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Dynamic Time Warping (DTW) J.-S Roger Jang ( 張智星 ) MIR LabMIR Lab, CSIE Dept National Taiwan University.

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Presentation on theme: "Dynamic Time Warping (DTW) J.-S Roger Jang ( 張智星 ) MIR LabMIR Lab, CSIE Dept National Taiwan University."— Presentation transcript:

1 Dynamic Time Warping (DTW) J.-S Roger Jang ( 張智星 ) MIR LabMIR Lab, CSIE Dept National Taiwan University

2 Dynamic Time Warping  Goal  To align two sequences under certain constraints, such that the distance between these two sequences is as small as possible.  Method  Dynamic programming

3 Distance between Same-length Sequences  Distance between  Alignment

4 Distance between Different-length Sequences

5 Alignment Constraints: Type 1  Temporal constraints  Other alignment constraints  One-to-one mapping  No consecutive skip-over x1x1 x2x2 x3x3 y1y1 x4x4 x5x5 y2y2 y3y3 y4y4 y5y5 y6y6 y7y7 y8y8

6 Alignment Constraints: Type 2  Temporal constraints  Other alignment constraints  1-to-1, 1-to-many, or many-to-1 mapping  No skip-over x1x1 x2x2 x3x3 y1y1 x4x4 x5x5 y2y2 y3y3 y4y4 y5y5 y6y6 y7y7 y8y8

7 Type-1 DTW: Table Fillup i j x(i-1) y(j) x, y: input vector/matrix Local paths: degrees DTW formulation: y(j-1) x(i)

8 Type-2 DTW: Table Fillup x, y: input vector/matrix Local paths: degrees DTW formulation: i j x(i-1) y(j) y(j-1) x(i)

9 Local Path Constraints zType 1: y local paths zType 2: y local paths

10 -10- Path Penalty for Type-1 DTW zAlignment path of type-1 DTW y45-degree paths are likely to be avoided since we are minimizing the total distance. ySo we can add penalty for paths deviated from 45-degree.

11 -11- Path Penalty for Type-2 DTW zAlignment path of type-1 DTW y45-degree paths are likely to be taken since we are minimizing the total distance. ySo we can add penalty for paths of 45-degree.

12 -12- Other Minutes about DTW zTypical applications ySpeech recognition: MFCC matrices as inputs (where x(i) is the MFCC vector of frame i) yQuery by singing/humming: Pitch vectors as inputs (where x(i) is the pitch value of frame i) zAbundant variants for various applications yRecurrent formulas yLocal path constraints

13 -13- Applications zApplications of DTW yDTW for speech recognitionDTW for speech recognition yDTW for query by singing/hummingDTW for query by singing/humming


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