Using Non-Additive Measure for Optimization-Based Nonlinear Classification

• 作者: Guimin Huang Nian Yan Yong Shi Zhengxin Chen Zhenyuan Wang
• 来源期刊: 美国运筹学期刊(英文)
• 学科: 医学
• 关键词: NONLINEAR PROGRAMMING NONLINEAR CLASSIFICATION Non-Additive MEASURE Choquet INTEGRAL Support Vector Machines
• 年，卷（期）: mgycxqkyw_2012,（3）
• 页码范围: 364-373
• 页数: 10页
• 分类号: R73

摘要

Over the past few decades, numerous optimization-based methods have been proposed for solving the classification problem in data mining. Classic optimization-based methods do not consider attribute interactions toward classification. Thus, a novel learning machine is needed to provide a better understanding on the nature of classification when the interaction among contributions from various attributes cannot be ignored. The interactions can be described by a non-additive measure while the Choquet integral can serve as the mathematical tool to aggregate the values of attributes and the corresponding values of a non-additive measure. As a main part of this research, a new nonlinear classification method with non-additive measures is proposed. Experimental results show that applying non-additive measures on the classic optimization-based models improves the classification robustness and accuracy compared with some popular classification methods. In addition, motivated by well-known Support Vector Machine approach, we transform the primal optimization-based nonlinear classification model with the signed non-additive measure into its dual form by applying Lagrangian optimization theory and Wolfes dual programming theory. As a result, 2n – 1 parameters of the signed non-additive measure can now be approximated with m (number of records) Lagrangian multipliers by applying necessary conditions of the primal classification problem to be optimal. This method of parameter approximation is a breakthrough for solving a non-additive measure practically when there are relatively small number of training cases available (mn-1). Furthermore, the kernel-based learning method engages the nonlinear classifiers to achieve better classification accuracy. The research produces practically deliverable nonlinear models with the non-additive measure for classification problem in data mining when interactions among attributes are considered.