Ch6-Dynamic_Time_Warping&Search2

Ch6-Dynamic_Time_Warping&Search2 - Speech...

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Speech Recognition Search
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2/13/12 Veton Këpuska 2 u Dynamic time warping  u Search  n Graph search algorithms  n Dynamic programming algorithms 
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2/13/12 Veton Këpuska 3 Word-Based Template Matching  u  Whole word representation:  n No explicit concept of sub-word units (e.g., phones)  n No across-word sharing  u Used for both isolated-and connected-word recognition  u Popular in late 1970s to mid 1980s  Feature Measurement Pattern Similarity Decision Rule Word Reference Templates Spoken Word Output Word
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2/13/12 Veton Këpuska 4 Template Matching Mechanism  u Test pattern,  , and reference patterns, { R 1 ,...,  R },are  represented by sequences of feature measurements  u Pattern similarity is determined by aligning test pattern,  ,with  reference pattern,  R , 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 * =
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2/13/12 Veton Këpuska 5 Alignment Example 
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2/13/12 Veton Këpuska 6 Digit Alignment Examples 
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2/13/12 Veton Këpuska 7 Dynamic Time Warping (DTW)  u Objective: an optimal alignment between variable length  sequences  = { t 1 ,...,  t N } and  = { 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  and  via a point-to- point mapping,  f   =( f t,  f r ), of length  Kf   t f t(k)    r f r(k)    1≤k≤Kf 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 = = = φ 1 , 1 , , min ,
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2/13/12 Veton Këpuska 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). = = φ K k k m M 1
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2/13/12 Veton Këpuska 9 DTW Issues: Local Continuity 
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2/13/12 Veton Këpuska 10 DTW Issues: Global Constraints 
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Graph Search Methods 2/13/12 Veton Këpuska 11
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2/13/12 Veton Këpuska 12 Computing DTW Alignment 
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2/13/12 Veton Këpuska 13 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
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2/13/12 Veton Këpuska 14 Search Space Tree 
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2/13/12 Veton Këpuska 15
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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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Ch6-Dynamic_Time_Warping&Search2 - Speech...

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