Comparison between statistical approaches and linear programming for resolving classification problem

Abstract

The applications that are related to classification problem are wide-ranging. In fact, differentiating between patients with strong prospects for recovery and those highly at risk, between good credit risks and poor ones, or between promising new firms and those likely to fail, are among the most known of these applications. To solve such classification problem, several approaches have been applied. In this paper, on one hand, we dealt with the parametric approach illustrated by the use of Fisher's linear discriminant function, Smith's quadratic discriminant function and the logistic discriminant model. On the other hand, we studied the non-parametric approach such as linear programming models as alternatives to the parametric 3126 Slah Ben Youssef and Abdelwaheb Rebaiapproach when hypothesises of this later are not satisfied. Such hypothesises are: the distribution's normality, the homogeneity of variance-covariance matrix, the sample's size and the absence of outliers in data. Our study showed that, being more flexible in such a way to allow the analyst to incorporate some a priori information in the models, the non-parametric approach outperforms the parametric one. Nevertheless, this does not exclude the use of statistical techniques once the required hypothesises are satisfied.

Performance Analysis of Classification Methods and Alternative Linear Programming Integrated with Fuzzy Delphi Feature Selection

“…This method separates classes by linear frontiers to group the data to be classified around the centre of gravity (average) of each class and to create a linear hyperplane between the classes. This method requires certain assumptions: the normality distribution of the samples, homogeneity of the variances -covariances matrices [2]. If we have n variables, the discriminant function is as follows:…”

“…Differentiat ing 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.…”