Eigenspectrum Regularization on Grassmann Discriminant Analysis With Image Set Classification

Set-based image classification has become popular in recent years since it can provide a relatively large amount of within-set information that benefits classification. Grassmann Discriminant Analysis (GDA) models image sets as points (subspaces) on a Grassmann manifold and then explicitly maps them to a higher-dimensional Hilbert space, where Euclidean geometry applies, for Linear Discriminant Analysis (LDA). However, due to the noise disturbance and finite number of training samples in practice, the conventional problems of LDA, such as the singularity of the within-class scatter matrix and the instability of its inverse, also appear with GDA, which result in recognition performance deterioration. Inspired by eigenspectrum regularization techniques, we propose an eigenspectrum Regularized GDA (RGDA) method to alleviate the conventional problems of GDA in Grassmannian space. Moreover, we implement it with the graph embedded framework, three different eigenspectrum regularization models are incorporated into the proposed approach respectively. Extensive experimental results on set-based face recognition and object categorization tasks have confirmed the effectiveness of our approaches.