LDA pre-processing for classification: class-dependent single objective GA and multi-objective GA approaches

Authors:
Modjtaba Khalidji;Hossein Moeinzadeh;Ahmad Akbari;Bijan Raahemi
Affiliations:
Department of Computer Engineering, Iran University of Science and Technology, Tehran, Iran;Department of Computer Engineering, Iran University of Science and Technology, Tehran, Iran;Department of Computer Engineering, Iran University of Science and Technology, Tehran, Iran;Department of Computer Engineering, Iran University of Science and Technology, Tehran, Iran
Venue:
IDEAL'09 Proceedings of the 10th international conference on Intelligent data engineering and automated learning
Year:
2009

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Abstract

Pre-processing of classification data can be helpful regardless of the type of classifier. The objective of this pre-processing step is to achieve a high degree of separation among classes before the classifier is trained or tested. This results into a trace ratio problem which is difficult to solve. Methods such as Linear Discriminant Analysis (LDA) have already been used for the solution of this problem by turning it into a simpler yet inexact problem. Also, in classical LDA, the covariances of different classes are assumed to be similar, which is not the case in real-world problems. In this paper, a class-dependent approach to finding the linear transformation is proposed. This method solves the trace ratio problem directly and also removes the requirement of similar covariance matrices. While giving good results, the method is computationally expensive. To reduce the computational cost while maintaining the benefits of the class-dependent method, a multi-objective formulation is proposed and solved using NSGA-II. Simulation results show great improvement in classification using various classifiers.