A Convex Model for Matrix Factorization and Dimensionality Reduction on Physical Space and its Application to Blind Hyperspectral Unmixing

Abstract

A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is introduced. We restrict the columns of the dictionary matrix A to coincide with certain columns of X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. As an example, we show applications of the proposed framework on hyperspectral endmember and abundances identification.