Although multiple criteria mathematical program （MCMP）, as an alternative method of classification, has been used in various real-life data mining problems, its mathematical structure of solvability is still challengeable. This paper proposes a regularized multiple criteria linear program （RMCLP） for two classes of classification problems. It first adds some regularization terms in the objective function of the known multiple criteria linear program （MCLP） model for possible existence of solution. Then the paper describes the mathematical framework of the solvability. Finally, a series of experimental tests are conducted to illustrate the performance of the proposed RMCLP with the existing methods： MCLP, multiple criteria quadratic program （MCQP）, and support vector machine （SVM）. The results of four publicly available datasets and a real-life credit dataset all show that RMCLP is a competitive method in classification. Furthermore, this paper explores an ordinal RMCLP （ORMCLP） model for ordinal multigroup problems. Comparing ORMCLP with traditional methods such as One-Against-One, One-Against-The rest on large-scale credit card dataset, experimental results show that both ORMCLP and RMCLP perform well.
This paper is concerned with the theoretical foundation of support vector machines (SVMs). The purpose is to develop further an exact relationship between SVMs and the statistical learning theory (SLT). As a representative, the standard C-support vector classification (C-SVC) is considered here. More precisely, we show that the decision function obtained by C-SVC is just one of the decision functions obtained by solving the optimization problem derived directly from the structural risk minimization principle. In addition, an interesting meaning of the parameter C in C-SVC is given by showing that C corresponds to the size of the decision function candidate set in the structural risk minimization principle.
ZHANG ChunHua 1 , TIAN YingJie 2 & DENG NaiYang 3,1 School of Information, Renmin University of China, Beijing 100872, China
