A Nonparametric Discriminant Stepwise Algorithm for Classification to Two Populations

S. Padmanaban¹ , Martin L. William²

Section:Review Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.123-129, Dec-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.123129

Online published on Dec 31, 2018

Copyright © S. Padmanaban, Martin L. William . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
This paper provides a nonparametric discriminant stepwise algorithm to discriminate two multivariate populations and an optimal decision rule for classification of a member to either of the two populations. This ‘two-way-stepwise algorithm’ is a combination of the `forward-stepwise` and the ‘backward-stepwise’ approaches recently proposed for the same classification problem by Padmanaban and William (2016a, b). As has been done in the above-referred papers, this paper relaxes the `equal variance-covariance matrices` condition traditionally imposed and develops a discrimination-classification procedure by including variables that contribute to effective discrimination in a ‘forward’ manner one-by-one and excluding variables that do not contribute to effective `discrimination` in a ‘backward’ manner one-by-one. The inclusion of variables in the discriminant is determined on the basis of maximum discriminating ability and exclusion is on the basis of least `discriminating ability` as reflected in `difference` between the distributions of the discriminant in the two populations. A decision-rule for classification or membership-prediction with a view to maximizing correct predictions is provided as done in the forward and backward approaches referred above. The proposed algorithm is applied to develop an optimal discriminant for predicting respiratory tract disease(RD) among newborns of mothers with PPROM in the city of Chennai, India, and its performance is compared with logistic regression.

Key-Words / Index Term :
Classification, Discriminant, Kolmogorov-Smirnov Statistic

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