Nonconvex Optimization Tools for Large-Scale Matrix and Tensor Decomposition with Structured Factors

15 Jun 2020Xiao FuNico VervlietLieven De LathauwerKejun HuangNicolas Gillis

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of problems, e.g., nonnegativity or sparsity-constrained factorization, we take a {\it top-down} approach: we start with general optimization theory (e.g., inexact and accelerated block coordinate descent, stochastic optimization, and Gauss-Newton methods) that covers a wide range of factorization problems with diverse constraints and regularization terms of engineering interest... (read more)

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