Ranking 2DLDA features based on fisher discriminance

In classification of matrix-variate data, two-directional linear discriminant analysis (2DLDA) methods extract discriminant features while preserving and utilizing the matrix structure. These methods provide computational efficiency and improved performance in small sample size problems. Existing 2DLDA solutions produce a feature matrix which is commonly vectorized for processing by conventional vector-based classifiers. However, the vectorization step requires a one-dimensional ranking of features according to their discriminance power. We first demonstrate that independent column-wise and row-wise ranking provided by 2DLDA is not sufficient for uniquely sorting the resulting features, and does not guarantee the selection of the most discriminant features. Then, we theoretically derive the desired global ranking score based on Fisher's criterion. The current results focus on non-iterative solutions, but future extensions to iterative 2DLDA variants are possible. Face recognition experiments using images from the PIE data set are used to demonstrate the theoretically proved improvements over the existing solutions.