ChinChia Michael Yeh Helga Van Herle Eamonn Keogh httpwwwcsucredueamonnMatrixProfilehtml Outline Motivation Proposed method Experiment result Conclusion 2 Outline Motivation ID: 539623
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Slide1
Matrix Profile III: The Matrix Profile allows Visualization of Salient Subsequences in Massive Time Series
Chin-Chia Michael Yeh, Helga Van Herle, Eamonn Keogh
http://www.cs.ucr.edu/~eamonn/MatrixProfile.htmlSlide2
Outline
MotivationProposed methodExperiment resultConclusion
2Slide3
Outline
MotivationProposed methodExperiment resultConclusion
3Slide4
Motivation
4
You have a heartbeat time seriesSlide5
Motivation
5
You know where the heartbeats areSlide6
Motivation
6
You can easily visualize heartbeats by mapping them into 2D with algorithm like
MultiDimensional
Scaling (MDS)
If the scatter plot and corresponding subsequences are shown to domain expert, the correct label can be easily recoveredSlide7
Motivation
7
Normal Best
Abnormal Best
Normal beats forms one cluster while abnormal beat forms two clusters
You can easily visualize heartbeats by mapping them into 2D with algorithm like
MultiDimensional
Scaling (MDS)
If the scatter plot and corresponding subsequences are shown to domain expert, the correct label can be easily recoveredSlide8
Motivation
8
However, segmentation of time series is rarely available as annotation is usually expensive (even if possible)Slide9
Motivation
9
If we simply slide a window across the time series, the resulting scatter plot is not interpretable because
being forced to “explain”
all
subsequences is condemned to be meaningless
[a]
[a] J. Lin, E. Keogh and W.
Truppel
, “Clustering of time-series subsequences is meaningless: implications for previous and future research,” in
Knowledge and Information Systems
, 2005.Slide10
Motivation
10
This is a chicken-and-egg paradox as we only want to explain the subsequence that explainableSlide11
Problem statement
Given a time series
and a desired subsequence length
, how do we select a subsequences of length from
so that the result low dimensional projection is meaningful?
11
, time series
, subsequence length
Slide12
Problem statement
Given a time series
and a desired subsequence length
, how do we select a subsequences of length from
so that the result low dimensional projection is meaningful?
12
, time series
, subsequence length
We want to find subsequences that produce meaningful low dimensional projectionSlide13
Outline
MotivationProposed methodExperiment resultConclusion
13Slide14
Minimum description length principle
14
Minimum Description Length (MDL) principle: the best hypothesis for a given set of data is the one that leads to the
best compression of the data [a]Given a set of all possible subsequence
of a time series, how do we pick a set of hypothesis
which optimally compresses
?
[a] https://en.wikipedia.org/wiki/Minimum_description_lengthSlide15
Toy example in text
Given a string with relevant substring’s locationa
fat cat plays hide and seek in
fog with dog
15
two rhyming pairs forms two clusters in the scatter plot (projected with hamming distance and MDS)
fat
cat
fog
dogSlide16
Toy example in text
Given a string without relevant substring’s locationafatcatplayshideandseekinfogwithdog
16
To make this string more like “time series”, spaces are removedSlide17
Toy example in text
Given a string without relevant substring’s locationafatcatplayshideandseekinfogwithdog
17
If each char requires 8 bits to store, total bits to store the string is 280 bitsSlide18
Toy example in text
Given a string without relevant substring’s location
={
:fog
},
={
:fat
}
a
__
__
playshideandseekin
__
with__ 18With hypothesis and , the string can be store with 206 bits (without compress is 280 bits)If the hypothesis substrings {fog, fat} and compressed substrings {dog, cat} are projected to 2D with MDS, the 2 cluster rhythm pairs are recovered fatcatfogdogSlide19
Brute force solution
If the time series’ length is
and the desired subsequence length is
, all possible subsequences set contains
subsequences
If we know in advance that there are
hypothesis in the time series, the time complexity of brute force search is
19
However,
is unknown in most case
The true time complexity is even higher and intractable for most real time series
Slide20
Heuristic rule for approximate search
A subsequences with closer nearest neighbor is more likely be a good hypothesis
20
Neighbor
pair
3,000
0
3,000 float takes 96,000 bits to store Slide21
Heuristic rule for approximate search
A subsequences with closer nearest neighbor is more likely be a good hypothesis
21
noise section: 2,400 float = 76,800 bits
pattern: 300 float = 9,600 bits
pattern position: 2
int
= 64 bits
Total = 86,464 (was 96,000)
3,000
0
__
__
__
__
Slide22
Matrix profile
22
Matrix profile [a] is a meta time series that annotate
which compactly stores the nearest neighbor information of each subsequencesTime complexity is
[a] http://www.cs.ucr.edu/~eamonn/MatrixProfile.html
local minimums are motifs
3,000
0
P
, matrix
profile
T
,
synthetic data
, subsequence length
By searching just the subsequences around the local minimums of matrix profile, good hypothesis set can be recovered more efficientlySlide23
Outline
MotivationProposed methodExperiment resultConclusion
23Slide24
Heartbeat
24
Normal Beats
Premature
Contractions Ventricular Beats
Normal Beats
PVC Beats
Type A
PVC Beats
Type B
False
Positive
Ground truth
Our methodSlide25
Heartbeat
Ground truth
Our method
25
Normal Beats
Premature
Contractions Ventricular Beats
Normal Beats
PVC Beats
Type A
PVC Beats
Type B
False
Positive
While
A
and
B
are both PVCs, their morphology (which is related to where in the ventricle they initiate) are different. It appears that type
B
is a right bundle branch pattern, coming from right side of the heart, and Type
A
is more likely to be the of the fusion of a normal beat and an aberrant beat. Moreover, there is also evidence of a retrograde P-wave in type
B
.Slide26
Human motions
26
From this time series, our algorithm selects 11 subsequences
They form three clustersSlide27
Human motions
27
Bowing
Waving
Crouching
When we check the class label for each subsequence, they are indeed from different classSlide28
Human motions
28
0
60
120
Bowing
Waving
Crouching
Subsequence from the same cluster has very similar shapeSlide29
Nursery rhyme: London bridge falling down
29
What'll you take to set him
fr
..
broke my chain, broke my chain
(piano)
G
b
-B
b
-D
b
F-Ab-Db Gb-Bb-Db…it up with penny loavesMy fair lady silver and gold, silver and g…silver and gold, silver and..My fair lady(piano) Gb-Bb-Db F-Ab-Db Gb-Bb-Db…d it up with penny loavesWhat'll you take to set him fr..…fair lady, buil.. ..fair lady, pin.. broke my chain, broke my chain….. man to watch all night….. man to watch all nightSlide30
Small extension: from ED-MDS to DTW-MDS
30
ED-MDS
DTW-MDS
miss
walking very slow
normal walking
Nordic walking
running
cycling
rope jumping
Because matrix profile + MDL is able to select a small set of subsequences, applying MDS with DTW is computable (some dataset requires DTW for warping invariance)Slide31
Outline
MotivationProposed methodExperiment resultConclusion
31Slide32
Conclusion
Project subsequences into 2D space is a good way to explore time series dataWe generally should not attempt to explain all the data, but rather only consider salient subsequencesMatrix profile + MDL can be used as the heuristic rules for selecting salient subsequence for visualization
Limitation: only repeated subsequence is selected, sometimes the more interested subsequence is the unique one (anomaly)
32