Fuzzy Canonical Discriminant Analysis: Theory and Practice

Abstract

In this article, we propose a new classification method called fuzzy canonical discriminant analysis (FCDA) based on the Fisher's canonical discriminant analysis (CDA) to deal with some vagueness in natural and social science and to improve its prediction accuracy. By establishing the fuzzy canonical discriminant function and triangular function transformation, we obtain the estimators of parameters. We also design an efficient algorithm for calculation of the parameters. We compare it with CDA using the original Iris data, samples of the Iris data, and seven other popular data sets. The results confirms that the FCDA is an effective tool in prediction and is better than the CDA.

Keywords:

• Classification
• Fuzzy canonical discriminant analysis
• Fuzzy set theory

Mathematics Subject Classification:

• Primary 62H30
• Secondary 62H86

Acknowledgments

This work was supported by the Fundamental Research Funds for the Central Universities (2010221040), China National Social Science Fund (09AZD045), and China National Bureau of Statistics Fund (2009LZ045). We would like to thank the Editor, Associate Editor, and referees for careful review and insightful comments, which led to significant improvement of the article.