Hyperspectral Image Classification Based on a Fast Bregman Sparse Multinomial Logistic Regression Algorithm

The Sparse Multinomial Logistic Regression (SMLR) method introduced in (Krishnapuram, 2005) is among the state-of-the-art in supervised learning. However its application to large datasets, such as hyperspectral imagery is still a rather challenging task from the computational point of view, sometimes even impossible to perform. In this paper, the Bregman iteration-based SMLR method (Bregman-SMLR) recently introduced in (Bioucas-Dias, 2008) is applied to hyperspectral data classification problems. The Bregman method allows replacing a difficult, non-smooth convex problem with a sequence of quadratic plus diagonal l2-l1 problems which are very easy to solve (Bioucas-Dias, 2008). Compared with the SMLR algorithm, the reduction of computational complexity is on the order of d(m-1) 3 (d is the number of features, and m is the number of classes.) The effectiveness of the proposed method is evaluated with simulated data sets and a real AVIRIS image. Results are presented and compared with others obtained by state-of-the-art supervised algorithms. * Corresponding author. This work was supported by Marie Curie Grant MEST-CT-2005-021175 from the European Commission.