  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.
