The Hidden Convexity of Spectral Clustering

author: Mikhail Belkin, Department of Computer Science and Engineering, Ohio State University
published: Oct. 6, 2014,   recorded: December 2013,   views: 1900

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Spectral clustering has become a standard method for data analysis used in a broad range of applications. I will describe a new class of algorithms for multiway spectral clustering based on optimization of a certain class of functions after the spectral embedding. These algorithms can be interpreted geometrically as recovering a discrete weighted simplex. They have some resemblance to Independent Component Analysis and involve optimization of "contrast functions" over a sphere. However, in our case theoretical guarantees can be provided for a much broader class of functions satisfying a "hidden convexity" condition. The algorithms are straightforward to implement, efficient and are not initialization-dependent.

(with Luis Rademacher and James Voss)

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