Choquet distances and their applications in data classification

Article type: Research Article

Authors: Ma, Yingcang^{a; *} | Chen, Hong^a | Song, Weini^a | Wang, Zhenyuan^b

Affiliations: [a] School of Science, Xi’an Polytechnic University, Xi’an, China | [b] Department of Mathematics, University of Nebraska at Omaha, Omaha, USA

Correspondence: [*] Corresponding author. Yingcang Ma, School of Science, Xi’an Polytechnic University, Xi’an 710048, China. Tel.: +86 15934838276; Fax: +86 29 82330234; E-mail: mayingcang@126.com.

Abstract: In the last decades, numerous optimization-based methods have been proposed for solving classification problems in pattern recognition. These methods mainly construct a straight line or a hyperplane to separate a given data set to be two classes. In this paper, we propose a new nonlinear classifier based on the Choquet integral with respect to a signed efficiency measure, and the boundary is a broken line (two considered attributes) or a Choquet broken-hyperplane (more considered attributes). Firstly, the Choquet distance of two points in n-dimensional space is proposed. Secondly, according to the Choquet distance, two nonlinear classification optimal models are presented. Finally, some experimental results show that the efficiency of the models for solving classification problems. The related results enrich the research of classification problems in pattern recognition.

Keywords: Nonlinear classification, signed efficiency measure, Choquet integral, Choquet distance

DOI: 10.3233/JIFS-16249

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 589-599, 2017