediction and higher

than �aring and it is very close to the FLDA classi�cation results. However, we

found that the FD feature always classi�es regions as non-�aring regions and skill

score values are very small and close to zero. This may indicate that the FD is

not good in future �are prediction, or it is not good to use the FD feature alone

to predict �ares. Finally, the EFR and wavelet features were noticed to have a

71

good prediction of non-�aring regions while the �aring accuracies is not bad.

In feature selection, it is important to reminde that the process was repeated

100 times (100-fold cross validation) and the histogram of all featurers was plotted

which shows how many times each feature was selected as an optimal feature. That

procedure was also repeated for all timescales [2,24] hours. Then both the FLDA

and the RVM classi�cation methods were used to classify active regions using the

top 6 ranked features. Also, a subset includes 3 top-ranked features was used

because, at di�erent timescales, we noticed that the top 3 ranked features are

mostly the same: �Gradient Std�, �NL no Fragments�, and �NL Gradient�. It is

interesting to see the feature (�Gradient Std�) as one of the top ranked features,

because Figure 3 shows how this feature is related to future �ares for one active

region.

The feature selection process improves RVM classi�cation speed. However,

the accuracies for RVM and FLDA classi�cation appear more consistent across

timescales when we used all features in classi�cation. RVM classi�cation using the

top 3 ranked features had more consistency in �aring and non-�aring accuracies

than classi�cation using 6 top-ranked features and the skill score values had a

good trends between 6 and 22 hours timescales.

72

6 FUTURE WORK

There are several avenues for potential future work. In terms of the image

analysis work, we may consider the use of additional features from the solar analy-

sis literature or general feature extraction literature. While this has the potential

to provide an increase in performance, the results achieved with the 35 features

used in this work are encouraging. As such, we will �rst focus our attention on

improvement of the statistical modeling in the classi�cation.

It will be an important step to relate these analysis back to the physical pro-

cesses underlying �are activity. As such, we want to get some physical explanation

of the features behaviour related to their result accuracies of �aring and non-�aring

classi�cation as we found that some of the features are good in �aring prediction

while others are not.

In relation to the classi�cation methods, we can provide better probabilistic

models by considering a priori distributions of �are activities (to better model the

rarity of �ares). We also plan to extend the classi�cation work presented here

(i.e., discrete labels) to a regression analysis (i.e., continuous labels). We expect

that this will provide a more natural framework for �are prediction, since �ares

are known to occur across a continuum of energy levels. We will use Relevance

Vector Machine (RVM) regression or Support Vector Machine (SVM) regression

methods to classify active regions as �aring regions with �are type A,B,C,M or

73

X-type or non-�aring regions.

Additionally, we want to determine a relationship or mapping between coronal

features and photospheric magnetic �eld to get more information and to extract

more features related to the active region's magnetic �eld complexity. The rela-

tionship of features extracted from di�erent solar layers may provide important

insight into the physical mechanisms of solar activity.

74

APPENDICES

APPENDIX A

MATLAB CODE

A MATLAB CODE

A.1 Gradient Analysis Code

clear a l l

close a l l

clc

base_directory = '/home/amani/Desktop/Amani/master thesis/active region/';

5 data_directory = dir(base_directory );

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

for p =3: length(data_directory)

Data_directory = data_directory(p).name;

filenames = dir ([ base_directory ,Data_directory ,'/*. fits']);

10

Gradient_mean =[]; Gradient_std =[]; Gradient_max =[]; Gradient_min =[];

Gradient_median =[]; no_of_images =[]; Gradient_skewness =[]; Gradient_kurtosis =[];

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% M a g n e t o g r a m i m a g e s l o o p :

15 for k = 1: length(filenames)

filename = filenames(k).name;

A = fitsread ([ base_directory ,Data_directory ,'/',filename],'raw');

i f A(end,1) <-3000

A (A==A(end,1))= NaN;

20 end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% H e a d e r i n f o r m a t i o n : i g n o r e t h e i m a g e s w h i c h h a v e a r a d i u s ( d i s t a n c e

% f r o m AR c e n t e r to d i s k c e n t e r ) g r e a t e r t h a n 6 5 0 a r c s e c o n d s .

hdr = fitsinfo ([ base_directory ,Data_directory ,'/',filename ]);

25 hdr.PrimaryData.Keywords;

radius = sqrt(cell2mat(hdr.PrimaryData.Keywords (187 ,2))^2 +...

cell2mat(hdr.PrimaryData.Keywords (188 ,2))^2);

i f radius > 650

77

A=[];

30 else

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% H e r e is t h e g r a d i e n t m a g n i t u d e c o d e :

w= [-1 0 1;-2 0 2;-1 0 1]; % s o b e l m a s k s

wm = [-1 -2 -1;0 0 0;1 2 1];

35 s = imfilter (A,w,'replicate '); % f i l t e r i n g

g = imfilter (A,wm ,'replicate ');

grad_image = sqrt(s.^2 + g.^2); % t h e r e s u l t g r a d i e n t i m a g e

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% T h e s e v e c t o r s c o n t a i n v a l u e s of std , mean , a n d m a x f o r a l l g r a d i m a g e s :

40 Gradient_mean= [Gradient_mean mean(mean(grad_image ))];

Gradient_std = [Gradient_std std(std(grad_image ))];

Gradient_median = [Gradient_median median(median(grad_image ))];

Gradient_min = [Gradient_min min(min(grad_image ))];

Gradient_max = [Gradient_max max(max(grad_image ))];

45 Gradient_skewness = [Gradient_skewness skewness(skewness(grad_image ))];

Gradient_kurtosis = [Gradient_kurtosis kurtosis(kurtosis(grad_image ))];

no_of_images = [no_of_images k]; % n u m b e r of i m a g e s

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

end

50 end

Active_Region_number = Data_directory

Gradient_features = [Gradient_mean; Gradient_std; Gradient_median;...

