Sequential Dimensionality Reduction for Extracting Localized Features

TL;DR

This paper introduces a spatially-aware variant of nonnegative matrix underapproximation (NMU) that enhances image feature extraction by promoting localized, sparse features, outperforming existing methods on various image datasets.

Contribution

A novel NMU variant that incorporates spatial information to improve localization and sparsity of features in image analysis.

Findings

Outperforms state-of-the-art techniques on synthetic images

Effective on facial image datasets

Excels in hyperspectral image analysis

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.