Dimension reduction (DR) is an efficient and effective preprocessing step of hyperspectral images (HSIs) classification. Graph embedding is a frequently used model for DR, which preserves some geometric or statistical properties of original data set. The embedding using simple graph only considers the relationship between two data points, while in real-world application, the complex relationship between several data points is more important. To overcome this problem, we present a linear semi-supervised DR method based on hypergraph embedding (SHGE) which is an improvement of semi-supervised graph learning (SEGL). The proposed SHGE method aims to find a projection matrix through building a semi-supervised hypergraph which can preserve the complex relationship of the data and the class discrimination for DR. Experimental results demonstrate that our method achieves better performance than some existing DR methods for HSIs classification and is time saving compared with the existed method SEGL which used simple graph.

In this letter, we propose a novel supervised dimensionality reduction (DR) method termed linear discriminant analysis based on kernel-based possibilistic c-means (LDA-KPCM) for hyperspectral images (HSIs). The basic idea of this method is to use KPCM algorithm to generate different weights for different samples so that the newly-proposed method can learn the optimal transformation directions according to the relative importance of samples. The weights generated by KPCM are relatively higher for important samples but relatively lower for outliers. The experimental results on two HSI benchmark data sets demonstrate that LDA-KPCM can achieve better performance than the other state-of-the-art DR methods.