A Novel Geometric Mean Feature Space Discriminant Analysis Method for Hyperspectral Image Feature Extraction

Hyperspectral image contains abundant spectral information with hundreds of spectral continuous bands that allow us to distinguish different classes with more details. However, the number of available training samples is limited and the high dimensionality of hyperspectral data increases the computational complexity and even also may degrade the classification accuracy. In addition, the bottom line is that only original spectral is difficult to well represent or reveal intrinsic geometry structure of the hyperspectral image. Thus, feature extraction is an important step before classification of high dimensional data. In this paper, we proposed a novel supervised feature extraction method that uses a new geometric mean vector to construct geometric between-class scatter matrix (\(S_b^G\)) and geometric within-class scatter matrix (\(S_w^G\)) instead of traditional mean vector of state-of-the-art methods. The geometric mean vector not only can reveal intrinsic geometry structure of the hyperspectral image, but also can improve the ability of learning nonlinear correlation features by maximum likelihood classification (MLC). The proposed method is called geometric mean feature space discriminant analysis (GmFSDA) that uses three measures to produce the extracted features. GmFSDA, at first, maximizes the geometric between-spectral scatter matrix to increase the difference between extracted features. In the second step of GmFSDA, maximizes the between-class scatter and minimizes the within-class scatter simultaneously. The experimental results on three real-world hyperspectral image datasets show the better performance of GmFSDA in comparison with other feature extraction methods in small sample size situation by using MLC.