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

A Fast and Robust Framework for Hyperspectral Image Classification Faxian Cao1, Zhijing Yang1*, Jinchang Ren2, Wing-Kuen Ling1 1 School of Information Engineering, Guangdong University of Technology, Guangzhou, 510006, China; [email protected]; [email protected]; [email protected] 2 Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, G1 1XW, UK; [email protected] * Correspondence: [email protected]; Tel.: +86-20-39322438 Abstract: 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.