Related papers: Nonconvex Matrix Completion with Linearly Paramete…

We study the problem of robust matrix completion (RMC), where the partially observed entries of an underlying low-rank matrix is corrupted by sparse noise. Existing analysis of the non-convex methods for this problem either requires the…

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical…

We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…

In this paper, we present a unified analysis of matrix completion under general low-dimensional structural constraints induced by {\em any} norm regularization. We consider two estimators for the general problem of structured matrix…

The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a…

This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…

Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…

In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…

Matrix completion refers to completing a low-rank matrix from a few observed elements of its entries and has been known as one of the significant and widely-used problems in recent years. The required number of observations for exact…

Given a collection of data points, non-negative matrix factorization (NMF) suggests to express them as convex combinations of a small set of `archetypes' with non-negative entries. This decomposition is unique only if the true archetypes…

In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…

Matrix Factorization plays an important role in machine learning such as Non-negative Matrix Factorization, Principal Component Analysis, Dictionary Learning, etc. However, most of the studies aim to minimize the loss by measuring the…

Efficiently representing real world data in a succinct and parsimonious manner is of central importance in many fields. We present a generalized greedy pursuit framework, allowing us to efficiently solve structured matrix factorization…

Factorization-based gradient descent is a scalable and efficient algorithm for solving low-rank matrix completion. Recent progress in structured non-convex optimization has offered global convergence guarantees for gradient descent under…

Given a known matrix that is the sum of a low rank matrix and a masked sparse matrix, we wish to recover both the low rank component and the sparse component. The sparse matrix is masked in the sense that a linear transformation has been…

Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…

Nonnegative matrix factorization (NMF) has become a very popular technique in machine learning because it automatically extracts meaningful features through a sparse and part-based representation. However, NMF has the drawback of being…

Matrix completion is a well-studied problem with many machine learning applications. In practice, the problem is often solved by non-convex optimization algorithms. However, the current theoretical analysis for non-convex algorithms relies…

On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…