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In this work, we consider nonnegative matrix factorization (NMF) with aregularization that promotes small volume of the convex hull spanned by thebasis matrix. We present highly efficient algorithms for three different volumeregularizers, and compare them on endmember recovery in hyperspectral unmixing.The NMF algorithms developed in this work are shown to outperform thestate-of-the-art volume-regularized NMF methods, and produce meaningfuldecompositions on real-world hyperspectral images in situations whereendmembers are highly mixed (no pure pixels). Furthermore, our extensivenumerical experiments show that when the data is highly separable, meaning thatthere are data points close to the true endmembers, and there are a fewendmembers, the regularizer based on the determinant of the Gramian producesthe best results in most cases. For data that is less separable and/or containsmore endmembers, the regularizer based on the logarithm of the determinant ofthe Gramian performs best in general.

Algorithms and Comparisons of Non-negative Matrix Factorization with Volume Regularization for Hyperspectral Unmixing