From a discussion on the Advanced Matrix Factorization group, Adrien Todeschini let us know of his recent paper on another heuristics to the Rank functional:
Our paper gives another concave penalty surrogating the rank.A. Todeschini, F. Caron, M. Chavent. Probabilistic Low Rank Matrix Completion with Adaptive Spectral Regularization Algorithms. Neural Information Processing Systems (NIPS'2013), Lake Tahoe, USA, 2013.It is available at my webpage with a Matlab code:Adrien.
Thanks Adrien !
Probabilistic Low-Rank Matrix Completion with Adaptive Spectral Regularization Algorithms by Adrien Todeschini, François Caron, Marie Chavent
We propose a novel class of algorithms for low rank matrix completion. Our approach builds on novel penalty functions on the singular values of the low rank matrix. By exploiting a mixture model representation of this penalty, we show that a suitably chosen set of latent variables enables to derive an Expectation-Maximization algorithm to obtain a Maximum A Posteriori estimate of the completed low rank matrix. The resulting algorithm is an iterative soft-thresholded algorithm which iteratively adapts the shrinkage coefficients associated to the singular values. The algorithm is simple to implement and can scale to large matrices. We provide numerical comparisons between our approach and recent alternatives showing the interest of the proposed approach for low rank matrix completion.
The implementation is here.
It has been added to Advanced Matrix Factorization Jungle page.
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