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Unformatted text preview: constant values in 2 nd eigenvector 4/6/10 COT 6936 4 Graph Bisection (Continued) Eigenvalues indicate strength of bisection How to get bisections with n/2 vertices? Use median value in second eigenvector How to get k partitions? Perform bisections recursively Use more eigenvectors 4/6/10 COT 6936 5 Spectral Clustering: Strategy Given data points and a distance function, construct a weighted graph Let A be its adjacency matrix; let D be diagonal matrix with degrees along diagonal Construct Laplacian L ( PSD , non-neg eigenv .) Unnormalized: L = D A Normalized symmetric: L = D-1/2 LD 1/2 Random Walk: L = D-1 L Matrix L k has cols = first k eigenvectors of L Cluster rows of L k . 4/6/10 COT 6936 6 3 Spectral Clustering Need distance measure (need not be a metric), i.e., triangle inequality not needed Not Model-based Global method Turns discrete problem into continuous 4/6/10 COT 6936 7...
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- Spring '12