PCA-tutorial-HowTo jp

A tutorial on Principal Components AnalysisLindsay I SmithFebruary 26, 2002Chapter 1IntroductionThis tutorial is designed to give the reader an understanding of Principal ComponentsAnalysis (PCA). PCA is a useful statistical technique that has found application infields such as face recognition and image compression, and is a common technique forfinding patterns in data of high dimension.Before getting to a description of PCA, this tutorial first introduces mathematicalconcepts that will be used in PCA. It covers standard deviation, covariance, eigenvec-tors and eigenvalues. This background knowledge is meant to make the PCA sectionvery straightforward, but can be skipped if the concepts are already familiar.There are examples all the way through this tutorial that are meant to illustrate theconcepts being discussed. If further information is required, the mathematics textbook“Elementary Linear Algebra 5e” by Howard Anton, Publisher John Wiley & Sons Inc,ISBN 0-471-85223-6 is a good source of information regarding the mathematical back-ground.1Chapter 2Background MathematicsThis section will attempt to give some elementary background mathematical skills thatwill be required to understand the process of Principal Components Analysis. Thetopics are covered independently of each other, and examples given. It is less importantto remember the exact mechanics of a mathematical technique than it is to understandthe reason why such a technique may be used, ...