I.J. Information Technology and Computer Science, 2013, 10, 9-20 Published Online September 2013 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijitcs.2013.10.02 Copyright © 2013 MECS I.J. Information Technology and Computer Science, 2013, 10, 9-20 Performance Analysis of Classification Methods and Alternative Linear Programming Integrated with Fuzzy Delphi Feature Selection Bahram Izadi, Bahram Ranjbarian, Saeedeh Ketabi Department of Management, Faculty of Administrative Sciences and economics, University of Isfahan, Iran E-mail: bahram.izadi@ase.ui.ac.ir, bahram1@ase.ui.ac.ir, sketabi@ase.ui.ac.ir, izady.bahram@gmail.com Faria Nassiri-Mofakham Department of Information Technology Engineering, Faculty of Engineering, University of Isfahan, Iran E-mail: fnasiri@eng.ui.ac.ir Abstract — Among various statistical and data mining discriminant analysis proposed so far for group classification, linear programming discriminant analysis have recently attracted the researchers’ interest. This study evaluates multi-group discriminant linear programming (MDLP) for classification problems against well-known methods such as neural networks, support vector machine, and so on. MDLP is less complex compared to other methods and does not suffer from local optima. However, sometimes classification becomes infeasible due to insufficient data in databases such as in the case of an Internet Service Provider (ISP) small and medium-sized market considered in this research. This study proposes a fuzzy Delphi method to select and gather required data. The results show that the performance of MDLP is better than other methods with respect to correct classification, at least for small and medium-sized datasets. Index Terms— Fuzzy Delphi Feature Selection, Customer Classification Problem, Multi-Group Linear Programming, Artificial Neural Network, Logistic Regression, Support Vector Machine I. Introduction The applications of classification methods are wide- ranging and the advent of powerful information systems since the mid-1980s has renewed interest about classification techniques [1]. Differentiating between patients with strong prospects for recovery and those highly at risk, between customers with good credit risks and poor ones, or between promising new firms and those likely to fail, are among the most known applications [2]. Especially managers use classification techniques to make decisions in different business operation areas. At its broadest, classification could cover any context in which some decision is made on the basis of currently available information. Then, classification is a method for making judgments in new situations [3]. For instance, rather than targeting all customers equally or providing the same incentive offers to all customers, managers can select those customers who meet some profitability criteria based on purchasing behaviors [4]. However, due to the nature of classification problem, a spectrum of techniques is needed because no single technique always outperforms others under all situations [5]. Various methods have been proposed for solving classification problems which can be divided into two categories: parametric and non-parametric discriminant methods. There are no pre-defined assumptions in non-parametric methods. However, parametric methods make strong parametric assumptions such as multivariate normal populations with the same variance/covariance structure, absence of multi co-linearity, and absence of specification errors [6]. Classification methods can also be grouped as statistical approaches such as Linear Discriminant Analysis (LDA) and Logistic Regression (LR), artificial intelligence or machine learning techniques such as Artificial Neural Network (ANN) and Support Vector Machine (SVM) and Operation Research techniques such as Linear Programming (LP) and Goal Programming (GP). The earliest discriminant method proposed by Fisher in 1936. This method of discrimination requires that the sample to be distributed normally and the variance- covariance matrices of the two groups to be homogeneous. Mangasarian also was the first who used LP method for classification problems [7]. Linear Programming method have some advantages over other approaches which can be enumerated as follow: First, there is no assumption about the functional form and hence it is distribution free. Second, they are less sensitive to outliers. Third, they do not need large datasets. Nonetheless, linear programming methods also have a disadvantage, which is the lengthy computation. However, immense increase in computing power and drop in computing cost overcome the disadvantage and made LP methods practical.