Sparse Representation Based Augmented Multinomial Logistic Extreme Learning Machine with Weighted Composite Features for Spectral Spatial Hyperspectral Image Classification

Although extreme learning machine (ELM) has been successfully applied to a number of pattern recognition problems, it fails to pro-vide 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 op-timized 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 effi-ciently 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 compo-site 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.