Gradient_min; Gradient_max; Gradient_skewness;...

Gradient_kurtosis ];

55 disp(['save at:',base_directory ,Data_directory ,'/','_Gradientfeatures.mat'])

save([ base_directory ,Data_directory ,'/','_Gradientfeatures.mat'],...

'Gradient_features ');

end

78

A.2 Neutral Line Analysis Code

clear a l l

close a l l

clc



%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

for p =3: length(data_directory)



10 NL_Length =[]; NL_no_Fragments =[]; NL_Gradient =[]; NL_Curvature_mean =[];

NL_Curvature_std =[]; NL_Curvature_max =[]; NL_Curvature_min =[];

NL_Curvature_median =[]; NL_Bendingenergy_mean =[]; NL_Bendingenergy_std =[];

NL_Bendingenergy_max =[]; NL_Bendingenergy_min =[]; NL_Bendingenergy_median =[];

no_of_images =[];

15 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−


for k = 1: length(filenames)



20 i f A(end,1) <-3000

A (A==A(end,1))= NaN;

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−


25 % f r o m AR c e n t e r to d i s k c e n t e r ) g r e a t e r t h a n 6 5 0 a r c s e c o n d s .


hdr.PrimaryData.Keywords;



30 i f radius >650

79

A=[];

else

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 1. F i l t e r i n g :

35 D = std(std(abs(A)));

f i l t e r = fspecial('average ' ,10);

filter_A = imfilter(double(A), f i l t e r , 'replicate ');

% F i x N a N file , L E B

i f sum(sum( isnan(filter_A ))) == s ize (A,1)* s ize (A,2)

40 filter_A = randn( s ize (filter_A ));

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 2. C o n t o u r ( b o u n d a r i e s )

[C,H]= imcontour(filter_A ,[0 ,0]);colorbar;

45 m = C(1 ,:)~= 0;

x = C(1,m); y = C(2,m);

i = sub2ind( s ize (A),round(y),round(x));

C_im = zeros( s ize (A));

C_im(i) = 1;

50 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 3. G r a d i e n t :

w= [-1 0 1;-2 0 2;-1 0 1];

wm = [-1 -2 -1;0 0 0;1 2 1];

s = imfilter (double(A),w,'replicate ');

55 g = imfilter (double(A),wm,'replicate ');

grad_A = sqrt(s.^2 + g.^2);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% M u l t i p l y t h e g r a d i e n t i m a g e w i t h t h e c o n t o u r i m a g e

neutral_A =( grad_A ).*( C_im);

60 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% F i n d t h e l e n g t h of t h e n e u t r a l l i n e

80

% P e r c e n t a g e t h r e s h o l d i n g 2 0 % t h r e s h o l d i n g :

alfa = 0.1; % l e s s t h a n 1 / 3

I_max = max(max(neutral_A ));

65 I_min = min(min(neutral_A ));

level1 = alfa*(I_max -I_min)+I_min; % 1 0 % t h r e s h o l d i n g

level2 = 2* level1; % 2 0 % t h r e s h o l d i n g

thresh2 = max(neutral_A ,level2 .*ones( s ize (neutral_A ))); % N e u t r a l l i n e i m a g e .

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

70 small= min(min(thresh2 ));

binary_thresh2 = thresh2 > small; % b i n a r y i m a g e

ON_pixels = find(binary_thresh2 == 1);

[m,n]= s ize (ON_pixels );

NL_Length = [NL_Length m*n];

75 % N u m b e r of f r a g m e n t s or o b j e c t s on t h e n e u t r a l l i n e :

[L,ss] = bwlabel(binary_thresh2 ,8); % 8 c o n n e c t e d

NL_no_Fragments =[ NL_no_Fragments ss];

% W e i g h t e d NL :

weighted = binary_thresh2 .* grad_A;

80 NL_Gradient = [NL_Gradient sum(sum(weighted ))];

no_of_images = [no_of_images k]; % n u m b e r of i m a g e s

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% T h i s f u n c t i o n c o m p u t e s t h e b o u n d a r y c u r v a t u r e a n d b e n d i n g e n e r g y

conn =4;

85 B = bwboundaries(binary_thresh2 ,conn);

Curvature = [];

BendingEnergy = [];

for g = 1: length(B)

Boundary = B{g};

90 curvature = atan2(- d i f f (Boundary (:,1)), d i f f (Boundary (: ,2)));

Curvature = [Curvature ; curvature ];

bendingenergy = sum( d i f f (curvature ).^2)/ length(curvature );

81

BendingEnergy = [BendingEnergy ; bendingenergy ];

end

95 i f length(B)==0 % L E B

Curvature = [Curvature ; 0];

BendingEnergy = [BendingEnergy ; 0];

end

% C u r v a t u r e F e a t u r e s :

100 NL_Curvature_mean =[ NL_Curvature_mean mean(Curvature )];

NL_Curvature_std =[ NL_Curvature_std std(Curvature )];

NL_Curvature_median =[ NL_Curvature_median median(Curvature )];

