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Low-rank matrix reconstruction and clustering via approximate message passing
Ryosuke Matsushita · Toshiyuki Tanaka

Fri Dec 06 07:00 PM -- 11:59 PM (PST) @ Harrah's Special Events Center, 2nd Floor

We study the problem of reconstructing low-rank matrices from their noisy observations. We formulate the problem in the Bayesian framework, which allows us to exploit structural properties of matrices in addition to low-rankedness, such as sparsity. We propose an efficient approximate message passing algorithm, derived from the belief propagation algorithm, to perform the Bayesian inference for matrix reconstruction. We have also successfully applied the proposed algorithm to a clustering problem, by formulating the problem of clustering as a low-rank matrix reconstruction problem with an additional structural property. Numerical experiments show that the proposed algorithm outperforms Lloyd's K-means algorithm.

Author Information

Ryosuke Matsushita (NTT DATA Mathematical Systems Inc.)
Toshiyuki Tanaka (Kyoto University)

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