Bayesian Nonnegative Matrix Factorization with Volume Prior for Unmixing of Hyperspectral Images

Morten Arngren, Mikkel N. Schmidt and Jan Larsen

Abstract: In hyperspectral image analysis the objective is to unmix a set of acquired pixels into pure spectral signatures (endmembers)and corresponding fractional abundances. Since Lee and Seung presented Non-negative Matrix Factorization (NMF) with multiplicative updates, the NMF methods has received a lot of attention for the unmixing proces.

In addition to the non-negativity of the data many Bayesian NMF methods include additional sparsity priors, which encourage pure spectra endmembers on the fractional abundances. In food applications however pure spectra are rarely observed and a sparsity prior is hence not optimal. Due to the natural non-negativity and the fractional abundances summing to one (additivity constraint) the pixels are ideally structured in a multidimensional simplex form. Hence incorporating a prior based on the volume of the simplex seems optimal.

In this context a Bayesian framework employing a minimum simplex volume constraint for the NMF algorithm is presented, where the posterior distribution is numerically sampled from using a Gibbs sampling procedure. Hyperspectral data both synthetically generated and real acquired images of wheat kernels are used as the data set. Applying our method will show how the Bayesian approach provide high unmixing performance while rivaling current volume regulated NMF methods.

Cite
Morten Arngren, Mikkel N. Schmidt and Jan Larsen, Bayesian nonnegative matrix factorization with volume prior for unmixing of hyperspectral images, Machine Learning for Signal Processing, IEEE Workshop on (MLSP), 2009

Bibtex
@inproceedings{arngren09mlsp,
title        = "Bayesian nonnegative matrix factorization with volume prior for unmixing of hyperspectral images",
author    = "Morten Arngren and Mikkel N. Schmidt and Jan larsen",
booktitle = "Machine Learning for Signal Processing, IEEE Workshop on (MLSP)",
month    = "Sep",
year       = "2009"
}