Bilayer Elastic Net Regression Model for Supervised Spectral-Spatial Hyperspectral Image Classification

Abstract

In this paper, we propose a novel bilayer elastic net (ELN <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) regression model for hyperspectral image (HSI) classification, exploiting the spectral-spatial information. The proposed model is designed to address the special problematic characteristics of HSI, namely, high dimensionality of hyperspectral pixels, limited labeled samples, and spatial variability of spectral signatures. To alleviate these problems, by exploiting the spectral and spatial information, the proposed model features in the following two components: 1) spectral-only elastic net regression in the first layer and 2) spatial contextual driven elastic net regularization in the second layer. In the first layer, to encourage a grouping effect and feature selection, we use multinomial logistic regression (MLR) model penalized by the ELN to optimize the spectral-only classifier parameters for the initial HSI classification. In the second layer, spatial Markov-random-field-based gradient profiles are incorporated into the ELN penalty over the hidden marginal probability of the posterior distribution to encourage the spatial smoothness. Furthermore, the true labels of training samples are fixed as an additional constraint in the second-layer optimizing model to further improve the classification accuracy. Moreover, an effective algorithm named as ELN <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> _RegMLR is developed by coupling the path-wise coordinate descent algorithm, and variable splitting and augmented Lagrangian approach to solve the proposed model. Experimental results on several popular datasets show that the proposed method outperforms many state-of the-art classifiers in terms of the overall accuracy, average accuracy, statistic coefficient kappa, and visual classification map quality.