Sparse nonnegative matrix underapproximation and its application to hyperspectral image analysis

Nicolas Gillis, Robert J. Plemmons

Abstract: Dimensionality reduction techniques such as principal component analysis (PCA) are powerful tools for the analysis of high-dimensional data. In hyperspectral image analysis, nonnegativity of the data can be taken into account, leading to an additive linear model called nonnegative matrix factorization (NMF), which improves interpretability of the decomposition. Recently, another technique based on under-approximations (NMU) has been introduced, which allows the extraction of features in a recursive way, such as PCA, but preserving nonnegativity, such as NMF. However, for difficult hyperspectral datasets, even NMU can mix some materials together, and is therefore not able to separate of all materials properly for accurate target identification. In this paper we introduce sparse NMU by adding a sparsity constraint on the abundance matrix and use it to extract materials individually in a more efficient way than NMU. This is experimentally demonstrated on a HYDICE image of the San Diego airport.