Graphical Procedure for Determining Useful Principal Components

Nahed. A. Mokhlis, Sahar A. N. Ibrahim and Nadia B. Gregni.

Abstract: One of the purposes of principal component analysis is to reduce the dimensionality of the set of variables. Several approaches have been suggested by different authors for determining the number of principal components that should be kept for further analysis. In this paper we present a graphical procedure depending on the computation of the coefficient of multiple determination of each variable when this variable is regressed on the other variables. A comparison of our criterion with the eigenvalue-one criterion, the Scree test criterion and the percentage criterion is given through examples. Our criterion can be considered as a lower bound for principal components retained. It is a precise one, in the sense that when different people analyze the same data they will obtain the same result. In addition it takes into account the components with variance smaller than one but important.

Key Words: Eigenvalues, Scree Test, Communality, Coefficient of Multiple Determination

Authors:
Nahed. A. Mokhlis, nahedmokhlis@hotmail.com
Sahar A. N. Ibrahim, sahar_nyazy@hotmail.com
Nadia B. Gregni, nadia_b_gr@yahoo.com

Editor: : Naik, Dayanand N.,dnaik@odu.edu

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