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Clustering by Sum of Norms: Stochastic Incremental Algorithm, Convergence and Cluster Recovery
Ashkan Panahi · Devdatt Dubhashi · Fredrik D Johansson · Chiranjib Bhattacharya

Wed Aug 09 01:30 AM -- 05:00 AM (PDT) @ Gallery #10

Standard clustering methods such as K-means, Gaussian mixture models, and hierarchical clustering are beset by local minima, which are sometimes drastically suboptimal. Moreover the number of clusters K must be known in advance. The recently introduced the sum-of-norms (SON) or Clusterpath convex relaxation of k-means and hierarchical clustering shrinks cluster centroids toward one another and ensure a unique global minimizer. We give a scalable stochastic incremental algorithm based on proximal iterations to solve the SON problem with convergence guarantees. We also show that the algorithm recovers clusters under quite general conditions which have a similar form to the unifying proximity condition introduced in the approximation algorithms community (that covers paradigm cases such as Gaussian mixtures and planted partition models). We give experimental results to confirm that our algorithm scales much better than previous methods while producing clusters of comparable quality.

Author Information

Ashkan Panahi (NC state university)
Devdatt Dubhashi (Chalmers University)
Fredrik D Johansson (MIT)
Chiranjib Bhattacharya (Indian Institute of Science)

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