1

1

Multi-dimensional Visualization

based on Bidimensional Mapping

Rosane Minghim

Instituto de Ciências Matemáticas e de

Computação

USP-São Carlos2

Projection Techniques

• : xi, xj R, xi,xj X

• d: yi, yj R, yi,yj Y

• f: X Y,|(xi,xj) – d(f(xi), f(xj))| 0, xi,xj X

X Rm Y Rp={1,2,3}f

3

Ex: Mapping to plane of patents

surgery, drugs, molecular bio

4

Problems PCA

390 dimensions

2

5

Problems PCA

6

Problems PCA

7

• Let X be the points in theoriginal space Rn, we apply adistance measure dij* betweenXi an Xj., and find Y, theprojected point, ex. R2 and dij

the Euclidean distancebetween them.

• Sammon’s method applies anerror function to measure thetarget.

Ex: Sammon Mapping

8

Force Based Point Placement

3

9

Force Scheme [Tejada et al.,

2003]

x'

q'

10

Force Based Point Placement

11

Force Scheme [Tejada et al.,

2003]

x'

q'

12

Force Scheme [Tejada et al.,

2003]

x'

q'

4

13

Force Scheme [Tejada et al.,

2003]

x'

q'

< 0

14

Force Scheme [Tejada et al.,

2003]

x'

< 0

< 0

< 0 > 0

> 0

15

• Let Vi = {pi1,…,piki} be a neighborhood of a point pi and

let ci be the coordinates of pi em Rp

• Each pi is the centroid of points in Vi

pi

pi1

pi2 pi3

pi4

pi5

ij Vp

ji cki

c 01

LSP: Laplacian Matrix

16

LSP: Laplacian Matrix

Lx1=0, Lx2=0, …, Lxp=0

Where x1, x2,…, xp are vectors containing

the coordinates of the points and L is the

matrix given by:

therwise o

V pki

ji

Lij ij

0

1

1 0

0

...

0

0

L

1

2

n

x

x

x

=

5

17

LSP: Adicionando os Pontos de

Controle

C

LA

therwise

pocontrolais pCij

j

o0

int1

ncninx

nib

icpi

0

0100

0010

L

1

2

n

x

x

x

1

2

0

0

0

c

c

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LSP: Overview

Escolher os pontos de

controle

Determinar a

vizinhança dos pontos

Pontos

em Rm

Projetar os

pontos de controle

Resolver um

sistema linear esparso

Pontos em Rp

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Choosing the Control Points

• In order to select the control points

• the space Rm is split into nc clusters

using k-medoids.

• the control points are the medoids of

each cluster

20

Choosing the Control Points

• Once the control points are chosen, these

points are projected onto Rd through a

fast dimensionality reduction method

• Fast Projection (Fastmap or NNP)

• Force Placement

6

21

Control points

in blue

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Content – based by Projections

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Example

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Projection Example: IDH

7

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Projection Example: voting in US

Senate

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Point Placement by Phylogenetic Tree

Construction Algorithms (N-J Trees)

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Point Placement by Phylogenetic Tree

Construction Algorithms (N-J Trees)

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NJ similarity Tree

8

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• Alternate view (N-J Tree)

30

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Exploration

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• Finding Relationships

Exploration

9

33 34

• Building a Surface

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RSS News Flash

Bird and Flu 36Palestinian

10

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Bush Iraq

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Bush Iraq

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Application 1: Visual Text

Mapping

• Approach 1: Relationship Based

(Metadata)

• Approach 2: Content based

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Relationships :

Topic Bursts and co-word

(Mane and Borner)

2004

11

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Relationships :

Citation and Co-citation

(Borner)

(2003)

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Content-based Text Mapping

• Approach 1: Pre-clustering & View

• Approach 2: Dimension reduction

(Projections)

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Content - based

(Skupin)

(2002)

(abstracts)

SOM

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Content - based

(Dimensional

Reduction)

News flash

IN-SPIRE

(PNL)

12

45

Content - based

(Surface

View)

IN-SPIRE

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• Self-Organization Maps (SOMs) cartográficos (ex.

Skurpin 2002)

SOM based

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Mapeamento para o plano permitindo a

exploração.

Ex: Patents surgery, drugs, molecular bio

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Exemplos de Mapas

13

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Exemplos de Mapas

50

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• Detailing topics

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14

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Time Series – Streamflow in Hidroelectrics

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• Cattle performance data

• Translated to text from categorical

information, e.g.,

• Ranges of weight to words such as:

{weight_below_fifty_percent;

weight_between_fifty_seventy_five; etc..}

• 9135 individuals

Text from attributes

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Cattle performance data

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Cattle performance data

Colored

by word

‘top’

15

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Cattle performance data

Colored

by

female

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Cattle performance data

Colored

by farm

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Images?

