Fuzzy kernel alignment with application to attribute reduction of heterogeneous data

Fuzzy similarity relation is a function to measure the similarity between two samples. It is widely used to learn knowledge under the framework of fuzzy machine learning, and the selection of a suitable fuzzy similarity relation is obviously important for the learning task. It has been pointed out that fuzzy similarity relations can be brought into the framework of kernel functions in machine learning. This fact motivates us to study fuzzy similarity relation selection for fuzzy machine learning utilizing kernel selection methods in machine learning. Kernel alignment is a kernel selection method that is effective and has low computational complexity. In this paper we present novel methods for fuzzy similarity relation selection based on kernel alignment, and their use in attribution reduction for heterogeneous data. Firstly, we define an ideal kernel for classification problems, based on which a novel fuzzy kernel alignment model is proposed. Secondly, we present a method for fuzzy similarity relation selection based on the minimization of fuzzy alignment between the defined ideal kernel and a kernel for the learning problem at hand. In order to show the correctness of this selection method, we prove that the lower bound of the classification accuracy of a support vector machine will increase with the decrease of the fuzzy alignment value. Furthermore, we apply the proposed fuzzy similarity relation selection to attribute reduction for heterogeneous data. Finally, we present experimental results to show that the proposed method of fuzzy similarity relation selection based on fuzzy kernel alignment is effective.