Abstract

COMPARATIVE STUDY OF TWO DATA REDUCTION TECHNIQUES IN PRINCIPAL COMPONENT ANALYSIS USING BOTH REAL AND SIMULATED DATA

Haruna Suleiman,1 Yusuf Muhammad Kufena2 and Lukman Lawal3

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Conceptually, the goal of PCA is to reduce the number of variables of interest into a smaller set of components and also it analyzes all the variance in the variables and reorganizes it into a new set of components equal to the number of original variables. In this paper, we consider two different data set, both real and simulated for a rationally and a reliable comparisons. Two of the methods were adopted which were; ?Eigenvalue 0ne-criteria and proportion of variance accounted for?. The method was applied on data of Cholesterol level in Humans for PC?s selection. Model adequacy checking was used to test the fitted models. It was found that six (6) principal components were retained by using ?proportion of variance accounted for? R-squared and R-squared-Adjusted from this research were 6.5% and 2.3% respectively. For the ?eigenvalue one-criterion? three principal components were retained, R-squared and R-squared adjusted were 10.9%, and 3.7% respectively. By considering the result obtained it is clear that eigenvalue one criterion is more preferred and desired in dimensionality reduction in Principal Component Analysis. For authentication, simulation was carried out and the R-squared and R-squared adjusted of the fitted model were 28.3% and 7.1% by Eigenvalue one-criterion, 23.6% and 5.3% by proportion of variance accounted for respectively. This shows without any reasonable doubt that, eigenvalue one-criterion method is more preferable in the reduction of a set of data for cholesterol level in human body over the proportion of variance accounted for. Keywords: Principal Component, Eigenvalue one ? criterion, Proportion of Variance accounted for, Real and Simulated data set.

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