Learning Fuzzy equivalence relation kernels with prior knowledge

This paper introduces a method of learning kernel by fuzzy equivalence relation (FER) based on prior knowledge. Firstly, prior knowledge is represented through fuzzy membership functions and fuzzy inference rules. Consequently features of prior knowledge are obtained by proper inference methods. Secondly, the learning rules of FER-kernel are obtained in terms of FER semantic interpretation and fuzzy inference. According to the proposed method, the representation of FER-kernel is incorporated with prior knowledge. Moreover, decision functions with the obtained FER-kernel generalize well with unseen examples corresponding to prior knowledge owing to the transitivity of FER-kernel with respect to triangular norm. Finally, some experiments of binary classification are conducted to demonstrate the performance of FRE-kernels in SVM.