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

Background/foreground separation is the first step in video surveillance system to detect
moving objects. Recent research on problem formulations based on decomposition into low …

In this paper we develop a new framework that captures the common landscape underlying
the common non-convex low-rank matrix problems including matrix sensing, matrix …

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

Learning graphs from data automatically have shown encouraging performance on
clustering and semisupervised learning tasks. However, real data are often corrupted, which …

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 …

Can we recover a complex signal from its Fourier magnitudes? More generally, given a set
of m measurements, y_k=\left| a _k^* x\right| yk= ak∗ x for k= 1, ..., mk= 1,…, m, is it possible …

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 …

Recent years have seen a flurry of activities in designing provably efficient nonconvex
optimization procedures for solving statistical estimation problems. For various problems like …

Matrix factorization is a popular approach for large-scale matrix completion. The optimization
formulation based on matrix factorization, even with huge size, can be solved very efficiently …