NL_Curvature_min =[ NL_Curvature_min min(Curvature )];

NL_Curvature_max = [NL_Curvature_max max(Curvature )];

105 % B e n d i n g E n e r g y F e a u t e r s :

NL_Bendingenergy_mean =[ NL_Bendingenergy_mean mean(BendingEnergy )];

NL_Bendingenergy_std =[ NL_Bendingenergy_std std(BendingEnergy )];

NL_Bendingenergy_median =[ NL_Bendingenergy_median median(BendingEnergy )];

NL_Bendingenergy_min =[ NL_Bendingenergy_min min(BendingEnergy )];

110 NL_Bendingenergy_max =[ NL_Bendingenergy_max max(BendingEnergy )];

end

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

NL_features =[ NL_Length;NL_no_Fragments;NL_Gradient;NL_Curvature_mean;...

115 NL_Curvature_std;NL_Curvature_median;NL_Curvature_min;...

NL_Curvature_max;NL_Bendingenergy_mean;NL_Bendingenergy_std;...

NL_Bendingenergy_median;NL_Bendingenergy_min;NL_Bendingenergy_max ];

disp(['save at:',base_directory ,Data_directory ,'/','_NLfeatures.mat'])

save([ base_directory ,Data_directory ,'/','_NLfeatures.mat'],'NL_features ');

120 end

82

A.3 Fractal Dimension Analysis Code

clear a l l

close a l l

clc


5 ARs = dir(base_directory );

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

for p = 3: length(ARs)

AR = ARs(p).name;

filenames = dir ([ base_directory ,AR ,'/*. fits']); FD=[];

10 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−


for k = 1: length(filenames)


A = fitsread ([ base_directory ,AR,'/',filename],'raw');

15 i f A(end,1) <-3000

disp('Here!');

A(A==A(end,1))=NaN;

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

20 % H e a d e r i n f o r m a t i o n : i g n o r e t h e i m a g e s w h i c h h a v e a r a d i u s ( d i s t a n c e


hdr = fitsinfo ([ base_directory ,AR,'/',filename ]);



25 cell2mat(hdr.PrimaryData.Keywords (188 ,2))^2);

i f radius >650

A=[];

else

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

30 % 1. F i l t e r i n g : a v e r a g e f i l t e r , s i z e 10 x 1 0

83

f i l t e r = fspecial('average ' ,10);

filter_A = imfilter(double(A), f i l t e r , 'replicate ');

% F i x N a N file , L E B

i f sum(sum( isnan(filter_A ))) == s ize (A,1)* s ize (A,2)

35 filter_A = randn( s ize (filter_A ));

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 2. C o n t o u r ( b o u n d a r i e s )

[C,H]= imcontour(filter_A ,[0 ,0]);colorbar; % s h o w t h e b o u n d e r i e s

40 m = C(1 ,:)~= 0;

x = C(1,m); y = C(2,m);

i = sub2ind( s ize (A),round(y),round(x));

C_im = zeros( s ize (A));

C_im(i) = 1;

45 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 3. G r a d i e n t of A ( o r i g i n a l i m a g e ):

w= [-1 0 1;-1 0 1;-1 0 1];

wm = [-1 -1 -1;0 0 0;1 1 1];

s = imfilter (double(A),w,'replicate ');

50 g = imfilter (double(A),wm,'replicate ');

f_A = sqrt(s.^2 + g.^2);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% m u l t i p l y t h e g r a d i e n t i m a g e w i t h t h e c o n t o u r i m a g e

Neutral_line =(f_A ).*( C_im); % t h i s is t h e n e u t r a l l i n e i m a g e

55 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 1. P e r c e n t a g e t h r e s h o l d i n g :

alfa = 0.1; % l e s s t h a n 1 / 3

I_max = max(max(Neutral_line ));

I_min = min(min(Neutral_line ));

60 level1 = alfa*(I_max -I_min)+I_min; % 1 0 % t h r e s h o l d i n g

level2 = 2* level1; % 2 0 % t h r e s h o l d i n g

84

thresh2 = max(Neutral_line ,level2 .*ones( s ize (Neutral_line ))); % N e u t r a l l i n e .

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

small= min(min(thresh2 ));

65 binary_thresh2 = thresh2 > small; % NL b i n a r y i m a g e

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% F r a c t a l D i m e n s i o n C a l c u l a t i o n

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 1. C r e a t a s t r u c t u r e : f i r s t l y d i s k s h a p e

70 SE=[]; Area_Dilate =[]; Radius =[];

for R=1:10

SE = [SE strel('disk',R,6)];

Dilate_image = imdilate(binary_thresh2 ,SE);

Area_Dilate =[ Area_Dilate bwarea(Dilate_image )]; % F i n d t h e a r e a a f t e r d i l a t e d

75 Radius= [Radius R];

end

Radii_of_strctr= log(Radius );

Areas_Dilate= log(Area_Dilate );

% 2. F i t a s t r a i g h t l i n e b e t w e e n t h e a r e a s of t h e d i l a t e d i m a g e a n d r a d i i of d i s k .

