Although 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.Keywords: hyperspectral image (HSI) classification; sparse multinomial logistic regression (SMLR); extreme sparse multinomial logistic regression (ESMLR); extended multi-attribute profiles (EMAPs); linear multiple features learning (MFL); Lagrange multiplier

Although extreme learning machine (ELM) has been successfully applied to a number of pattern recognition problems, it fails to provide sufficient good results in hyperspectral image (HSI) classification due to two main drawbacks. The first is due to the random weights and bias of ELM, which may lead to ill-posed problems. The second is the lack of spatial information for classification. To tackle these two problems, in this paper, we propose a new framework for ELM based spectral-spatial classification of HSI, where probabilistic modelling with sparse representation and weighted composite features (WCF) are employed respectively to derive the optimized output weights and extract spatial features. First, the ELM is represented as a concave logarithmic likelihood function under statistical modelling using the maximum a posteriori (MAP). Second, the sparse representation is applied to the Laplacian prior to efficiently determine a logarithmic posterior with a unique maximum in order to solve the ill-posed problem of ELM. The variable splitting and the augmented Lagrangian are subsequently used to further reduce the computation complexity of the proposed algorithm and it has been proven a more efficient method for speed improvement. Third, the spatial information is extracted using the weighted composite features (WCFs) to construct the spectral-spatial classification framework. In addition, the lower bound of the proposed method is derived by a rigorous mathematical proof. Experimental results on two publicly available HSI data sets demonstrate that the proposed methodology outperforms ELM and a number of state-of-the-art approaches.Index Terms-hyperspectral image (HSI), spectral-spatial classification, extreme learning machine (ELM), maximum a posterior (MAP), sparse representation, Laplacian prior, variable splitting, augmented Lagrangian.

Index ELM MSELM LBMSELM4 LBMSELM8 OA 85.90±1.55 86.99±1.52 89.41±1.26 90.03±1.05 AA 92.62±0.70 93.58±0.69 95.05±0.50 95.34±0.46 k 84.34±1.70 85.54±1.67 88.22±1.39 88.91±1.16

Due to its excellent performance in terms of fast implementation, strong generalization capability and straightforward solution, extreme learning machine (ELM) has attracted increasingly attentions in pattern recognition such as face recognition and hyperspectral image (HSI) classification. However, the performance of ELM for HSI classification remains a challenging problem especially in effective extraction of the featured information from the massive volume of data. To this end, we propose in this paper a new method to combine convolutional neural network (CNN) with ELM (CNN-ELM) for HSI classification. As CNN has been successfully applied for feature extraction in different applications, the combined CNN-ELM approach aims to take advantages of these two techniques for improved classification of HSI. By preserving the spatial features whilst reconstructing the spectral features of HSI, the proposed CNN-ELM method can significantly improve the accuracy of HSI classification without increasing the computational complexity. Comprehensive experiments using three publicly available HSI datasets, Pavia University, Pavia center, and Salinas have fully validated the improved performance of the proposed method when benchmarking with several state-of-the-art approaches.

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