learning Spectral Clustering, With Application To Speech Separation

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.