This paper explores the use of SVD-based column subset selection (SVDSS) algorithms for endmember extraction in hyperspectral unmixing. We are using a version of the column subset selection problem that selects the subset of columns that better predicts the remaining columns in the matrix. It has been shown that this problem is related to the problem of selecting a maximum volume sub-matrix of a matrix. This is related to the problem of finding the spectral signatures from the image that provide the simplex of maximum volume that can be inscribed within the hyperspectral data set, which is the base of some endmember extraction algorithms like N-FINDR. In this paper, we present a numerical comparison between SVDSS and several endmember extraction algorithms such as N-FINDR, PPI and VCA. Simulated and real hyperspectral imagery from the HYDICE Urban Scene are used in numerical experiments to determine which algorithm extracts the endmembers with the highest simplex volume. Results show that SVDSS outperforms other approaches for endmember extraction.

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Miguel Velez-Reyes and Maher Aldeghlawi, "Using a column subset selection method for endmember extraction in hyperspectral unmixing," Proc. SPIE 10644, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIV, 106440A (Presented at SPIE Defense + Security: April 17, 2018; Published: 16 May 2018); https://doi.org/10.1117/12.2309867.