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?
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