COMPARATIVE STUDY OF TWO DATA REDUCTION TECHNIQUES IN PRINCIPAL COMPONENT ANALYSIS

COMPARATIVE STUDY OF TWO DATA REDUCTION TECHNIQUES IN PRINCIPAL COMPONENT ANALYSIS

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##### Date

2015-08

##### Authors

SULEIMAN, HARUNA

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##### Abstract

Principal Components Analysis is a mathematical procedure of data reduction technique that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of uncorrelated variables. This transformation is defined in such a way that the first principal components have the largest possible variance. Different methods for selecting the principal component to be retained exist in many literatures. In this dissertation, a comparative study of the two methods was carried out. The two methods considered are ―proportion of variance accounted for‖ and ―eigenvalue one-criterion‖. The method was applied on data of Cholesterol level in Human for PC’s selection. Model adequacy checking was used to test the fitted models. It was found that six 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%. 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 the fact that the first three PC’s could replace twelve variables by sacrificing a negligible information about the total variation in the system. For authentication, simulation was carried out, R-squared and R-squared adjusted of the fitted model were 28.3% and 7.1% by eigenvalue one-criterion and 23.6% and 5.3% by proportion of variance accounted for respectively. So this authentication, 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, also for the fact that the first five PC’s retained account for most of the variance, and could replace twelve variables by sacrificing a negligible information about the total variation in the system.

##### Description

A DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF A MASTERS DEGREE IN STATISTICS. DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE AHMADU BELLO UNIVERSITY, ZARIA NIGERIA

##### Keywords

COMPARATIVE STUDY,, TWO DATA REDUCTION TECHNIQUES,, PRINCIPAL COMPONENT ANALYSIS,