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

The extreme learning machine (ELM) is a novel and effective machine learning method. It has been successfully applied to many pattern recognition problems. However, the classification results are not good enough when it is applied to the hyperspectral image (HSI) classification. This is because the ELM suffers from some drawbacks. One is the randomness of input weights and bias can result in ill-posed problems, then this would result in the optimal output weight of ELM can not obtain. Another one is this method fails to extract the spatial information. To overcome these two difficulties, this paper proposes a new framework for applying the ELM to perform the hyperspectral image (HSI) classification. First, the ELM is represented by a probabilistic model under the maximum a posteriori (MAP). Then it was represented by a concave logarithmic likelihood function. Second, the sparse representation is adopted to the Laplacian prior in order to find a logarithmic posterior with a unique maximum. This can improve the speed of the proposed algorithm. Besides, the variable splitting and the augmented Lagrangian are subsequently used. It can also significantly reduce the computation complexity of the proposed algorithm. Third, the spatial information is utilized to construct the spectral-spatial framework for performing the HSI classification based on the weighted composite features (WCFs) method. This can further improve the performance of the proposed algorithms. The lower bound of the proposed methods is also derived by a rigorous mathematical proof. Experimental results on the real HSI data sets such as the Indian Pines data set and the Pavia University data set demonstrate that the proposed approach outperforms many state of the art methods.