Singular value decomposition and principal component analysis: Misconceptions and disparities

Abstract

The application of singular value decomposition to perform principal component analysis is becoming increasingly evident in certain areas such as machine learning. The objective of this study is to differentiate these methods by clearly elucidating the disparities that exist theoretically and empirically. The study discovered that the PCA method is a product of the Eigen decomposition applied to the covariance/correlation matrix while SVD is achieved via a direct application to the dataset matrix after normalization. This was verified by carrying out a comparative analysis of both methods on a dataset consisting of standing heights and physical attributes (one dependent variable and seven independent variables) of 33 females applying for police officer positions in Akwa ibom state. The analysis was done using a MATLAB software program. The final results from the outputs obtained for both methods were the same. The study concluded that both methods are products of matrix decompositions and can be used to achieve the purpose of data reduction but the difference lies in how they are being applied.