Regularized generalized eigen-decomposition with applications to sparse supervised feature extraction and sparse discriminant analysis

• We propose a new technique called Regularized Generalized Eigen Decomposition (RGED).
• RGED solves generalized eigenvalue problems and obtains sparse solutions.
• It is easy and straightforward applying RGED to sparse discriminant analysis and feature extraction.
• An algorithm is developed to solve it with monotonically decreasing convergence.
• RGED has competitive classification performance comparing with other methods.

We propose a general technique for obtaining sparse solutions to generalized eigenvalue problems, and call it Regularized Generalized Eigen-Decomposition (RGED). For decades, Fisher׳s discriminant criterion has been applied in supervised feature extraction and discriminant analysis, and it is formulated as a generalized eigenvalue problem. Thus RGED can be applied to effectively extract sparse features and calculate sparse discriminant directions for all variants of Fisher discriminant criterion based models. Particularly, RGED can be applied to matrix-based and even tensor-based discriminant techniques, for instance, 2D-Linear Discriminant Analysis (2D-LDA). Furthermore, an iterative algorithm based on the alternating direction method of multipliers is developed. The algorithm approximately solves RGED with monotonically decreasing convergence and at an acceptable speed for results of modest accuracy. Numerical experiments based on four data sets of different types of images show that RGED has competitive classification performance with existing multidimensional and sparse techniques of discriminant analysis.