80 p =polyf it (Areas_Dilate ,Radii_of_strctr ,1);

FD =[FD 2-p(1 ,1)]; % F R A C T A L D I M E N S I O N V A L U E FD =2− S L O P E ( l o g ( a r e a )/ l o g ( r a d i i ))

end

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

85 FD_feature =FD;

disp(['saving ',base_directory ,AR,'/','_FDfeatures.mat']);

maximum_FD = max(FD_feature)

minimum_FD = min(FD_feature)

save([ base_directory ,AR,'/','_FDfeatures.mat'],'FD_feature ');

90 end

85

A.4 Emerging Flux Region Analysis Code

clear a l l

close a l l

clc



%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

for p = 3: length(data_directory)



10 no_of_images =[]; EFR_Gradient =[]; EFR_AbsGradient =[]; EFR_Area_3sigma =[];

EFR_Sum =[]; EFR_AbsSum =[]; EFR_std =[]; EFR_mean =[];

EFR_min =[]; EFR_max =[]; EFR_median =[]; newfiles =[];

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% R e a r r a n g e t h e n a m e s of i m a g e s in e a c h a c t i v e r e g i o n a n d c r e a t a n e w

15 % v e c t o r h a s t h e n a m e s of a l l i m a g e s w i t h r a d i u s <= 6 5 0 to m a k e s u r e we

% u s e t h e s a m e i m a g e s u s e d in o t h e r a l g o r i t h m s .

for k = 1:( length(filenames ))

filename=filenames(k).name;

F = fitsread ([ base_directory ,Data_directory ,'/',filename ]);

20 i f F(end,1) <-3000

F(F==F(end,1))=0;

end



25 radius = sqrt(cell2mat(hdr.PrimaryData.Keywords (187 ,2))^2 +...


i f radius >650

F=[];

else

30 newfiles =[ newfiles;filename ];

86

end

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

for x = 1: s ize (newfiles ,1)-1

35 % T h e F i r s t i m a g e

filename1 = newfiles(x,:);

A = fitsread ([ base_directory ,Data_directory ,'/',filename1 ]);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% T h e n e x t i m a g e

40 filename2 = newfiles(x+1,:);

B = fitsread ([ base_directory ,Data_directory ,'/',filename2 ]);

% T h e d i f f e r e n c e i m a g e w h i c h g i v e s t h e E F R :

resize_A = imresize(A, [152 152]); % T h e s a m e s i z e f o r a l l i m a g e s

resize_B = imresize(B, [152 152]); % I n t e r p o l a t i o n , or d o w n s a m p l i n g or s a m e

45 EFR_image = (resize_A) - (resize_B ); % T h e d i f f e r e n c e i m a g e

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% E F R i m a g e w e i g h t e d u s i n g t h e G r a d i e n t i m a g e :

% 1. E F R i m a g e t h r e s h o l d i n g by 3 s i g m a :

level = std(std(EFR_image ));

50 Triple_sigma = 3*level;

thresh_EFR = max(EFR_image ,Triple_sigma .*ones( s ize (EFR_image )));

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 2. G r a d i e n t of E F R i m a g e

w= [-1 0 1;-2 0 2;-1 0 1];

55 wm = [-1 -2 -1;0 0 0;1 2 1];

s = imfilter (EFR_image ,w,'replicate ');

g = imfilter (EFR_image ,wm,'replicate ');

grad_EFR = sqrt(s.^2 + g.^2);

sum_grad_EFR = sum(sum(grad_EFR ));

60 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% 3. W e i g h t e d E F R :

87

weighted = thresh_EFR .* grad_EFR;

EFR_Gradient =[ EFR_Gradient sum(sum(weighted ))];

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

65 % a l s o by u s i n g t h e t h r e s h _ E F R we w a n t to f i n d no of p i x e l s in t h e

% t h r e s h o l d i n g i m a g e of E F R

small= min(min(thresh_EFR )); % b i n a r y i m a g e

binary_thresh_EFR = thresh_EFR > small;

ON_pixels = find(binary_thresh_EFR == 1);

70 [m,n]= s ize (ON_pixels );

EFR_Area_3sigma =[ EFR_Area_3sigma m*n];

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

EFR_Sum =[ EFR_Sum sum(sum(EFR_image ))];

EFR_AbsSum =[ EFR_AbsSum sum(sum(abs(EFR_image )))];

75 EFR_mean =[ EFR_mean mean(mean(EFR_image ))];

EFR_std = [EFR_std std(std(EFR_image ))];

EFR_median =[ EFR_median median(median(EFR_image ))];

EFR_min = [EFR_min min(min(EFR_image ))];

EFR_max =[ EFR_max max(max(EFR_image ))];

80 no_of_images =[ no_of_images x]; % n u m b e r of i m a g e s

end

EFR_features = [EFR_Sum; EFR_AbsSum; EFR_Gradient; EFR_Area_3sigma;...

EFR_mean; EFR_std; EFR_median; EFR_min; EFR_max ];

disp(['save at:',base_directory ,Data_directory ,'/','_EFRfeatures.mat'])

85 save([ base_directory ,Data_directory ,'/','_EFRfeatures.mat'],'EFR_features ');

end

88

A.5 Wavelet Analysis Code

clear a l l

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%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

for p = 3: length(data_directory)



10

waveletType_L1 =[]; waveletType_L2 =[]; waveletType_L3 =[]; waveletType_L4 =[];

waveletType_L5 =[];

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% m a g n e t o g r a m i m a g e s l o o p :

15 for k = 1: length(filenames)



i f A(end,1) <-3000

20 A (A==A(end,1))= NaN;

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−



25 hdr = fitsinfo ([ base_directory ,Data_directory ,'/',filename ]);




i f radius >650

30 A=[];

89

else

[Lo_D ,Hi_D] = wfilters('haar'); N = 5;

