Spectral Clustering

Statistical Learning and Data Science, ASA

American Statistical Association, Statistical Learning and Data Science webinar

<p>Spectral clustering is one of the most popular algorithms to group high-dimensional data. It is easy to implement, computationally efficient, and has achieved tremendous success in many applications. The idea behind spectral clustering is dimensionality reduction. It first performs a spectral decomposition on the dataset and only keeps the leading few spectral components to reduce the dimension of the data. It then applies some standard methods such as the k-means on the low-dimensional space to do clustering. In this talk, we demystify the success of spectral clustering by providing a sharp statistical analysis of its performance under mixture models. For isotropic Gaussian mixture models, we show spectral clustering is optimal. For sub-Gaussian mixture models, we derive exponential error rates for spectral clustering. To establish these results, we develop a new spectral perturbation analysis for singular subspaces.</p><p>Presenter: Dr. Anderson Ye Zhang is an Assistant Professor in the Department of Statistics and Data Science at the University of Pennsylvania. Before joining Penn, he was a William H. Kruskal Instructor in the Department of Statistics at the University of Chicago. He completed his Ph.D. in Statistics and Data Science at Yale University. His research interests include spectral analysis, network analysis, clustering, ranking, and synchronization.</p>

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Spectral Clustering

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