Visualization and Exploration of Temporal Trend Relationships in

Multivariate Time-Varying Data

Teng-Yok Lee & Han-Wei Shen

Introduction: Temporal Trends in Multivariate Time-Varying Data

• Each variable over time on each spatial point forms a time series

• Temporal trends• Salient time series patterns• Represent physical phenomena

• What are the relationships among these trends on different variables?

Motivation

• Extract the relationships among user-specified trends in multivariate data• Where, when and how long do they exist?• What’s their order to appear on the same region? • Do they overlap in time/space?• What’s their order to disappear on the same region?

• Requirements• Detection of temporal trends• Find and describe their relationship within multivariate data• Effective visualizations and interaction

3

4

Overview

User Specification of Temporal Trends

Temporal Trend Detection by SUBDTW

Temporal Trend Relationship Modeling and Extraction

Tend-based Interaction & Visualization

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Time series fβ ∈β

Trend Detection

• Trend: a time series of scalars

• Given a trend p, how to detect it in a multivariate data set?

Time series at xTime series

fα∈α

t0 t1Time series

fγ ∈γ

for each spatial point x, compare p with the time series of the same variable on x:

check each sliding window [t0,t1]if ( ||fβ[t0…t1], p|| <δ )

p exists on x in [t0,t1]A brute force algorithm

Trend p∈β

t

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Trend Detection: Challenge

• The trend can be deformed over time• Conventional distance metrics

cannot work

• How do other communities handle this problem?• DTW in speech recognition

Original Trend

CompressedStretched Shifted & Repeated Nonlinearly

deformed

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DTW: Dynamic Time Warping

• DTW• A popular pattern matching

method in speech recognition

• Time complexity O(T2)

• Invariant under shift/stretch/compression/deform

• Can DTW be used with the brute force algorithm?

Courtsey: E. J. Keogh and M. J. Pazzani. Derivative dynamic time warping.

In Proceedings of the First SIAM International Conference on Data Mining, 2001

DTW: mapping time steps from one time series to the other w/ minimal distance

From Brute-force to SUBDTW

• SUBDTW: our O(T2) trend detection algorithm

for each sliding window [t0,t1] DTW(p, fβ[t0…t1])if ( distance after DTW <δ )

p exists in [t0,t1]

A DTW-based brute-force algorithm to detect p in fβ[1...T]

Time complexity:(#sliding windows)

x (DTW time complexity) = O(T2) x O(T2) = O(T4)

SUBDTW =

Brute force + DTW

O(T2) O(T4)<<

Functionality

Time complexity

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Trend Relationship Model

• Given a spatial location, various relationships among the trends exist• Which trends occur? • What’s their temporal order? • How long are their durations?• Do their durations overlap?

• Trend sequence• Our formal model to describe the trend relationships

Trend Sequence

• A state machine• Each state represents a set of trends• The state changes when any trends begin/end

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Trend A

t

t

t

Trend Detection

t4t1 t3 t5 t6

Time series at x

Trend B

Trend C

timet2

Trend Sequence at x

t4t1 t3 t5 t6

BAB

A

C

t2

Trend Sequence Clustering

• Extract the most common ones from millions of trend sequences

• A 1-pass clustering algorithm

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B A B A C

B A B A C

B A B A C

B A B A C

Trend Sequences

B A B AC

root C

A C

Clustered State Diagram

B A B A C

B A B A

A C

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Visualization

Trend sequence Icon: encodes the order of the trend sequences

Parallel Coordinate Plots (PCP): represents the transition times in the trend sequences

Trend-sequence-based transfer function: reveals the spatial and temporal information of the trend sequences

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Trend Sequence Icon

• Encode the state order of a trend sequence

t

t

t

#States

#Tre

nds

Trend A

Trend B

Trend C

t4t1 t3 t5 t6

BAB

A

C

t2

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Visualizing Trend Sequence Times

• In the same cluster, trend sequences can have different transition times

• From times to high dim vectors• Each trend sequence w/ n

states has n+1 time steps.

• Use PCP w/ n+1 axes to visually compare the trend sequences in the same cluster

t1 t2 t3 t4 t5 t6B A B A C

t1

t2

t3

t4

t5

t6

Parallel Coordinates Plot (PCP)

t’1

t’2

t’3

t’4

t’5

t’6

Trend sequence At’1 t’2 t’3 t’4 t’5 t’6B A B A CTrend sequence B

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Visualizing Trend Sequence Times (contd’)

• Different techniques can be applied to enhance the PCP

By blending the polylines, the visual clutters can be reduced and the polylines can be visually grouped.

The groups can be then filtered out and colored

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Case StudyHurricane Isabel

• A simulation of an intense tropical weather system that occurred in September, 2003, over the west Atlantic region

• Questions1. Given a region, do the drop-and-rise patterns appear in both the

wind magnitude and the pressure?

2. Will the temperature increase so much only along the hurricane eye? Will it increase in other regions?

Testing trends

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Case StudyHurricane Isabel (contd’)

• Observations• The wind magnitude and the pressure will not

always drop together• If they drop together, where?

• The rising of temperature can occur in other regions• Where?

Most common trend sequencesWind Magnitude

Pressure

Temperature

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Trend-Sequence-based Transfer Function

• Reveal the spatial distribution of trend sequences

• Specification1. Browse the trend sequence

icons to select an icon

2. Select a polyline group on the PCP

3. Specify color and transparency

4. Color the corresponding data points accordingly

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Case StudyHurricane Isabel (contd’)

• How does the path of the hurricane eye influence the wind magnitude and pressure?

If too distant from the eye, the trends for both variables do not exist.

Only the trend for the pressure exists near the path

The trends for both variables coexist along the path of the hurricane eye

Wind Magnitude

Pressure

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Conclusion

• Contributions• A new way to explore/understand multivariate time-

varying data

• A model to describe trend relationships and an efficient clustering algorithm

• A new algorithm to detect time series patterns

Any questions?