[c,s]= wavedec2(A,N,Lo_D ,Hi_D);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

35 % F i n d t h e t h r e e h i g h p a s s d e t a i l s f o r e a c h l e v e l f r o m 1 to 5

for i=1:N

[H,V,D]= detcoef2('all',c,s,i); % E x t r a c t t h e t h r e e i m a g e s of e a c h l e v e l

[a,b] = s ize (V);

add_image = sum(abs(H(:)))+ sum(abs(V(:)))+ sum(abs(D(:))); % E n e r g y v a l u e

40 energy(i) = (add_image /(a*b)); % N o r m a l i z e t h e e n e r g y

no_of_levels(i)= i;

end

waveletEnergy_L1 = [waveletEnergy_L1 energy (1 ,1)];


45 waveletEnergy_L3 = [waveletEnergy_L3 energy (1 ,3)];



end

end

50 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Wavelet_features =[ waveletEnergy_L1; waveletEnergy_L2; waveletEnergy_L3;...

waveletEnergy_L4; waveletEnergy_L5 ];

disp(['saving ',base_directory ,Data_directory ,'/','_Waveletfeatures.mat']);

save([ base_directory ,Data_directory ,'/','_Waveletfeatures.mat'],...

55 'Wavelet_features ');end

90

A.6 Feature Selection Code

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clc

addpath '/home/amani/Documents/MATLAB/prtools '

5 base_directory = '/home/amani/Desktop/Amani/master thesis/active region/';

% L o a d i n g n a m e s of f e a t u r e s

load(['/home/amani/Documents/MATLAB/Amani_Work/classification_codes/'...

'Gradient_names.mat']);

load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/NL_names.mat');

10 load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/FD_names.mat');

load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/EFR_names.mat')

load(['/home/amani/Documents/MATLAB/Amani_Work/classification_codes/'...

'Wavelet_names.mat']);

featureNames =[ Gradient_features_names;NL_features_names;FD_features_names;...

15 EFR_Features_Names;Wavelet_features_names ];

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% F e a t u r e S e l e c t i o n P a r t

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

N=500; % 5 0 0 f l a r e a n d 5 0 0 n o f l a r e A R s u s e d to b a l a n c e t h e d a t a s e t A

20 M=100; % R e p e a t e t h e f e a t u r e s e l e c t i o n p r o c e s s M t i m e s

all_subset =[];

for f= 1:M

ARs= dir(base_directory );

ARs = ARs(3:end);

25 x_train =[]; y_train =[];i=randperm(2001);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

for k = 1:1000

AR = ARs(i(k)). name % i is s o m e r a n d o m f i l e

load([ base_directory ,AR,'/','_FDfeatures.mat']);

30 load([ base_directory ,AR,'/','_NLfeatures.mat']);

91

load([ base_directory ,AR,'/','_Gradientfeatures.mat']);

load([ base_directory ,AR,'/','_EFRfeatures.mat']);

load([ base_directory ,AR,'/','_Waveletfeatures.mat']);

% W o r k s p a c e : F e a t u r e s

35 Gradient_features=Gradient_features (: ,[1:end-1]);

NL_features=NL_features (:,[1:end-1]);

FD_feature=FD_feature (:,[1:end-1]);

Wavelet_features = Wavelet_features (:,[1:end-1]);

features =[ Gradient_features;NL_features;FD_feature;EFR_features;...

40 Wavelet_features ];

x_train = [x_train features ]; % F e a t u r e m a t r i x

load([ base_directory ,AR,'/','flare_labels_2h_0m.mat']);

load([ base_directory ,AR,'/','radius650.mat']);

s = find(1-radius650 );

45 flare_labels(s) = [];

flare_labels = flare_labels ([1:end-1] ,:);

y_train = [y_train; flare_labels ]; % l a b e l v e c t o r

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

50 x_train = x_train ';

% R e m o v e a n y N a N ∗ o b s e r v a t i o n s ∗

[O,Fnan] = find( isnan(x_train ));

O = unique(O);

x_train(O,:) = []; y_train(O) = [];

55 % N o r m a l i z e f e a t u r e c o l u m n s to be on [−1 ,1]

[X_train ,mx,mn]= normalize_feature_columns(x_train );

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% S t a r t i n g t h e f e a t u r e s s e l e c t i o n p a r t by f i r s t l y b a l a n c i n g t h e d a t a :

Y0 = find(y_train ==0); i0 = randperm( length(Y0));

60 Y1 = find(y_train ==1); i1 = randperm( length(Y1));

X_train_new = X_train ([Y0(i0(1:N)); Y1(i1(1:N))] ,:);

92

y_train_new = y_train ([Y0(i0(1:N)); Y1(i1(1:N))]);

% C r e a t p r T o o l s d a t a s e t

A=dataset(double(X_train_new),y_train_new ,'featlab ',featureNames );

65 % F e a t u r e s e l e c t i o n f u n c t i o n w i t h f i s h e r c as a t y p e of c l a s s i f i e r

[W,R] = featselp(A,fisherc ,0);

% T h e n e w s u b s e t of t h e s e l e c t e d f e a t u r e s .

all_subset = [all_subset; cellstr(getlab(W))];

end

70 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% S a v e t h e r e s u l t o r d e r of f e a t u r e s at e a c h t i m e s c a l e

save(['/home/amani/Documents/MATLAB/Amani_Work/classification_codes/'...

