Multiple Partial Empirical Kernel Learning with Instance Weighting and Boundary Fitting

Abstract

By dividing the original data set into several sub-sets, Multiple Partial Empirical Kernel Learning (MPEKL) constructs multiple kernel matrixes corresponding to the sub-sets, and these kernel matrixes are decomposed to provide the explicit kernel functions. Then, the instances in the original data set are mapped into multiple kernel spaces, which provide better performance than single kernel space. It is known that the instances in different locations and distributions behave differently. Therefore, this paper defines the weight of instance in accordance with the location and distribution of the instances. According to the location, the instances can be categorized into intrinsic instances, boundary instances and noise instances. Generally, the boundary instances, as well as the minority instances in the imbalanced data set, are assigned high weight. Meanwhile, a regularization term, which regulates the classification hyperplane to fit the distribution trend of the class boundary, is constructed by the boundary instances. Then, the weight of instance and the regularization term are introduced into MPEKL to form an algorithm named Multiple Partial Empirical Kernel Learning with Instance Weighting and Boundary Fitting (IBMPEKL). Experiments demonstrate the good performance of IBMPEKL and validate the effectiveness of the instance weighting and boundary fitting.