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Using Non-Additive Measure for Optimization-Based Nonlinear Classification

Author(s): Nian Yan | Zhengxin Chen | Yong Shi | Zhenyuan Wang | Guimin Huang

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 02;
Issue: 03;
Start page: 364;
Date: 2012;
Original page

Keywords: Nonlinear Programming | Nonlinear Classification | Non-Additive Measure | Choquet Integral | Support Vector Machines

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 (m

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