'All_subset_results/All_subset_2h.mat','all_subset '])

% P l o t i n g h i s t o g r a m of t h e r e s u l t f e a t u r e s :

75 [setout , mm, nn] = unique(all_subset );

for i=1: length(setout)

n(i,1)=sum(nn==i);

end

[n,IX] = sort(n);

80 setout = setout(IX) % f e a t u r e ’ s n a m e s s o r t e d f r o m l e a s t f r e q u e n t y to m a x i m u m

bar(1: length(n),n); % p l o t n u m b e r of f e a t u r e s a n d t h e r e p e t e t i o n of e a c h o n e

93

A.7 Fisher Linear Discriminant Analysis (FLDA) Classi�cation Code

close a l l

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addpath '/home/amani/Documents/MATLAB/prtools '

5 base_directory = '/home/amani/Desktop/Amani/master thesis/active region/';

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−


load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/',...

'Gradient_names.mat');

10 load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/NL_names.mat');

load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/FD_names.mat');


'EFR_names.mat');


15 'Wavelet_names.mat');

features ={'GradientFeatures ';'NLFeatures ';'fractal_dimension ';'EFRFeatures ';...

'Waveletfeatures '};


ARs = ARs(3:end);

20 x_train =[]; y_train =[];i=randperm(2001);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% T R A I N I N G P A R T

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

for k = 1:1000

25 AR = ARs(i(k)). name % i is s o m e r a n d o m f i l e


load([ base_directory ,AR,'/','_NLfeatures.mat']);



30 load([ base_directory ,AR,'/','_Waveletfeatures.mat']);

94

% W o r k s p a c e : a l l f e a t u r e s

Gradient_features=Gradient_features (: ,[1:end-1]);



35 Wavelet_features = Wavelet_features (:,[1:end-1]);


Wavelet_features ];

x_train = [x_train features ]; % F e a t u r e s m a t r i x

% w o r k s p a c e : l a b e l v e c t o r

40 load([ base_directory ,AR,'/','flare_labels_2h_0m.mat']);



flare_labels(s) = []; % R e m o v e a l l l a b e l s f o r w h i c h r a d i u s > 6 5 0


45 y_train = [y_train; flare_labels ]; % L a b e l v e c t o r f o r t r a i n i n g

end

x_train = x_train ';

% r e m o v e a n y N a N ∗ o b s e r v a t i o n s ∗

[O,Fnan] = find( isnan(x_train )); O = unique(O);

50 x_train(O ,:)=[]; y_train(O)=[];

% N o r m a l i z e f e a t u r e c o l u m n s to be on [−1 ,1]

[X_train ,mx,mn]= normalize_feature_columns(x_train );

save mx_mn mx mn

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

55 % T E S T I N G P A R T

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

x_test =[]; y_test =[];

for k = 1001:2000

AR = ARs(i(k)). name % i w i l l c h o o s e t h e r e s t f i l e s

60 load([ base_directory ,AR,'/','_FDfeatures.mat']);


95




65 % W o r k s p a c e : a l l f e a t u r e s

Gradient_features=Gradient_features (: ,[1:end-1]);




70 features =[ Gradient_features;NL_features;FD_feature;EFR_features;...

Wavelet_features ];

x_test =[ x_test features ];

% W o r k s p a c e : l a b e l v e c t o r


75 load([ base_directory ,AR,'/','radius650.mat']);




y_test =[ y_test; flare_labels ]; % l a b e l v e c t o r f o r t e s t i n g

80 end

x_test = x_test ';


[O,Fnan] = find( isnan(x_test ));

O = unique(O);

85 x_test(O ,:)=[]; y_test(O) = [];

% N o r m a l i z e f e a t u r e c o l u m n s to be on [−1 ,1]

[X_test ,mx,mn]= normalize_feature_columns(x_test );

save mx_mn mx mn

featureNames =[ Gradient_features_names;NL_features_names;FD_features_names;...

90 EFR_Features_Names;Wavelet_features_names ];

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% U s i n g t h e h i s t o g r a m of t h e f e a t u r e s s e l e c t e d to c h o o s e f e a t u r e s s u b s e t a n d

96

% r e d u c e t h e X _ t r a i n a n d X _ t e s t s i z e s r e l a t e d to s e l e c t e d f e a t u r e s

load(['/home/amani/Documents/MATLAB/Amani_Work/classification_codes/',...

95 'All_subset_results/All_subset_2h.mat']);

[setout , mm, nn] = unique(all_subset );


n(i,1)=sum(nn==i);

end

100 [n,IX] = sort(n);

setout = setout(IX); % F e a t u r s s o r t e d f r o m l e a s t f r e q u e n t y to m a x i m u m

setout = setout (30:35 ,:); % s e l e c t o p t i m a l f e a t u r e s s u b s e t or a l l ( 1 : 3 5 )

[f,indx] = ismember(setout ,featureNames );

X_train= X_train(:,indx); X_test = X_test(:,indx);

105 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% F i s h e r L i n e a r D i s c r i m i n a n t A n a l y s i s ( F L D A ) C l a s s i f i c a t i o n

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% B u i l d A ( t r a i n ) a n d B ( t e s t ) d a t a s e t s :

A = dataset(double(X_train),y_train ,'featlab ',setout );

110 B = dataset(double(X_test),y_test ,'featlab ',setout );

classifiers = {'fisherc '} % C l a s s i f i e r t y p e

num_features = s ize (y_test ,2);

M = 10; % M−f o l d c r o s s v a l i d a t i o n

N = 100; % N t r a i n i n g e x a m p l e s p e r c l a s s

115 train_classes = classsizes(A);

test_classes = classsizes(B);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

E_cum =[]; F_cum =[]; E_test_cum =[]; F_test_cum =[]; Hss =[]; Tss =[];

all_TP =[]; all_TN =[]; all_FP =[]; all_FN =[];

120 for m = 1:M



A_subset = dataset(double(X_train ([Y0(i0(1:N)); Y1(i1(1:N))],:)),...

