Computing Large-Scale Matrix and Tensor Decomposition With Structured Factors: A Unified Nonconvex Optimization Perspective
Xiao Fu, Nico Vervliet, Lieven De Lathauwer, Kejun Huang, Nicolas Gillis
Abstract
During the past 20 years, low-rank tensor and matrix decomposition models (LRDMs) have become indispensable tools for signal processing, machine learning, and data science. LRDMs represent high-dimensional, multiaspect, and multimodal data using low-dimensional latent factors in a succinct and parsimonious way. LRDMs can serve a variety of purposes, e.g., data embedding (dimensionality reduction), denoising, latent variable analysis, model parameter estimation, and big data compression; see [1]-[5] for surveys of applications.
Topics & Concepts
Coordinate descentMatrix decompositionFactorizationComputer scienceMathematical optimizationOptimization problemTheoretical computer scienceTensor (intrinsic definition)Dixon's factorization methodNon-negative matrix factorizationAlgorithmIncomplete LU factorizationMathematicsPure mathematicsQuantum mechanicsEigenvalues and eigenvectorsPhysicsTensor decomposition and applicationsSparse and Compressive Sensing TechniquesMatrix Theory and Algorithms