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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 , nonneg eigenv .) ± Unnormalized: L = D – A ± Normalized symmetric: L = D1/2 LD 1/2 ± Random Walk: L = D1 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 Modelbased ± Global method ± Turns discrete problem into continuous 4/6/10 COT 6936 7...
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 Spring '12
 Giri
 Linear Algebra, Algorithms, Matrices, Markov chain, Eigenvalue, eigenvector and eigenspace, Fundamental physics concepts, Orthogonal matrix

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