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

plantationscarfAI and Robotics

Nov 25, 2013 (3 years and 11 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?