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

2. 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

3. 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!!

4. 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

5. 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

6. 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

7. 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

8. Thank You 8