enumeration of time series motifs of all lengths

Enumeration of Time Series Motifs of All LengthsABDULLAH MUEEN

DEPARTMENT OF COMPUTER SCIENCE

UNIVERSITY OF NEW MEXICO

Example: Repeating Pattern (Motif)

0 2000 4000 6000 8000 100000

102030

0 100 200 300 400 500 600 700 800

Chiu et al. KDD 2003

Motivation: Enumerating MotifsFind the most similar pairs of time series at every lengths.

Brown A E X et al. PNAS 2013;110:791-796

Goals: Enumerating Motifs

Outline 1.Bounding correlation 2.Enumerating motifs of all lengths

◦ Intuitive Example◦Experimental Results◦Case Study: Activity Recognition

3.Conclusion

Pearson’s Correlation Coefficient

Correlation Advantage: 1. Scale and Shift invariant 2. Linear scans to compute Disadvantage: 1. Don’t consider warping 2. Is not a metric

Relationship with Euclidean Distance

Bounding Euclidean Distance

Values Changed

1 2 3 4 5

345678910

Without Normalization

1 2 3 4 5-4-3-2-101234

With Normalization

Intuition

1 2 3 4 5-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1 2 3 4 5-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

1 2 3 4 5-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Length 4 Length 5 Length 5

Append 10 and re-normalize Append 20 and re-normalizeNormalized


0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 1050

5

10

15

20

25

30

35

2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3x 105

2020.52121.52222.52323.52424.525

Pairs in ascending order of distances

Nor

mal

ized

Dis

tanc

e



3.Conclusion

Intuition

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-8.5

-8

-7.5

-7 x 103



3.Conclusion

Sanity Check

0 1000 2000 3000 4000 5000 6000-2

0

2

4

1380 1400 1420 1440 1460-5

0

5

Length :871320 1340 1360 1380 1400 1420

-5

0

5

Length :105600 700 800

-5

0

5

Length :2992200 2300 2400

-5

0

5

Length :299

(1) (2) (3) (4)

White Noise

http://www.cs.unm.edu/~mueen/Projects/MOEN/index.html

Experimental Results: Scalability

0 2 4 6 8 10 12 14 16x 104

0

1

2

3

4

5

6

7x 105

Data Length (n)

Exe

cuti

on T

ime

in S

econ

ds

Smart Brute ForceEEGEOGRandom WalkIterative MK

1 2 3 4 5 6 7 8 9 10

0

2

4

6

8

10

12

14

16

18x 104

Smart Brute ForceEEGRandom WalkEOG

Exe

cuti

on T

ime

in S

econ

ds

Range of Lengths (maxLen-minLen+1)x 102



3.Conclusion

Activity Recognition

x 104

AB

CE

F

A AA BCC

DDDDDD EEFF

0 0.5 1 1.5 2 2.5 3

0/20/22/4

1/41/21/2

0/30/40/2

0/40/40/4

Hip

Hand

Arm

Legxyz

xyz

xyz

xyz

H. Pohl et al. SMC 2010

Thank You

Backup Slides

Experimental Results

K

Exe

cuti

on T

ime

in S

econ

ds

4 6 8 10 12 14

0

2

4

6

8

10

12

n=10kn=20kn=40kn=80kn=160k

x 103

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

1

2

3

4

5

6

7

8

Exe

cuti

on T

ime

in S

econ

ds

n=10kn=20kn=40k

c

x 102

Sample Output

3960 3980 4000 4020 4040 4060 4080 4100 4120

Length :186

1.6341.6361.6381.64 1.6421.6441.6461.6481.65

x 104

-5

0

5

5260 5280 5300 5320 5340 5360 5380 5400 5420 5440-5

0

5

Length :187

9100 9120 9140 9160 9180 9200 9220 9240 9260

-5

0

5

3450 3500 3550 3600 3650-5

0

5

Length :255

8800 8850 8900 8950 9000

-5

0

5

7050 7100 7150 7200 7250 7300 7350 7400-5

0

5

Length :373

9600 9650 9700 9750 9800 9850 9900

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-8.5

-8

-7.5

-7 x 103

http://www.cs.unm.edu/~mueen/Projects/MOEN/index.html

Time Series Joinx1.5x10-3

100 200 300 400 500 600 700 800

0

0.5

1

1.5

2

0

0.5

1

1.5

2

Lengths

Best Match

CorrelationLength-adjusted Correlation

Motif Covering

0 50 100 150 200 250 300 350 4000

2000

4000

6000

8000

Length

Covering Motifs

Loca

tions

of t

he

Firs

t Occ

urre

nces

enumeration of time series motifs of all lengths

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