eduzhai > Applied Sciences > Engineering >

Computing Large-Scale Matrix and Tensor Decomposition with Structured Factors A Unified Nonconvex Optimization Perspective

  • Save

... pages left unread,continue reading

Document pages: 15 pages

Abstract: The proposed article aims at offering a comprehensive tutorial for thecomputational aspects of structured matrix and tensor factorization. Unlikeexisting tutorials that mainly focus on { it algorithmic procedures} for asmall set of problems, e.g., nonnegativity or sparsity-constrainedfactorization, we take a { it top-down} approach: we start with generaloptimization theory (e.g., inexact and accelerated block coordinate descent,stochastic optimization, and Gauss-Newton methods) that covers a wide range offactorization problems with diverse constraints and regularization terms ofengineering interest. Then, we go `under the hood to showcase specificalgorithm design under these introduced principles. We pay a particularattention to recent algorithmic developments in structured tensor and matrixfactorization (e.g., random sketching and adaptive step size based stochasticoptimization and structure-exploiting second-order algorithms), which are thestate of the art---yet much less touched upon in the literature compared to{ it block coordinate descent} (BCD)-based methods. We expect that the articleto have an educational values in the field of structured factorization and hopeto stimulate more research in this important and exciting direction.

Please select stars to rate!


0 comments Sign in to leave a comment.

    Data loading, please wait...