Determine the Kernel Parameter of KFDA Using a Minimum Search Algorithm

Abstract

In this paper, we develop a novel approach to perform kernel parameter selection for Kernel Fisher discriminant analysis (KFDA) based on the viewpoint that optimal kernel parameter is associated with the maximum linear separability of samples in the feature space. This makes our approach for selecting kernel parameter of KFDA completely comply with the essence of KFDA. Indeed, this paper is the first paper to determine the kernel parameter of KFDA using a search algorithm. Our approach proposed in this paper firstly constructs an objective function whose minimum is exactly equivalent to the maximum of linear separability. Then the approach exploits a minimum search algorithm to determine the optimal kernel parameter of KFDA. The convergence properties of the search algorithm allow our approach to work well. The algorithm is also simple and not computationally complex. Experimental results illustrate the effectiveness of our approach.