Volume regularized non-negative matrix factorizations

摘要

This work considers two volume regularized non-negative matrix factorization (NMF) problems that decompose a nonnegative matrix X into the product of two nonnegative matrices W and H with a regularization on the volume of the convex hull spanned by the columns of W. This regularizer takes two forms: the determinant (det) and logarithm of the determinant (logdet) of the Gramian of W. In this paper, we explore the structure of these problems and present several algorithms, including a new algorithm based on an eigenvalue upper bound of the logdet function. Experimental results on synthetic data show that (i) the new algorithm is competitive with the standard Taylor bound, and (ii) the logdet regularizer works better than the det regularizer. We also illustrate the applicability of the new algorithm on the San Diego airport hyperspectral image.