Finding Time Series Motifs on Disk-Resident Data

Abdullah Mueen, Dr. Eamonn Keogh

UC Riverside

Nima Bigdely-Shamlo Swartz Center for Computational

Neuroscience, UCSD

Outline• Motivation– Time Series Motif

• DAME: Disk-Aware Motif Enumeration• Performance Evaluation– Speedup and Efficiency

• Case Studies– Motifs in Brain-Computer Interfaces– Motifs in Image Database

• Conclusion

Sequence Motif

• Repeated Pattern in a sequence .

• A Pattern can be approximately similar.– Mismatch is allowed

• A Pattern can be overlapping.

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Structural MotifMotion Motif Time Series Motif

Time Series Motif• Repeated Pattern in a Time Series.

• Exact Motif.– The most similar pair under Euclidean Distance.

• Non Overlapping.• Euclidean distance (between normalized segments)

– Beats most similarity measures on large datasets.– Early abandoning.– Triangular inequality.

• d(P,Q) ≥ |d(P,R) - d(Q,R)|0 10 20 30 40 50 60-2

-1012

Motif Discovery in Disk-Resident Datasets

• Large datasets– Light Curves of Stars.– Performance Counters of Data Centers.

• Pseudo time series dataset– “80 million Tiny Images”

• Database of normalized subsequences– An hour long trace of EEG generates over one

million normalized subsequences.

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Geometric View Disk View

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Geometric View Disk ViewProjected View

Linear Representation in sorted order0 is the reference point

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Projected View

Divide the point-set into two partitionand solve the subproblem

Projected View

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Geometric View Disk View

Blocks of Interest

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The inner ring is the region for blocks 5 and 6The outer ring is the region for blocks 3 and 4

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Projected ViewProjected ViewBlocks

Bsf

Block 3 and block 6 do not

overlap. No comparison.

Loaded Blocks

bsf

No Comparison

1 Comparison 9 comparisons 1 comparison

Block-Pair (3,5) Block-Pair (3,6) Block-Pair (4,5) Block-Pair (4,6)

11 comparisons are made instead of 9*16=144

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Speedup

Algorithm

Largest Dataset Tested

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Largest Dataset

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CompletelyInMemory 10035

minutes37.8days

CompletelyInDisk 2001.50days

1.65years

DAME 4,0001.35days

1.35 days

NoAdditionalStorage(normalization done in memory)

2004.82 days

5.28years

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Performance Evaluation

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# of blocks

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Motif Length

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Case Study 1: Brain-Computer Interfaces

Biosemi, Inc.Target Non-Target

Case Study 1: Brain-Computer Interfaces

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Spatial filter (ICA)

Case Study 2: Image Motifs

• Concatenated color histogram is considered as pseudo time series.

• Each time series is of length 256*3 = 768.

• 80 million tiny images of 32X32 resolution.

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80 million tiny images : collected by Antonio Torralba, Rob Fergus, William T. Freeman at MIT.

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Case Study 2: Image Motifs

• DAME worked on the first 40 million time series in ~6.5 days • DAME found 3,836,902 images which have at least one duplicate.– 1,719,443 unique images.

• 542,603 images have near duplicates with distance less than 0.1.

Duplicate Image Near Duplicate Image

Conclusion

• DAME: The first exact-motif discovery algorithm that finds motif in disk-resident data.

• DAME is scalable to massive datasets of the order of millions of time series.

• DAME successfully finds motif in EEG traces and image databases.

BACKUP

Example of Multidimensional Motif

Top view of the dance floor and the trajectories of the dancers.

Motion-Motif

Dance Motions are taken from the CMU Motion Capture Database

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Example of Worst Case Scenario

Multiple References for Ordering

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