Sparse nonnegative matrix underapproximation and its application to hyperspectral image analysis

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 underapproximations (NMU) has been introduced, which allows the extraction of features in a recursive way, such as PCA, but preserving nonnegativity, such as NMF. Moreover, in some situations, NMU is able to detect automatically the materials present in the scene being imaged. However, for difficult hyperspectral datasets, NMU can mix some materials together, and is therefore not able to separate all of them properly. 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 the HYDICE images of the San Diego airport and the Urban dataset.