Algebraic and Geometric Basis of Principal Components: An Overview

Abstract

Principal Component Analysis is considered as a dimension-reduction tool which may be used to reduce a large set of possibly correlated variables to hopefully a smaller set of uncorrelated variables that still accounts for most of the variation of the original large set. To understand the inner constructs of principal components, concepts of algebraic as well as geometric basis of principal components are prerequisites. Hence, in the current study, an attempt has been made to provide a step by step and vivid discussion of the basis of principle components and its various important properties.