Sequential dimensionality reduction for extracting localized features. (March 2017) - Casalino, Gabriella; Gillis, Nicolas
Abstract: 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. Abstract : Highlights: We propose a new nonnegative matrix underapproximation model for images. We design an algorithm that runs in linear time in the dimensions of the input matrix. This allows us to extract sequentially localized and spatially coherent features. We illustrate the effectiveness of our approach on a synthetic data set, facial and hyperspectral images. We show that it competes favorably with comparable state-of-the-art techniques.