Fast Projection-Based Methods for the Least Squares Nonnegative Matrix Approximation Problem

Fast Projection-Based Methods for the Least Squares Nonnegative Matrix Approximation Problem

Nonnegative matrix approximation (NNMA) is a popular matrix decomposition technique that has proven to be useful across a diverse variety of fields with applications ranging from document analysis and image processing to bioinformatics and signal processing. Over the years, several algorithms for NNMA have been proposed, e.g. Lee and Seung’s multiplicative updates, alternating least squares (AL...

Fast Newton-type Methods for the Least Squares Nonnegative Matrix Approximation Problem

Nonnegative Matrix Approximation is an effective matrix decomposition technique that has proven to be useful for a wide variety of applications ranging from document analysis and image processing to bioinformatics. There exist a few algorithms for nonnegative matrix approximation (NNMA), for example, Lee & Seung’s multiplicative updates, alternating least squares, and certain gradient descent b...

Random Projections for the Nonnegative Least-Squares Problem

Constrained least-squares regression problems, such as the Nonnegative Least Squares (NNLS) problem, where the variables are restricted to take only nonnegative values, often arise in applications. Motivated by the recent development of the fast Johnson-Lindestrauss transform, we present a fast random projection type algorithm for the NNLS problem. Our algorithm employs a randomized Hadamard tr...

Nonnegative least-squares image deblurring: improved gradient projection approaches

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the illposedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have b...

A Nonnegative Projection Based Algorithm for Low-Rank Nonnegative Matrix Approximation