Angular Discriminant Analysis for Hyperspectral Image Classification

Hyperspectral imagery consists of hundreds or thousands of densely sampled spectral bands. The resulting spectral information can provide unique spectral “signatures” of different materials present in a scene, which makes hyperspectral imagery especially suitable for classification problems. To fully and effectively exploit discriminative information in such images, dimensionality reduction is typically undertaken as a preprocessing before classification. Different from traditional dimensionality reduction methods, we propose angular discriminant analysis (ADA), which seeks to find a subspace that best separates classes in an angular sense-specifically, one that minimizes the ratio of between-class inner product to within-class inner product of data samples on a unit hypersphere in the resulting subspace. In this paper, we also propose local angular discriminant analysis (LADA), which preserves the locality of data in the projected space through an affinity matrix, while angularly separating different class samples. ADA and LADA are particularly useful for classifiers that rely on angular distance, such as the cosine angle distance based nearest neighbor-based classifier and sparse representation-based classifier, in which the sparse representation coefficients are learned via orthogonal matching pursuit. We also show that ADA and LADA can be easily extended to their kernelized variants by invoking the kernel trick. Experimental results based on benchmarking hyperspectral datasets show that our proposed methods are greatly beneficial as a dimensionality reduction preprocessing to the popular classifiers.