  Linear dimensionality reduction techniques are powerful tools for image
analysis as they allow the identification of important features in a data set.
In particular, nonnegative matrix factorization (NMF) has become very popular
as it is able to extract sparse, localized and easily interpretable features by
imposing an additive combination of nonnegative basis elements. Nonnegative
matrix underapproximation (NMU) is a closely related technique that has the
advantage to identify features sequentially. In this paper, we propose a
variant of NMU that is particularly well suited for image analysis as it
incorporates the spatial information, that is, it takes into account the fact
that neighboring pixels are more likely to be contained in the same features,
and favors the extraction of localized features by looking for sparse basis
elements. We show that our new approach competes favorably with comparable
state-of-the-art techniques on synthetic, facial and hyperspectral image data
sets.
