The performance of the kernel-based learning algorithms, such as SVM, depends heavily on the proper choice of the kernel parameter. It is desirable for the kernel machines to work on the optimal kernel parameter that adapts well to the input data and the learning tasks. In this paper, we present a novel method for selecting Gaussian kernel parameter by maximizing a class separability criterion, which measures the data distribution in the kernel-induced feature space, and is invariant under any non-singular linear transformation. The experimental results show that both the class separability of the data in the kernel-induced feature space and the classification performance of the SVM classifier are improved by using the optimal kernel parameter.

Kernel biased discriminant analysis (KBDA), as a subspace learning algorithm, has been an attractive approach for the relevance feedback in content-based image retrieval. Its performance, however, still suffers from the “small sample learning” problem and “kernel learning” problem. Aiming to solve these problems, in this paper, we present a new semi-supervised scheme of KBDA (S-KBDA), in which the projection learning and the “kernel learning” are interweaved into a constrained optimization framework. Specifically, S-KBDA learns a subspace that preserves both the biased discriminant structure among the labeled samples, and the geometric structure among all training samples. In kernel optimization, we directly optimize the kernel matrix, rather than a kernel function, which makes the kernel learning more flexible and appropriate for the retrieval task. To solve the constrained optimization problem, a fast algorithm based on gradient ascent is developed. The image retrieval experiments are given to show the effectiveness of the S-KBDA scheme in comparison with the original KBDA, and the other two state-of-the-art algorithms.