A novel dimensionality reduction method with discriminative generalized eigen-decomposition

Dimensionality reduction plays a critical role in machine learning and computer vision for past decades. In this paper, we propose a discriminative dimensionality reduction method based on generalized eigen-decomposition. Firstly, we define the discriminative framework between pairwise classes inspired by the signal to noise ratio. Then the metric is given for intra-class compactness and inter-class separation. Finally, the framework for one against one class can be easily extended to one against all classes. Compared with traditional supervised dimensionality reduction methods, the proposed method can catch discriminative directions for pairwise classes rather than for all classes. Furthermore, it also can deal with non-Gaussian distributed data. The experimental results show that the proposed model can achieve high precisions in classification tasks.