Ch5-Vector_Quantization&Clustering

Ch5-Vector_Quantization&Clustering - Speech...

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Speech Recognition Vector Quantization and Clustering
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February 13, 2012 Veton Këpuska 2 Vector Quantization and  Clustering Introduction K -means clustering Clustering issues Hierarchical clustering Divisive (top-down) clustering Agglomerative (bottom-up) clustering Applications to speech recognition
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February 13, 2012 Veton Këpuska 3 Acoustic Modeling Signal representation produces feature vector sequence Multi-dimensional sequence can be processed by: Methods that directly model continuous space Quantizing  and modeling of discrete symbols Main advantages and disadvantages of quantization: Reduced storage and computation costs Potential loss of information due to quantization Signal  Representation Vector  Quantization Symbols Feature  Vectors Waveform
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February 13, 2012 Veton Këpuska 4 Vector Quantization (VQ) Used in signal compression, speech and image coding More efficient information transmission than scalar  quantization (can achieve less that 1 bit/parameter) Used for discrete acoustic modeling since early 1980s Based on standard clustering algorithms: Individual cluster centroids are called codewords Set of cluster centroids is called a codebook Basic VQ is  K -means clustering Binary VQ is a form of top-down clustering (used for efficient  quantization)
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February 13, 2012 Veton Këpuska 5 Clustering is an example of  unsupervised  learning Number and form of classes { C i }  unknown Available data samples { x i }  are unlabeled Useful for discovery of data structure before classification or  tuning or adaptation of classifiers Results strongly depend on the clustering algorithm
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February 13, 2012 Veton Këpuska 6 Acoustic Modeling Example   
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February 13, 2012 Veton Këpuska 7 Clustering Issues What defines a cluster? Is there a prototype representing each cluster? What defines membership in a cluster? What is the distance metric,  d ( x y )? How many clusters are there? Is the number of clusters picked before clustering? How well do the clusters represent unseen data? How is a new data point assigned to a cluster?
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Veton Këpuska 8 K -Means Clustering Used to group data into  clusters, { C 1 ,… ,C K } Each cluster is represented by mean of assigned data Iterative algorithm converges to a local optimum: Select  initial cluster means, { µ 1 ,… ,µ K } Iterate until stopping criterion is satisfied: 1. Assign  each data sample to the closest cluster X C i ; d ( x ; µ i )≤ d ( x ; µ j ) i j 1. Update   means from assigned samples µ i   E ( x ) X C i 1 ≤ 
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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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Ch5-Vector_Quantization&Clustering - Speech...

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