The Hidden Convexity of Spectral Clustering

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)