Improved Quaternion Discriminant Analysis for Feature Extraction and Classification of Hyperspectral Image

Real domain discriminant analysis (RDA) cannot solve the crosstalk of strong correlation between adjacent spectral bands, and also causes spectral information loss of hyperspectral image (HSI). As a result, the effect of feature extraction is not ideal. Besides, in the case of small samples, using quaternion discriminant analysis (QDA) based on Cos-sin decomposition, the matrix obtained by the first orthogonal trigonometric decomposition is not a diagonal matrix, that makes the projection axis not optimal. To solve these problems, first, a QDA method based on stable quaternion cos-sin decomposition (QDASG) is proposed to solve the small sample problem. Second, this article theoretically analyzes that when the number of projection axes in QDASG is smaller than that in traditional DA methods, the discriminant formula can achieve optimal results, and verifies this conclusion through experiments. Then, according to the number of training samples, the implementation process of QDA is discussed in two cases. Finally, spatial filtering is used to extract spatial information, and the distance quotient formula between classes is proposed as the standard for selecting the the optimal number of stacking layers for the filter. Experimental results show that this method is effective compared with deep learning method and and other traditional machine learning methods, especially in the case of small samples.