Kernel kmeans, Spectral Clustering and Normalized Cuts Export

@inproceedings{citeulike:332853, abstract = {Kernel k-means and spectral clustering have both been used to identify clusters that are non-linearly separable in input space. Despite significant research, these methods have remained only loosely related. In this paper, we give an explicit theoretical connection between them. We show the generality of the weighted kernel k-means objective function, and derive the spectral clustering objective of normalized cut as a special case. Given a positive definite similarity matrix, our results lead to a novel weighted kernel k-means algorithm that monotonically decreases the normalized cut. This has important implications: a) eigenvector-based algorithms, which can be computationally prohibitive, are not essential for minimizing normalized cuts, b) various techniques, such as local search and acceleration schemes, may be used to improve the quality as well as speed of kernel k-means. Finally, we present results on several interesting data sets, including diametrical clustering of large geneexpression matrices and a handwriting recognition data set.}, author = {Dhillon, Inderjit S. and Guan, Yuqiang and Kulis, Brian}, citeulike-article-id = {332853}, citeulike-linkout-0 = {http://www.cs.utexas.edu/users/inderjit/public_papers/kdd_spectral_kernelkmeans.pdf}, comment = {Proof that weighted spectral clustering is a special case of weighted kernel kmeans}, keywords = {clustering, datamining, kmeans, spectral}, posted-at = {2005-09-27 10:17:48}, priority = {4}, title = {Kernel kmeans, Spectral Clustering and Normalized Cuts}, url = {http://www.cs.utexas.edu/users/inderjit/public_papers/kdd_spectral_kernelkmeans.pdf} }

TY - CONF ID - citeulike:332853 L3 - citeulike-article-id:332853 N2 - Kernel k-means and spectral clustering have both been used to identify clusters that are non-linearly separable in input space. Despite significant research, these methods have remained only loosely related. In this paper, we give an explicit theoretical connection between them. We show the generality of the weighted kernel k-means objective function, and derive the spectral clustering objective of normalized cut as a special case. Given a positive definite similarity matrix, our results lead to a novel weighted kernel k-means algorithm that monotonically decreases the normalized cut. This has important implications: a) eigenvector-based algorithms, which can be computationally prohibitive, are not essential for minimizing normalized cuts, b) various techniques, such as local search and acceleration schemes, may be used to improve the quality as well as speed of kernel k-means. Finally, we present results on several interesting data sets, including diametrical clustering of large geneexpression matrices and a handwriting recognition data set. TI - Kernel kmeans, Spectral Clustering and Normalized Cuts KW - clustering KW - datamining KW - kmeans KW - spectral N1 - Proof that weighted spectral clustering is a special case of weighted kernel kmeans AU - Dhillon, Inderjit AU - Guan, Yuqiang AU - Kulis, Brian UR - http://www.cs.utexas.edu/users/inderjit/public_papers/kdd_spectral_kernelkmeans.pdf ER -