Low-rank matrices play a fundamental role in modeling and computational methods for
signal processing and machine learning. In many applications where low-rank matrices …

Low-rank modeling plays a pivotal role in signal processing and machine learning, with
applications ranging from collaborative filtering, video surveillance, and medical imaging to …

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

We consider the recovery of a low rank real-valued matrix M given a subset of noisy discrete
(or quantized) measurements. Such problems arise in several applications such as …

Matrix completion is a basic machine learning problem that has wide applications,
especially in collaborative filtering and recommender systems. Simple non-convex …

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 …

Principal components analysis (PCA) is a well-known technique for approximating a tabular
data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets …

While many statistical models and methods are now available for network analysis,
resampling of network data remains a challenging problem. Cross-validation is a useful …

Consider the problem of estimating the entries of a large matrix, when the observed entries
are noisy versions of a small random fraction of the original entries. This problem has …

Optimization problems with rank constraints arise in many applications, including matrix
regression, structured PCA, matrix completion and matrix decomposition problems. An …