The Hidden Convexity of Spectral Clustering
This provides a novel optimization approach for spectral clustering, a standard data analysis method, but appears incremental as it builds on existing techniques like Independent Component Analysis.
The paper tackles the problem of multiway spectral clustering by proposing a new class of algorithms based on optimizing a contrast function over the unit sphere, showing encouraging experimental results on real and simulated data.
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by certain Independent Component Analysis techniques, are simple, easy to implement and efficient. Geometrically, the proposed algorithms can be interpreted as hidden basis recovery by means of function optimization. We give a complete characterization of the contrast functions admissible for provable basis recovery. We show how these conditions can be interpreted as a "hidden convexity" of our optimization problem on the sphere; interestingly, we use efficient convex maximization rather than the more common convex minimization. We also show encouraging experimental results on real and simulated data.