Multiple criteria mathematical programming and data mining

Abstract

Recently, researchers have extensively applied quadratic programming into classification, known as V. Vapnik's Support Vector Machine, as well as various applications. However, using optimization techniques to deal with data separation and data analysis goes back to more than forty years ago. Since 1998, the authors and their colleagues extended such a research idea into classification via multiple criteria linear programming (MCLP) and multiple criteria quadratic programming (MQLP). The purpose of the paper is to share our research results and promote the research interests in the community of computational sciences. These methods are different from statistics, decision tree induction, and neural networks. In this paper, starting from the basics of Multiple Criteria Linear Programming (MCLP), we further discuss penalized MCLP Multiple Criteria Quadratic Programming (MCQP), Multiple Criteria Fuzzy Linear Programming, Multi-Group Multiple Criteria Mathematical Programming, as well as regression method by Multiple Criteria Linear Programming. A brief summary of applications of Multiple Criteria Mathematical Programming is also provided. © 2008 Springer-Verlag Berlin Heidelberg.