A Bandwidth- Efficient Nearest Neighbor Search for Dynamic Time Warping Distance in Distributed Environment

Transcription

1 A Bandwidth- Efficient Nearest Neighbor Search for Dynamic Time Warping Distance in Distributed Environment Intel Team Topic 3 Pernghwa, Chin- Chi, Yen- Hua, Kung- Ting

2 Problem DescripIon Time series are distributed among sites in a distributed environment Find query s K nearest neighbors (KNN) under dynamic 8me warping (DTW) Goal : reduce total communica8on cost (bandwidth) as much as possible P 5 Query... P P M P 2 P 4... P

3 Time Series A collecion of observaions in Ime sequenially MulI- dimensional feature vector where adjacent ordered features are highly dependent

4 Distributed Environment Server: A central site which has a Ime series as query to find its KNN

5 K Nearest Neighbors Find K candidate 8me series that are the most similar to the query Similar: Measure by distance Smaller distance <- > more similar KNN: K candidate Ime series that have the smallest distance to the query KNN is usually used to solve other problems such as classificaion

6 K Nearest Neighbors Example: KNN classificaion

7 Dynamic Time Warping DTW: A kind of distance measure Beyond Dynamic Programming algorithm Considered bewer than Euclidean distance (ED) and many applicaions in different areas DTW(Q, C) = D(q n, c n ) = d(q n, c n ) + min{d(q n- 1, c n- 1 ), D(q n- 1, c n ), D(q n, c n- 1 )} d(q n, c n ) = (q n - c n ) 2 (our seang is ED) ED(Q, C) = D(q n, c n ) = d(q n, c n ) + D(q n- 1, c n- 1 )

8 Dynamic Time Warping Example: Compute distance between A = (1, 3, 6, 4), B = (3, 6, 4, 2) B looks like a led shid of A B should be similar to A from human view ED(A, B) = (1-3) (4-2) 2 = 21 = ED((1, 3, 6, 4), (3, 6, 4, 2)) = (4-2) 2 + ED((1, 3, 6), (3, 6, 4)) DTW(A, B) = DTW((1, 3, 6, 4), (3, 6, 4, 2)) = (4-2) 2 + min{ DTW((1, 3, 6), (3, 6, 4)), DTW((1, 3, 6), (3, 6, 4, 2)), DTW((1, 3, 6, 4), (3, 6, 4)) } = 8

9 Dynamic Time Warping ED DTW

10 Naïve Approach

11 Improvement transmiang the complete query leads to very high bandwidth Two methods for saving bandwidth Segmenta8on Bounding technique The soluions can help the server prune candidate Ime series without compu8ng exact DTW

12 SoluIons SegmentaIon Query is split into segments Segments can be represented as local maximum and minimum, which are the sampled data points Only the sampled data points are transmifed

13 SegmentaIon

14 SegmentaIon between Levels ObservaIon: min / max at level L will be sill min / max at level (L + 1) Transmiang signals instead of the same min / max between levels to save bandwidth At the final level (all segment size = 1), all data points of the query are transmifed exactly once => Total bandwidth = (complete query length) * 1 + (some signal overhead) In the worst case, not much lose to direct transmission

15 SegmentaIon between Levels Example: For 4 sub- segments, we use 2- bit signals

16 SoluIons Bounding Technique Any site can construct an envelope of the query with sampled data points received Using the approximate query, sites can compute an upper bound and a lower bound of DTW locally prune candidate Ime series with these bounds Lower bound Real DTW value always Upper bound Real DTW value always

17 Bounding Technique Current Work: FTW2 Edited from FTW (proposed in 2005) CalculaIon formula is like DTW Providing a Ight lower bound and upper bound of the real DTW value

18 Pruning Flow At level L Yes => To level (L+1), transmit more sampled data points of the query End because KNN are found No Are more than K Ime series not pruned? Pruning candidate Ime series with the informaion of bounds

19 Pruning Flow Yes Are more than K Ime series not pruned? Pruning candidate Ime series with the informaion of bounds Is it at the final level? No Yes To next level CompuIng the exact DTW of remaining Ime series SorIng DTW and finding KNN End

20 Pruning Framework How to prune candidates since we have the segmentaion and bounding technique? There are two proposed frameworks Framework 1: Global pruning Framework 2: Local pruning

21 Framework 1 Overview

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28 Framework 2 Overview

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35 Challenges How to set proper parameters of segmentaion? BeWer segmentaion? What situaion do we use Framework 1 or Framework 2 in? Balance between bandwidth and computaion Tighter bounds => Higher computaion cost