Support vector machine based on hierarchical and dynamical granulation

Abstract

Support vector machine (SVM) has been a promising method for classification and regression areas due to its solid statistical foundations, such as margin maximization and kernel methods. However, SVM is not typically used for large-scale data mining problems because its training complexity is highly dependent on the dataset size. This paper presents an improved granular support vector machine learning model based on hierarchical and dynamical granulation, namely, HD_GSVM, to solve the low learning efficiency and generalization performance problem of traditional granular support vector machines (GSVM). For HD_GSVM, the original data will be mapped into a high-dimensional space by a Mercer kernel. Then, the data are divided into several granules, and those granules near the approximate hyperplane are extracted and re-granulated on a subtle level by their density and radius degree. Finally, the decision hyperplane will be obtained through all of the granules at different hierarchical and dynamical granulation levels effectively. During the granulation process, the granulation level of all granules can be dynamically changed continuously. With this method, different classification information can be obtained from different levels of granules; to meet a variety of needs for various practical problems from different perspectives. The experimental results on the UCI benchmark datasets demonstrate that the proposed HD_GSVM model can improve the generalization performance greatly with high efficiency synchronously.