Substantial progress has been made recently on developing provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

Industrial process data are usually mixed with missing data and outliers which can greatly
affect the statistical explanation abilities for traditional data-driven modeling methods. In this …

Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

In this monograph, we have attempted to summarize the actively developing field of
statistical learning with sparsity. A sparse statistical model is one having only a small …

Recently, a growing number of biological research and scientific experiments have
demonstrated that microRNA (miRNA) affects the development of human complex diseases …

Random matrices now play a role in many areas of theoretical, applied, and computational
mathematics. Therefore, it is desirable to have tools for studying random matrices that are …

Principal component analysis (PCA) is one of the most widely used dimension reduction
techniques. A related easier problem is termed subspace learning or subspace estimation …

In this paper, we present a spatial spectral hyperspectral image (HSI) mixed-noise removal
method named total variation (TV)-regularized low-rank matrix factorization (LRTV). In …

Robust principal component analysis (RPCA) via decomposition into low-rank plus sparse
matrices offers a powerful framework for a large variety of applications such as image …

This monograph is about a class of optimization algorithms called proximal algorithms. Much
like Newton's method is a standard tool for solving unconstrained smooth optimization …