Regularized multiple criteria linear programs for classification  

作　　者：SHI Yong TIAN YingJie CHEN XiaoJun ZHANG Peng 

机构地区：[1]Research Center on Fictitious Economy & Data Science, Chinese Academy of Sciences, Beijing 100190, China [2]Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong [3]School of Information Science and Engineering, Graduate University of Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Science in China(Series F)》2009年第10期1812-1820,共9页中国科学（F辑英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 70621001, 70531040, 70501030, 10601064, 70472074);the Natural Science Foundation of Beijing (Grant No. 9073020);the National Basic Research Program of China (Grant No. 2004CB720103);Ministry of Science and Technology, China, the Research Grants Council of Hong Kong and BHP Billiton Co., Australia

摘　　要：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.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.

关 键 词：multiple criteria mathematical program regularized multiple criteria mathematical program CLASSIFICATION data mining 

分 类 号：O221.1[理学—运筹学与控制论] G254.1[理学—数学]