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To enable low-rank tensor completion and factorization, this paper puts forth a novel tensor rank regularization method based on the ℓ1,2-norm of the tensor's parallel factor analysis (PARAFAC) factors. Specifically, for an N-way tensor, upon collecting the magnitudes of its rank-1 components in a vector, the proposed regularizer controls the tensor's rank by inducing sparsity in the vector of magnitudes...
We give an overview of recent developments in numerical optimization-based computation of tensor decompositions that have led to the release of Tensorlab 3.0 in March 2016 (www.tensorlab.net). By careful exploitation of tensor product structure in methods such as quasi-Newton and nonlinear least squares, good convergence is combined with fast computation. A modular approach extends the computation...
This paper considers decentralized consensus optimization problems where different summands of a global objective function are available at nodes of a network. The method of multipliers is well studied for centralized optimization; however, it is not applicable to decentralized optimization problems since the augmented Lagrangian is not decomposable. We propose ESOM as a decentralized primal-dual...
We describe a method for unmixing mixtures of ‘freely’ independent random variables in a manner analogous to the independent component analysis (ICA) based method for unmixing independent random variables from their additive mixture. Random matrices play the role of free random variables in this context so the method we develop, which we call Free component analysis (FCA), unmixes matrices from an...
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