Kernel matrix approximation for learning the kernel hyperparameters

The selection of kernel hyperparameters is addressed in this article. The proposed method is based on the approximation of an empirical ideal kernel matrix using three measures of similarity between matrices. The conventional kernel alignment, the Frobenius distance and the correlation between matrices are investigated. A quadratic gradient optimization is proposed to find the set of hyperparameters maximizing the similarity between the empirical ideal kernel matrix and the sample kernel matrix. The Gaussian kernel is used in this article for numerical experiments. Classification of several real data sets are performed. In terms of classification accuracies and processing time, results show that the proposed approach is effective for tuning the kernel hyperparameters.