# Which eigenvector to choose after calculating PCA

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?

• Could you proive me (and further readers) with an explanation what PCA stands for?
– Deve
Jul 12, 2013 at 6:31
• Jul 12, 2013 at 13:46

## 2 Answers

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).

• Care to add some citation , figures and/or examples ? Jul 11, 2013 at 11:47
• 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. Jul 11, 2013 at 11:52

I think my answer is pretty aptly given here :

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