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After calculating the principal component analysis (PCA) of a given data set, we are normally left with a matrix containing the eigenvectors sorted in order of the size of the eigenvalues. Now, in pattern recognition which eigenvector should we choose: the first eigenvector or do we have to do further processing of the eigenvector in order to choose the desired eigenvector?

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The eigenvectors are in the order of explained variance. Usually one uses PCA for dimension reduction, that is, selects some N first components. The problem of choosing appropriate N is called dimension estimation. Easiest way would be to take such N that the selected PCs explain 90% or 95% of the variance in the original data. Alternatively, you could use some information-theoric method such as minimum description length (MDL).

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  • $\begingroup$ Care to add some citation , figures and/or examples ? $\endgroup$ – motiur Jul 11 '13 at 11:47
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    $\begingroup$ PCA is a well known method which was invented in 1901. You are asking very basic things, so any text book on the subject will do. If you want more spesific answer, you should tell what you data is, how many samples and variables you have, etc. Try Wikipedia. $\endgroup$ – user5004 Jul 11 '13 at 11:52
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I think my answer is pretty aptly given here :

http://ufldl.stanford.edu/wiki/index.php/PCA#Number_of_components_to_retain

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