Range space super spherical cap discriminant analysis

To overcome the separability problem caused by sample fusion in the process of sample vectors normalization, this paper presents a unit super spherical cap discriminant analysis in the range space of the total scatter matrix. It is proved that the unit super spherical cap model can maintain the topological invariability of the structural characteristics of sample vectors. Furthermore, a sufficient condition is derived for improving the separability of sample data under the proposed model. The proposed algorithm projects sample data to the range space of the total scatter matrix, and then adds one dimension to each sample of the range space and nonlinearly maps it on the surface of the unit super spherical cap. We put forth a new classifier called the “spherical inner product nearest neighbor classifier'' for the transformed data. It is designed for the deviation problem of the discriminant vector and the separability problem caused by sample vectors normalization when different sub-classes are located in different low-dimensional subspaces or manifolds. Experimental results on different databases show that our method outperforms other methods in terms of recognition accuracy and numerical stability.