Sequential Dimensionality Reduction for Extracting Localized Features
This work addresses the need for improved feature extraction in image analysis, particularly for applications like facial and hyperspectral imaging, but it is incremental as it builds on existing nonnegative matrix underapproximation methods.
The paper tackled the problem of extracting localized features in image analysis by proposing a variant of nonnegative matrix underapproximation that incorporates spatial information to favor sparse, localized basis elements. The result showed that the new approach competes favorably with state-of-the-art techniques on synthetic, facial, and hyperspectral image datasets.
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.