A new kernel fuzzy based feature extraction method using attraction points

This paper aims at introducing a novel supervised feature extraction method to be used in small sample size situations. The proposed approach considers the class membership of samples and exploits a nonlinear mapping in order to extract the relevant features and to mitigate the Hughes phenomenon. The proposed objective function is composed of three different terms, namely, attraction function, repulsion function, and the between-feature scatter matrix, where the last term increases the difference between extracted features. Subsequently, the attraction function and the repulsion function are redefined by incorporating the membership degrees of samples. Finally, the proposed method is extended using the kernel trick to capture the inherent nonlinearity of the original data. To evaluate the accuracy of the proposed feature extraction method, four remote sensing images are used in our experiments. The experiments indicate that the proposed feature extraction method is anappropriate choice for classification of hyperspectral images using limited training samples.