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Although the sparse multinomial logistic regression (SMLR) has provided auseful tool for sparse classification, it suffers from inefficacy in dealingwith high dimensional features and manually set initial regressor values. Thishas significantly constrained its applications for hyperspectral image (HSI)classification. In order to tackle these two drawbacks, an extreme sparsemultinomial logistic regression (ESMLR) is proposed for effectiveclassification of HSI. First, the HSI dataset is projected to a new featurespace with randomly generated weight and bias. Second, an optimization model isestablished by the Lagrange multiplier method and the dual principle toautomatically determine a good initial regressor for SMLR via minimizing thetraining error and the regressor value. Furthermore, the extendedmulti-attribute profiles (EMAPs) are utilized for extracting both the spectraland spatial features. A combinational linear multiple features learning (MFL)method is proposed to further enhance the features extracted by ESMLR andEMAPs. Finally, the logistic regression via the variable splitting and theaugmented Lagrangian (LORSAL) is adopted in the proposed framework for reducingthe computational time. Experiments are conducted on two well-known HSIdatasets, namely the Indian Pines dataset and the Pavia University dataset,which have shown the fast and robust performance of the proposed ESMLRframework.

Extreme Sparse Multinomial Logistic Regression: A Fast and Robust Framework for Hyperspectral Image Classification