### Transcription of Principal Component Analysis - Columbia University

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**Principal** **Component** AnalysisFrank WoodDecember 8, 2009 This lecture borrows andquotesfrom Joliffe s Principle **Component** **Analysis** book. Go buy it! **Principal** **Component** AnalysisThe central idea of **Principal** **Component** **Analysis** (PCA) isto reduce the dimensionality of a data set consisting of alarge number of interrelated variables, while retaining asmuch as possible of the variation present in the data is achieved by transforming to a new set of variables,the **Principal** components (PCs), which are uncorrelated,and which are ordered so that the firstfewretain most ofthe variation present inallof the original variables.

matrix is to utilize the **singular value decomposition** of S = A0A where A is a matrix consisting of the eigenvectors of S and is a diagonal matrix whose diagonal elements are the eigenvalues corresponding to each eigenvector. Creating a reduced dimensionality projection of X is accomplished by selecting the q largest eigenvalues in and retaining ...

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