The Maximum Vector-Angular Margin Classifier and its fast training on large datasets using a core vector machine

摘要

Although pattern classification has been extensively studied in the past decades, how to enecnveiy solve the corresponding training on large datasets is a problem that still requires particular attention. Many kernelized classification methods, such as SVM and SVDD, can be formulated as the corresponding quadratic programming (QP) problems, but computing the associated kernel matrices requires 0(n2) (or even up to O(n3)) computational complexity, where n is the size of the training patterns, which heavily limits the applicability of these methods for large datasets. In this paper, a new classification method called the Maximum Vector-Angular Margin Classifier (MAMC) is first proposed based on the Vector-Angular Margin to find an optimal vector c in the pattern feature space, and all the testing patterns can be classified in terms of the maximum vector-angular margin p, between the vector c and all the training data points. Accordingly, it is proved that the kernelized MAMC can be equivalently formulated as the kernelized Minimum Enclosing Ball (MEB), which leads to a distinctive merit of MAMC, i.e. it has the flexibility of controlling the sum of support vectors like u-SVC and may be extended to a Maximum Vector-Angular Margin Core Vector Machine (MAMCVM) by connecting the Core Vector Machine (CVM) method with MAMC such that the corresponding fast training on large datasets can be effectively achieved. Experimental results on artificial and real datasets are provided to validate the power of the proposed methods.