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Unformatted text preview: Speech Recognition Dynamic Time Warping & Search 2/13/12 Veton Kpuska 2 Dynamic Time Warping & Search u Dynamic time warping u Search n Graph search algorithms n Dynamic programming algorithms 2/13/12 Veton Kpuska 3 WordBased Template Matching u Whole word representation: n No explicit concept of subword units (e.g., phones) n No acrossword sharing u Used for both isolatedand connectedword recognition u Popular in late 1970s to mid 1980s Feature Measurement Pattern Similarity Decision Rule Word Reference Templates Spoken Word Output Word 2/13/12 Veton Kpuska 4 Template Matching Mechanism u Test pattern, T , and reference patterns, { R 1 ,..., R V },are represented by sequences of feature measurements u Pattern similarity is determined by aligning test pattern, T ,with reference pattern, R v , with distortion D( T , R v ) u Decision rule chooses reference pattern, R* , with smallest alignment distortion D( T , R* ) u Dynamic time warping (DTW) is used to compute the best possible alignment warp, f v, between T and R v, and associated distortion D( T , R v ) ( 29 v R T D R , min arg v * = 2/13/12 Veton Kpuska 5 Alignment Example 2/13/12 Veton Kpuska 6 Digit Alignment Examples 2/13/12 Veton Kpuska 7 Dynamic Time Warping (DTW) u Objective: an optimal alignment between variable length sequences T = { t 1 ,..., t N } and R = { r 1 ,..., r M } u The overall distortion D( T , R ) is based on a sum of local distances between elements d ( t i, r j ) u A particular alignment warp, f , aligns T and R via a pointto point mapping, f =( f t, f r ), of length Kf t f t(k) &#243; r f r(k) 1kKf u 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 , 2/13/12 Veton Kpuska 8 DTW Issues u Endpoint constraints: f t (1)= f r (1)=1 f t ( K )= N f r ( K )= M u Monotonicity: f t (k+1) f t (k) f r (k+1) f r (k) u Path weights, mk, can influence shape of optimal path u Path normalization factor, M f , allows comparison between different warps (e.g., with different lengths). = = K k k m M 1 2/13/12 Veton Kpuska 9 DTW Issues: Local Continuity 2/13/12 Veton Kpuska 10 DTW Issues: Global Constraints 2/13/12 Veton Kpuska 11 Computing DTW Alignment 2/13/12 Veton Kpuska 12 Graph Representations of Search Space u Search spaces can be represented as directed graphs u Paths through a graph can be represented with a tree 2/13/12 Veton Kpuska 13 Search Space Tree 2/13/12 Veton Kpuska 14 Graph Search Algorithms u Iterative methods using a queue to store partial paths...
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 Summer '09
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 Algorithms, C Programming

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