97

y_train ([Y0(i0(1:N)); Y1(i1(1:N))]));

125 W_class = eval([ classifiers{c},'(A_subset)']); % T r a i n c l a s s i f i e r

[E,F] = testc(A_subset*W_class ); % C o m p u t e e r r o r s on t r a i n d a t a

[E_test ,F_test] = testc(B*W_class ); % C o m p u t e e r r o r s on t e s t d a t a

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% C o n f u s i o n m a t r i x a n d S k i l l s c o r e H S S a n d T S S

130 tot0 = s ize ( find(y_test ==0) ,1); tot1 = s ize ( find(y_test ==1) ,1);

TP = tot1 - F_test (2); all_TP =[ all_TP TP];

TN = tot0 - F_test (1); all_TN =[ all_TN TN];

FP = F_test (2); all_FP =[ all_FP FP];

FN = F_test (1); all_FN =[ all_FN FN];

135 [HSS ,TSS] = SkillScore(TP,FN,FP,TN); % C a l c u l a t e H S S a n d T S S

Hss=[Hss; HSS]; Tss=[Tss; TSS];

E_cum = [E_cum ; E]; F_cum = [F_cum ; F];

E_test_cum =[ E_test_cum;E_test ]; F_test_cum =[ F_test_cum;F_test ];

end

140 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% D i s p l a y t h e c l a s s i f i c a t i o n r e s u l t s

disp(['Classifier: ',classifiers{c}]);

disp('Training accuracies:');

disp(['Average accuracy: ',num2str(1-mean(E_cum ))]);

145 disp(['Class accuracies: ',num2str(1-mean(F_cum ,1)./N)]);

disp('Test accuracies:');

disp(['Average accuracy: ',num2str(1-mean(E_test_cum ))]);

disp(['Class accuracies: ',num2str(1-mean(F_test_cum ,1)./ test_classes )]);

disp('Skill Score : HSS /\ TSS ');

150 disp(['Average values: ',num2str(mean(Hss)), ' /\ ', num2str(mean(Tss ))]);

98

A.8 Relevance Vector Machine (RVM) Classi�cation Code

close a l l

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clc

addpath '/home/amani/Documents/MATLAB/RVMtoolbox ';

5 addpath '/home/amani/Documents/MATLAB/stprtool ';

stprpath('/home/amani// Documents/MATLAB/stprtool ')



'Gradient_names.mat']);

10 load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/NL_names.mat');

load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/FD_names.mat');

load('/home/amani/Documents/MATLAB/Amani_Work/classification_codes/EFR_names.mat')


'Wavelet_names.mat']);

15 featureNames =[ Gradient_features_names;NL_features_names;FD_features_names;...

EFR_Features_Names;Wavelet_features_names ];



ARs = ARs(3:end);

20 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% T R A I N I N G P A R T : F e a t u r e M a t r i x ( X _ t r a i n ) a n d l a b e l v e c t o r ( y _ t r a i n )

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

x_train =[]; y_train1 =[];i=randperm(2001);

for k = 1:1000

25 AR = ARs(i(k)). name % i is s o m e r a n d o m f i l e





30 load([ base_directory ,AR,'/','_Waveletfeatures.mat']);

99

% W o r k s p a c e : a l l f e a t u r e s

Gradient_features = Gradient_features (:,[1:end-1]);

NL_features = NL_features (:,[1:end-1]);

FD_feature = FD_feature (: ,[1:end-1]);

35 Wavelet_features = Wavelet_features (:,[1:end-1]);

features = [Gradient_features;NL_features;FD_feature;EFR_features;...

Wavelet_features ];

x_train = [x_train features ];


40 load([ base_directory ,AR,'/','flare_labels_2h_0m.mat']);





45 y_train1 = [y_train1;flare_labels ]; % L a b e l v e c t o r f o r t r a i n i n g

end

x_train = double(x_train ');


[O,Fnan] = find( isnan(x_train ));

50 O = unique(O);

x_train(O,:) = []; y_train1(O) = [];

[X_train1 ,mx,mn] = normalize_feature_columns(x_train );

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% T E S T I N G P A R T : F e a t u r e M a t r i x ( X _ t e s t ) a n d l a b e l v e c t o r ( y _ t e s t )

55 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

x_test =[]; y_test1 =[];

for k = 1001:2000

AR = ARs(i(k)). name % c h o o s e t h e r e s t f i l e s


60 load([ base_directory ,AR,'/','_NLfeatures.mat']);


100



% W o r k s p a c e : f e a t u r e s

65 Gradient_features = Gradient_features (:,[1:end-1]);

NL_features = NL_features (:,[1:end-1]);

FD_feature = FD_feature (: ,[1:end-1]);



70 Wavelet_features ];

x_test =[ x_test features ];




75 s = find(1-radius650 );

flare_labels(s) = [];


y_test1 =[ y_test1; flare_labels ]; % L a b e l v e c t o r f o r t e s t i n g

end

80 x_test = x_test ';


[O,Fnan] = find( isnan(x_test ));

O = unique(O);

x_test(O,:) = [];

85 y_test1(O) = [];

[X_test1 ,mx,mn]= normalize_feature_columns(x_test );

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% U s i n g t h e h i s t o g r a m of t h e f e a t u r e s to c h o o s e f e a t u r e s s u b s e t a n d

% r e d u c e t h e X _ t r a i n a n d X _ t e s t s i z e s r e l a t e d to s e l e c t e d f e a t u r e s

90 load(['/home/amani/Documents/MATLAB/Amani_Work/classification_codes/',...

