22%20Principle%20Component%20Analysis%204_17_08

22%20Principle%20Component%20Analysis%204_17_08 - Principle...

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1 1 Principle Component Analysis Peng Liu 4/17/2008 2 Principle Component Analysis ± PCA is concerned with explaining the variance- covariance structure. ± The general objectives of PCA are: Data reduction Interpretation 3 Principal Components ± Principal components can be useful for providing low-dimensional views of high-dimensional data. 1 2 . .. m 1 2 X = . . . n Data Matrix or Data Set x 11 x 12 . . . x 1m x 21 . . . x n1 x 2m . . . x nm x n2 . . . object variable number of variables number of observations 4 Principal Components (continued) ± Each principal component of a data set is a variable obtained by taking a linear combination of the original variables in the data set. ± A linear combination of m variables x 1 , x 2 , . .., x m is given by c 1 x 1 + c 2 x 2 + + c m x m . ± For the purpose of constructing principal components, the vector of coefficients is restricted to have unit length, i.e., c 1 + c 2 + + c m = 1. ... ... 22 2
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2 5 Principal Components (continued) ± The first principal component is the linear combination of the variables that has maximum variation across the observations in the data set.
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This note was uploaded on 08/27/2009 for the course STAT 447 taught by Professor Staff during the Spring '08 term at Iowa State.

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22%20Principle%20Component%20Analysis%204_17_08 - Principle...

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