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Doruk Sart, Abdullah Mueen, Walid Najjar, Eamonn Keogh, Vit Niennatrakul 1

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Subsequence Search Given a query series : Q : Find the occurrences of Q in a time series S : Distance smaller than a threshold. Dynamic Time Warping 2 Time C Q C Q Warping path w Mapping

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Time Warping Subsequence Search Previous Method: SPRING – Reuses computation for subsequence matching 3 S Q Match 1Match 2Match 3Match 4 Yasushi Sakurai, Christos Faloutsos, Masashi Yamamuro: Stream Monitoring under the Time Warping Distance. ICDE 2007:1046-1055 For every new subsequence only one column is added on the right Not Always Possible!!

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Normalization IS Necessary Wandering Baseline Problem Z-Normalization: (x-µ)/σ – Shift and Scale Invariance Reuse of computation is no longer possible 4 -5 -3 1 3 0100 -5 -3 1 3 Query Distance to the query 05001000 1500 0 40 80 120 Threshold = 30 300500700900110013001500 0 1 2 3 4 5 6 20040060080010001200 0 1 2 3 4 5 6 Subsequence at time tSubsequence at time t+300 Value Reduced at = 600

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Parallelizing DTW search 5 -8000 -7500 -7000... Slide a window of a fixed size. Compute the distance between the query and the z-normalized sliding window. Report those that result less than t. Possibly try it for other lengths. Assign each distance computation to one GPU core or one systolic array in an FPGA. Q

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Speedups 6 Upto 4500x speedup using FPGA. Upto 29x speedup using GPU. Capable of processing a very high speed stream of hundreds of hertz. Capable of processing several low speed streams simultaneously. 10020030040050060070080090010001100 0 100 200 300 400 500 600 700 800 Length of the Query (Q) Time in Seconds Software SSE GPU FPGA

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Case Study: Astronomy Rotation Invariant DTW -- O( n 3 ) – Try all possible rotations to find the minimum possible distance. 7 1-NN AccuracyTime FPGATime GPUTime CPU ED80.47%<1.0 seconds 2.5 seconds rED81.25%<1.0 seconds55.3 seconds43.6 minutes DTW86.72%<1.0 seconds43.6 seconds35.4 minutes rDTW91.41%9.54 minutes22.7 hours(42 days) 02004006008001000 OGLE052401.70-691638.3 OGLE052357.02-694427.3 020406080100120 1 5 9 020406080100120 1 5 9 DTW distance 53.49 rDTW distance 0 Important for cyclic time series. e.g. Star Light Curves

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Thank You 8

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Indexing Time Series Based on original slides by Prof. Dimitrios Gunopulos and Prof. Christos Faloutsos with some slides from tutorials by Prof. Eamonn.

Indexing Time Series Based on original slides by Prof. Dimitrios Gunopulos and Prof. Christos Faloutsos with some slides from tutorials by Prof. Eamonn.

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