Performance evaluation of classication methods: the case of equal mean discrimination.
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Date
2014-11-19
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Abstract
This study considered the equal mean discrimination problem by evaluating the
performance of Bartlett and Please method, Bayesian Posterior Probability Ap-proach, the Quadratic Discriminant Function (QDF) and the Absolute Euclidean
Distance Classi er method (AEDC) under equal and unequal prior probabilities
and non normality contamination. Stocks (1933) twin data recorded in London
on 832 children based on ten selected measurements was used because it satis- es the assumptions of the equal mean populations. Four discriminant functions
were derived and their error rate estimates determined using the Cross Valida-tion (CV) and Balanced Error Rate (BER) methods. Results from equal prior
probability showed the Bayesian Posterior Probability classi er performing bet-ter than the three other classi ers, thus it provides maximum separation with
a recorded mean error rate of 0.149. Under the unequal prior probability situa-tion, Bartlett and Please method outperformed both the QDF and the Bayesian
posterior probability classi ers under the sampling ratios, 1:2, 1:3 and 1:4. For
non-normality, all four classi cation methods recorded higher mean error rates
indicating abysmal performance of the methods. However, Bartlett and Please
method was found to be very sensitive to outliers. We recommend the Bayesian
approach and the AEDC methods for classifying observations with equal prior
probabilities, Bartlett and Please method under unequal prior probabilities and
QDF for non-normal contamination with equal prior probabilities.
Description
A thesis submitted to the Department of Mathematics,
Kwame Nkrumah University of Science and Technology in
partial fulfilment of the requirement for the degree
of MPhil Mathematical Statistics,.