'All_subset_results/All_subset_2h.mat']);

[setout , mm, nn] = unique(all_subset );

101


ni(i,1)=sum(nn==i);

95 end

[ni ,IX] = sort(ni);

setout = setout(IX); % F e a t u r e s s o r t e d f r o m l e a s t f r e q u e n t y to m a x i m u m

setout = setout (33:35 ,:); % S e l e c t o p t i m a l f e a t u r e s u b s e t or a l l ( 1 : 3 5 )

[f,indx] = ismember(setout ,featureNames );

100 X_train1= X_train1(:,indx);

X_test1 = X_test1(:,indx);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% R V M c l a s s i f i c a t i o n m e t h o d

% G a u s s i a n K e r n e l −b a s e d b i n a r y c l a s s i f i e r

105 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

M=10; % M−f o l d c r o s s v a l i d a t i o n

N=400; % N t r a i n i n g e x a m p l e s p e r c l a s s

true_positive_rate =[]; true_negative_rate =[]; Tss =[]; Hss =[];

all_TP =[]; all_TN =[]; all_FP =[]; all_FN =[];

110 for m =1:M

Y0 = find(y_train1 ==0); i0 = randperm( length(Y0));

Y1 = find(y_train1 ==1); i1 = randperm( length(Y1));

X_train_new = X_train1 ([Y0(i0(1:N)); Y1(i1(1:N))] ,:);

y_train_new = y_train1 ([Y0(i0(1:N)); Y1(i1(1:N))]);

115 K=[];

for n=1: s ize (X_train_new ,1)

v=[];

for j=1: s ize (X_train_new ,1)

v = [v exp(( -1/0.22)*((norm(X_train_new(n,:)- X_train_new(j ,:)))^2))];

120 end

K=[K; v]; % G a u s s i a n k e r n e l b a s e d b i n a r y c l a s s i f i e r

end

[parameter ,hyperparameter , diagnostic ]= SparseBayes('Bernoulli ',K,y_train_new );

102

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

125 a = parameter.Value;

index = parameter.Relevant;

X_relev = [X_train_new(index ,:)];

K_test =[];

for p=1: s ize (index ,1)

130 v2=[];

for s=1: s ize (X_test1 ,1)

v2=[v2 exp(( -1/0.22)*((norm(X_relev(p,:) - X_test1(s ,:)))^2))];

end

K_test =[ K_test; v2];

135 end

Y = K_test '*a; % R e s u l t v e c t o r Y f o u n d u s i n g t h e m o d e l ( a ) f r o m t h e t r a i n i n g p a r t

v1= find(Y >0.5); result(v1)=1;

v0= find(Y <=0.5); result(v0)=0;

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

140 % C o n f u s i o n m a t r i x a n d S k i l l s c o r e H S S a n d T S S

tot0= s ize ( find(y_test1 ==0) ,1); tot1 = s ize ( find(y_test1 ==1) ,1);

g0 = y_test1( find(result ==0)); TN = s ize ( find(g0==0) ,1); all_TN =[ all_TN TN];

g1 = y_test1( find(result ==1)); TP = s ize ( find(g1==1) ,1); all_TP = [all_TP TP];

g2 = result( find(y_test1 ==0)); FN = tot0 -TN; all_FN =[ all_FN FN];

145 g3 = result( find(y_test1 ==1)); FP = tot1 -TP; all_FP =[ all_FP FP];

[HSS ,TSS] = SkillScore(TP,FN ,FP,TN); % C a l c u l a t e H S S a n d T S S

Hss=[Hss; HSS]; Tss=[Tss; TSS];

false_negatives_rate = cerror(result ',y_test1 ,0);

false_positives_rate = cerror(result ',y_test1 ,1);

150 true_positive_rate = [true_positive_rate; 1-false_positives_rate ];

true_negative_rate = [true_negative_rate; 1-false_negatives_rate ];

end

[h,Fhnan] = find( isnan(Tss));

h = unique(h); Tss(h,:) = []; Hss(h ,:)=[];

103

155 %−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% D i s p l a y t h e c l a s s i f i c a t i o n r e s u l t s

disp('Test accuracies: No Flare (TN_rate) /\ Flare (TP_rate) ');

disp(['Class accuracies(rate):',num2str(mean(true_negative_rate )),'/\',...

num2str(mean(true_positive_rate ))]);

160 disp(['Confusion matrix:TP:',num2str(mean(all_TP)),...

'/\ FN: ', num2str(mean(all_FN ))]);

disp([' FP:',num2str(mean(all_FP)),...

' /\ TN: ', num2str(mean(all_TN ))]);

disp('Skill Score : HSS /\ TSS ');

165 disp(['Average values: ',num2str(mean(Hss)), ' /\ ', num2str(mean(Tss ))]);

104

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