learning Spectral Clustering, With Application To Speech Separation: Difference between revisions
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==Clustering== | ==Clustering== | ||
Clustering refers to partition a given dataset into clusters such that data points in the same cluster are similar and data points in different clusters are dissimilar. Similarity is usually measured over distance between data points. | Clustering refers to partition a given dataset into clusters such that data points in the same cluster are similar and data points in different clusters are dissimilar. Similarity is usually measured over distance between data points. | ||
Formally stated, given a set of data points <math>X=\{{{\mathbf x}}_1,{{\mathbf x}}_2,\dots ,{{\mathbf x}}_P\}</math>, we would like to find <math>K</math> disjoint clusters <math>{C{\mathbf =}\{C_k\}}_{k\in \{1,\dots ,K\}}</math> such that <math>\bigcup{C_k}=X</math>, that optimizes a certain objective function. | |||
Revision as of 12:31, 30 June 2009
Clustering
Clustering refers to partition a given dataset into clusters such that data points in the same cluster are similar and data points in different clusters are dissimilar. Similarity is usually measured over distance between data points.
Formally stated, given a set of data points [math]\displaystyle{ X=\{{{\mathbf x}}_1,{{\mathbf x}}_2,\dots ,{{\mathbf x}}_P\} }[/math], we would like to find [math]\displaystyle{ K }[/math] disjoint clusters [math]\displaystyle{ {C{\mathbf =}\{C_k\}}_{k\in \{1,\dots ,K\}} }[/math] such that [math]\displaystyle{ \bigcup{C_k}=X }[/math], that optimizes a certain objective function.