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Pipeline

Image

Data Set

Feature

AcquisitionFeature

Selection

Similarity

CalculationVisualizationClassification

Interaction

16

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PEx-Image – Sample Content

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PEx-Image – Group Content

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PEx-Image – Image as Visual

Mark

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PEx-Image – Coordination

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PEx-Image – Coordination

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Comparison of Distance Metrics

Euclidean City Block Cosine

512 MRI medical images

12 classes

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Comparison of Distance Metrics

Euclidean City Block Cosine

512 MRI medical images

12 classes

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Comparison of Feature Space (1)

16 Gabor

Filters

Fourier, Mean

and Deviation

72 co-ocurrence

matrices All combined

512 MRI medical images

12 classes

18

69

Comparison of Feature Space (1)

16 Gabor

Filters

Fourier, Mean

and Deviation

72 co-ocurrence

matrices All combined

512 MRI medical images

12 classes

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Comparison of Feature Space (2)

All combined

1000 X-Ray images from

ImageCLEF

116 classes

1024 Wavelet Features

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Comparison of Feature Space (2)

All combined

1000 X-Ray images from

ImageCLEF

116 classes

1024 Wavelet Features

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Detailed Inspection

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Detailed Inspection

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ImageCLEF Training Data Set (1)

9000 X-Ray

images

116 classes

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ImageCLEF Training Data Set (2)Class 108 Class 111

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• RSS Patent Data, recovered from the

Web http://www.freepatentsonline.com/

• Case 1:

• 170 files

• Graphics processing, printer, database,

document, ai

Further Examples on Text

20

77

Further Examples

78

Further Examples

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Further Examples

80

(ink jet,

document)

21

81 82

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Patents – case 2

• http://www.freepatentsonline.com/

• 172 files

• surgery (2), drugs(2), molecular biology

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Patents surgery, drugs, molecular bio

22

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Patents surgery, drugs, molecular bio

stopwords selection

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Patents surgery, drugs, molecular bio

topics

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Patents surgery, drugs, molecular bio

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Patents surgery, drugs, molecular bio

23

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Projection Explorer (PEx)

http://infoserver.lcad.icmc.usp.br/ 90

Alneu de Andrade Lopes – Mineração de textos

alneu@

Haim Levkowitz – Visualization

haim@cs.uml.edu

João E. S. Batista Neto – Imaging

jbatista@

Collaborators

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Maria Cristina F. Oliveira

cristina@

Rosane Minghim

Visualization Group

Luis Gustavo

Nonato

malhas

Fernando Vieira

Paulovich

Visualização/Projeções

92

Doutorandos

Danilo Medeiros Eler

Aretha Barbosa

Kátia Felizardo

Mestrandos

Jorge Poco Medina

Christian

Tácito Neves

Renato Oliveira

Gabrial Andery

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Other Partnerships

Sérgio Furuie (Poli – USP), Brazil

Lars Linsen (Jacobs University

Bremen), Germany

Charl Botha (TU Delft ); Anton Heijs

(Treparel Inc.), The Netherlands

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Link

• infoserver.lcad.icmc.usp.br (Pex, Pex-WEB, Pex-Temporal, Pex-Image).

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Referências

• Cuadros, A. M, Paulovich, F. V., Minghim, R., Telles, G. P - Point Placement by

Phylogenetic Trees and its Application to Visual Analysis of Document Collections

IEEE VAST 2007, Sacramento, CA, USA, IEEE CS Press, pp.99-106.

• Paulovih, F. V., Oliveira, M.C.F., Minghim, R. - The Projection Explorer: A Flexible

Tool for Projection-based Multidimensional Visualization, IEEE Sibgrapi 2007, IEEE

CS Press, Belo Horizonte, Brazil,pp. 27-34.

• Lopes, A. A., Minghim, R., Melo, V., Paulovich, F.V.; Mapping texts through

dimensionality reduction and visualization techniques for interactive exploration of

document collections, SPIE Conference on Visualization and Data Analysis, San

Jose, CA, USA Jan. 2006, 6060T-11.

• Minghim, R., Paulovich, F.V., Lopes, A. A.; Content-based text mapping using

multidimensional projections for exploration of document collections, SPIE

Conference on Visualization and Data Analysis, San Jose, CA, USA Jan. 2006,

6060T-11.

96

Referências

• Pinho, R. D. ; Oliveira, M. C. F. ; Minghim, R. ; Andrade, M. G. . Voromap: A Voronoi-based Tool

for Visual Exploration of Multidimensional Data. In: 10th International Conference on

Information Visualization, 2006, Londres. Proceedings of Information Visualisation 2006,

2006. v. 1. p. 39-44

• Paulovich, F. V. ; Minghim, R. . Text Map Explorer: a Tool to Create and Explore Document

Maps. In: Information Visualisation 2006 (IV06) 10th International Conference on Information

Visualisation, 2006, Londres. Proceedings of Information Visualisation 2006, 2006. v. 1. p. 245-

251.

• Paulovich, F. V. ; Nonato, L. G. ; MINGHIM, R. ; Levkowitz, H. . Least Square Projection: a fast

high precision multidimensional projection technique and its application to document mapping.

IEEE Transactions on Visualization and Computer Graphics, 2008.

• Minghim, R. ; Levkowitz, H. ; Nonato, L. G. ; Watanabe, L. S. ; Salvador, V. C. L. ; Lopes, H. ;

Pesco, S. ; Tavares, G. . Spider Cursor: A simple versatile interaction tool for data visualization

and exploration. In: ACM GRAPHITE'05 - 3rd International Conference on Computer Graphics

and Interactive Techniques in Australasia and Southeast Asia, 2005, Dunedin. Proceedings of

Graphite 2005, 2005. p. 307-314.