A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization

Supplementary Materials to “A Non-Euclidean Gradient Descent Framework for Non-Convex Matrix Factorization”

A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem.  At each step of ALS algorithms two convex least square problems should be solved, which causes high com...

Supervised non-negative matrix factorization for audio source separation

Source separation is a widely studied problems in signal processing. Despite the permanent progress reported in the literature it is still considered a significant challenge. This chapter first reviews the use of non-negative matrix factorization (NMF) algorithms for solving source separation problems, and proposes a new way for the supervised training in NMF. Matrix factorization methods have ...

Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation From Undersampled Data

Subspace learning and matrix factorization problems have a great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in a variety of contexts it has been observed that solving the non-convex problem directly is not only efficient but reliably accurate. We discuss convergence...

Iterative Weighted Non-smooth Non-negative Matrix Factorization for Face Recognition

Non-negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost fun...