Dynamic_Time_Warping&Search

Dynamic_Time_Warping&Search - Speech Recognition...

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Unformatted text preview: Speech Recognition Dynamic Time Warping & Search February 13, 2012 Veton Këpuska 2 Dynamic Time Warping & Search Dynamic time warping Search Graph search algorithms Dynamic programming algorithms February 13, 2012 Veton Këpuska 3 Word-Based Template Matching Whole word representation: No explicit concept of sub-word units (e.g., phones) No across-word sharing Used for both isolated-and connected-word recognition Popular in late 1970s to mid 1980s Feature Measurement Pattern Similarity Decision Rule Word Reference Templates Spoken Word OutputW ord February 13, 2012 Veton Këpuska 4 Template Matching Mechanism Test pattern, T , and reference patterns, { R 1 ,..., R V },are represented by sequences of feature measurements Pattern similarity is determined by aligning test pattern, T ,with reference pattern, R v , with distortion D( T , R v ) Decision rule chooses reference pattern, R * , with smallest alignment distortion D( T , R * ) Dynamic time warping (DTW) is used to compute the best possible alignment warp, φ v , between T and R v , and associated distortion D( T , R v ) ( 29 v R T D R , min arg v * = February 13, 2012 Veton Këpuska 5 Alignment Example February 13, 2012 Veton Këpuska 6 Digit Alignment Examples February 13, 2012 Veton Këpuska 7 Dynamic Time Warping (DTW) Objective: an optimal alignment between variable length sequences T = { t 1 ,..., t N } and R = { r 1 ,..., r M } The overall distortion D( T , R ) is based on a sum of local distances between elements d ( t i , r j ) A particular alignment warp, φ , aligns T and R via a point-to-point mapping, =( t , r ), of length K t t (k) r r (k) 1≤k≤K The optimal alignment minimizes overall distortion: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 k K k k k m r t d M R T D R T D R T D r t ∑ = = = 1 , 1 , , min , February 13, 2012 Veton Këpuska 8 DTW Issues Endpoint constraints: φ t (1)= r (1)=1 t ( K )= N r ( K )= M Monotonicity: t (k+1)≥ t (k) r (k+1)≥ r (k) Path weights, m k , can influence shape of optimal path Path normalization factor, M , allows comparison between different warps (e.g., with different lengths). ∑ = = K k k m M 1 February 13, 2012 Veton Këpuska 9 DTW Issues: Local Continuity February 13, 2012 Veton Këpuska 10 DTW Issues: Global Constraints February 13, 2012 Veton Këpuska 11 Computing DTW Alignment February 13, 2012 Veton Këpuska 12 Graph Representations of Search Space Search spaces can be represented as directed graphs Paths through a graph can be represented with a tree February 13, 2012 Veton Këpuska 13 Search Space Tree February 13, 2012...
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This note was uploaded on 02/11/2012 for the course ECE 5526 taught by Professor Staff during the Summer '09 term at FIT.

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Dynamic_Time_Warping&Search - Speech Recognition...

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