The support vector machines (SVMs) are one of the most effective classification techniques in several knowledge discovery and data mining applications. However, a SVM requires the user to set the form of its kernel function and parameters in the function, both of which directly affect to the performance of the classifier. This paper proposes a novel method, named a kernel-tree, the function of which is composed of multiple kernels in the form of a tree structure. The optimal kernel tree structure and its parameters is determined by genetic programming (GP). To perform a fine setting of kernel parameters, the gradient descent method is used. To evaluate the proposed method, benchmark datasets from UCI and dataset of text classification are applied. The result indicates that the method can find a better optimal solution than the grid search and the gradient search.

Finding a kernel mapping function for support vector machines (SVMs) is a key step towards construction of a high-performanced SVM-based classifier. While some recent methods exploited an evolutional approach to construct a suitable multifunction kernel, most of them searched randomly and diversely. In this paper, the concept of a family of identical-structured kernel trees is proposed to enable exploration of structure space using genetic programming whereas to pursue investigation of parameter space on a certain tree using evolution strategy. To control balance between structure and parameter search towards an optimal kernel, simulated annealing is introduced. By experiments on a number of benchmark datasets in the UCI and text classification collection, the proposed method is shown to be able to find a better optimal solution than other search methods, including grid search and gradient search.