A robust geometric mean-based subspace discriminant analysis feature extraction approach for image set classification

Discriminant analysis technique is an important research topic in image set classification because it can extract discriminative features. However, most existing discriminant analysis methods almost fail to work for feature extraction of data because there is only a small amount of valid discriminant information. The main weakness of most existing discriminant analysis models is that the class mean vector is constructed by using class sample average. That is not sufficient to provide an accurate estimation of the class mean. In this paper, we proposed a robust geometric mean-based subspace discriminant analysis feature extraction method for image set classification. This method is a combination of geometric mean vector, subspace and covariance matrix to jointly represent an image set because they are contain different discriminative information. The above three representation ways lie on different spaces. To reduce the dissimilarity between the heterogeneous spaces, a robust geometric mean-based subspace discriminant analysis learning (GMSDA) framework is developed, which includes three steps operation. At first, uses a new geometric mean vector to construct geometric between-class scatter matrix (S-gb) and geometric within-class scatter matrix (S-gw) instead of traditional mean vector of many methods. Secondly, maximizes the geometric between-class scatter matrix to increase the difference between extracted features. Finally, maximizes the subspace between-class scatter (S-gb(S)) and minimizes the subspace within-class scatter (S-gw(S)) simultaneously in the subspace of original space. Experiments on five datasets illustrate that our proposed GMSDA method works the best in small sample size situation by using maximum likelihood classification (MLC).