4. Rare Time Series Motif Discovery
from Unbounded Streams
Nurjahan Begum and Eamonn Keogh
VLDB 2015

5. Talk Outline
• Ubiquity of time series
• What are time series motifs?
• Rare Motif Discovery
• Conclusions

6. Talk Outline
• Ubiquity of time series
• What are time series motifs?
• Rare Motif Discovery
• Conclusions

7. Time Series is Ubiquitous
0 20
0
40
0
60
0
80
0
100
0
120
0
0 50 100 150 200 250 300 350 400 4500
0.5
1
Unstructured audio stream
Sesnors on machine Shapes Hand Writing
Motion Capture Human Speech Web Clicks
Electrocardiogram
Insect Wingbeat Sound

8. Talk Outline
• Ubiquity of time series
• What are time series motifs?
• Rare Motif Discovery
• Conclusions

9. What are time series motifs?
- Approximately repeated subsequences
- An example:
Activity Recognition
walking walking stretching walking
0 200 400 600 800 1000
vacuuming
Motifs are useful as a subroutine for:
-Classification
-Clustering
-Rule Discovery
-Anomaly Detection

10. Talk Outline
• Ubiquity of time series
• What are time series motifs?
• Rare Motif Discovery
• Conclusions

11. Rare Motif Discovery
• Motivation
• Algorithms
– Brute Force
– Limited cache
• Performance Improvement
– Changing Data Representation
– Sticky Cache
• Experiments

12. Rare Motif Discovery
• Motivation
• Algorithms
– Brute Force
– Limited cache
• Performance Improvement
– Changing Data Representation
– Sticky Cache
• Experiments

13. What are time series motifs?
- Approximately repeated subsequences
- An example:
Activity Recognition
walking walking stretching walking
0 200 400 600 800 1000
vacuuming
Situations where current motif finding algorithms can perform
poorly/ fail
Far apart in space (Motifs occurring in different data chunks )
Infrequent (Computationally expensive!)

14. Rare Motifs: A real life example
(Four months
omitted)
3 days ago 2 days ago now131 days ago 129 days ago 127 days ago : : : : :
0
20
40
Solar Panel
Current (mA)
A never-ending time series stream from a weather station’s solar panel,
only a fraction of which we can buffer.
A pattern we are observing now seems to have also occurred about
four months ago.

15. Rare Motif Discovery
• Motivation
• Algorithms
– Brute Force
– Limited cache
• Performance Improvement
– Changing Data Representation
– Sticky Cache
• Experiments

16. Brute Force Approach
I1 I2 I3 I4 …
“current item is a motif pattern” if we find that D(k + 1, j) < T and j < k + 1.
Ik

17. Brute Force Approach
• Brute Force with Limited Memory
– A cache of fixed size w
Success Metric
Expected number of objects we see before we report success
I1 I2 I3 I4 …
“current item is a motif pattern” if we find that D(k + 1, j) < T and j < k + 1.
Ik

18. Rare Motif Discovery
• Motivation
• Algorithms
– Brute Force
– Limited cache
• Performance Improvement
– Changing Data Representation
– Sticky Cache
• Experiments

19. Changing Data Representation
Emulating virtually large cache
- Downsampling the data
- Reducing the dimensionality of the data
- Reducing the cardinality of the data
16 20 24 30
0
2000
4000
6000
8000
10000
12000
2 4 8 12
Expectednumberofobjectsprocessed
beforesuccess
Virtual Cache Size
Dimensionality
Reduction
Cardinality
Reduction
Downsampling

20. Rare Motif Discovery
• Motivation
• Why the problem is hard?
• Algorithms
– Brute Force
– Limited cache
• Performance Improvement
– Changing Data Representation
– Sticky Cache
• Experiments

21. Sticky Cache
0 300 600 900 1200 1500
0.4
0.6
0.8
0.991
P100 = Probability of discarding an
element from R is 100 times greater
P50 = Probability of discarding an
element from R is 50 times greater
P100
P50
P1
Probabilityofsuccess
Number of objects seen before success
•A magic cache where potential motif
patterns tend to remain for longer
•Biased cache replacement policy

22. Sticky Cache
Algorithm for detecting potential motifs
– Discretize each time series subsequence
– Query the Bloom Filter for the instance in question
• If Bloom Filter saw the instance before
– Tag it as potential motif pattern
• Else
– Tag it as random pattern
0 300 600 900 1200 1500
0.4
0.6
0.8
0.991
P100 = Probability of discarding an
element from R is 100 times greater
P50 = Probability of discarding an
element from R is 50 times greater
P100
P50
P1
Probabilityofsuccess
Number of objects seen before success

23. 0 50 100 150 200 250 300 350
100
1000
400
Expectednumberofelementsseen
beforesuccess
Virtual Cache Size
Downsampling
Dimensionality
Reduction
Cardinality
Reduction
Cardinality
Reduction with Sticky cache
Which approach is best?
Comparison of all approaches in commensurate scale

24. Rare Motif Discovery
• Motivation
• Algorithms
– Brute Force
– Limited cache
• Performance Improvement
– Changing Data Representation
– Sticky Cache
• Case Studies

25. 7.88 7.9 7.92 7.94 7.96 7.98 8
x 10
4
Dish washer
TS: Dishwasher + Refrigerator
Motif Length: 160 (2 hrs 40 mins)
Sampling Rate: 0.017 Hz
Day 11 Day 19: : : : : : : : : : :
(omitted section)
Day 70 Day 140 Day 210 Day 280 Day 350
Day 70 Day 140 Day 210 Day 280 Day 350
Ground Truth
Motifs Detected

26. Time Series Length: 2245824 (10 hours)
Sampling Frequency: 62.3 Hz
Motif Length: 188 (3 sec)
White-crowned Sparrow (Zonotrichia leucophrys)
37 minutes : : : : : : : : : : : : : : : : : : : 140 minutes
(omitted section)
0 40 80 120 160 200
36 min 54 sec
2.3 hours
A
0 40 80 120 160 200
1 min 57 sec
B
0 40 80 120 160 200
31 min 27 sec
C

27. Dataset: NPR August 01, 2013
Time Series Length: 29 hr 21 min 57 sec
MFCC space length: 6596741 (6.5 million)
Sampling Frequency: 62.4 Hz
Motif Length: 4 sec

28. Conclusions
• We address the problem of detecting rare motifs
– Changing Data representation
– Sticky Cache
• All the code and data for this paper is publicly
available!

29. Thank you!