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?
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).