An MRF-based kernel method for nonlinear feature extraction

Nonlinear kernel-based feature extraction algorithms have recently been proposed to alleviate the loss of class discrimination after feature extraction. When considering image classification, a kernel function may not be sufficiently effective if it depends only on an information resource from the Euclidean distance in the original feature space. This study presents an extended radial basis kernel function that integrates multiple discriminative information resources, including the Euclidean distance, spatial context, and class membership. The concepts related to Markov random fields (MRFs) are exploited to model the spatial context information existing in the image. Mutual closeness in class membership is defined as a similarity measure with respect to classification. Any dissimilarity from the additional information resources will improve the discrimination between two samples that are only a short Euclidean distance apart in the feature space. The proposed kernel function is used for feature extraction through linear discriminant analysis (LDA) and principal component analysis (PCA). Experiments with synthetic and natural images show the effectiveness of the proposed kernel function with application to image classification. (C) 2009 Elsevier B.V. All rights reserved.