# Visualization and Exploration of Temporal Trend Relationships in Multivariate Time-Varying Data

AI and Robotics

Nov 25, 2013 (4 years and 7 months ago)

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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

5

Time series
f
β

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
x

Time series
f
α

α

t
0

t
1

Time series
f
γ

γ

for each spatial point
x
,

compare
p
with the time series of
the same variable on
x:

check each sliding window [
t
0
,t
1
]

if ( ||
f
β
[
t
0

t
1
],
p
|| <
δ

)

p

exists

on
x

in [
t
0
,
t
1
]

A brute force algorithm

Trend
p

β

t

6

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

Compressed

Stretched

Shifted & Repeated

Nonlinearly
deformed

7

DTW: Dynamic Time Warping

DTW

A popular pattern matching
method in speech recognition

Time complexity O(
T
2
)

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(
T
2
)
trend
detection

algorithm

for each sliding window [
t
0
,
t
1
]

DTW(
p
,
f
β
[
t
0

t
1
])

if ( distance after DTW <
δ

)

p

exists in
[
t
0
,
t
1
]

A DTW
-
based brute
-
force algorithm to
detect
p

in
f
β
[1...
T
]

Time
complexity
:

(#
sliding

windows
)

x

(DTW time
complexity
)

=

O(
T
2
) x O(
T
2
)

=

O(
T
4
)

SUBDTW

=

Brute force

+ DTW

O(
T
2
)

O(
T
4
)

<<

Functionality

Time
complexity

9

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

10

Trend A

t

t

t

Trend

Detection

t
4

t
1

t
3

t
5

t
6

Time series
at
x

Trend B

Trend C

time

t
2

Trend Sequence
at
x

t
4

t
1

t
3

t
5

t
6

B

A

B

A

C

t
2

Trend Sequence Clustering

Extract the most common ones from millions of trend
sequences

A 1
-
pass clustering algorithm

11

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

A

C

root

C

A

C

Clustered State Diagram

B

A B

A

C

B

A B

A

A

C

12

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

13

Trend Sequence Icon

Encode the state order of a trend sequence

t

t

t

#
States

#
Trends

Trend A

Trend B

Trend C

t
4

t
1

t
3

t
5

t
6

B

A

B

A

C

t
2

14

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

t
1

t
2

t
3

t
4

t
5

t
6

B

A B

A

C

t
1

t
2

t
3

t
4

t
5

t
6

Parallel
Coordinates Plot (
PCP)

t’
1

t’
2

t’
3

t’
4

t’
5

t’
6

Trend sequence A

t’
1

t’
2

t’
3

t’
4

t’
5

t’
6

B

A B

A

C

Trend sequence B

15

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

16

Case Study

Hurricane Isabel

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

Questions

1.
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

17

Case Study

Hurricane 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
sequences

Wind Magnitude

Pressure

Temperature

18

Trend
-
Sequence
-
based Transfer Function

Reveal the spatial distribution of
trend sequences

Specification

1.
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

19

Case Study

Hurricane 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

20

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?