  Although the sparse multinomial logistic regression (SMLR) has provided a
useful tool for sparse classification, it suffers from inefficacy in dealing
with high dimensional features and manually set initial regressor values. This
has significantly constrained its applications for hyperspectral image (HSI)
classification. In order to tackle these two drawbacks, an extreme sparse
multinomial logistic regression (ESMLR) is proposed for effective
classification of HSI. First, the HSI dataset is projected to a new feature
space with randomly generated weight and bias. Second, an optimization model is
established by the Lagrange multiplier method and the dual principle to
automatically determine a good initial regressor for SMLR via minimizing the
training error and the regressor value. Furthermore, the extended
multi-attribute profiles (EMAPs) are utilized for extracting both the spectral
and spatial features. A combinational linear multiple features learning (MFL)
method is proposed to further enhance the features extracted by ESMLR and
EMAPs. Finally, the logistic regression via the variable splitting and the
augmented Lagrangian (LORSAL) is adopted in the proposed framework for reducing
the computational time. Experiments are conducted on two well-known HSI
datasets, namely the Indian Pines dataset and the Pavia University dataset,
which have shown the fast and robust performance of the proposed ESMLR
framework.
