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

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.