The optimality of the centroid method

The aim of this note is to show that the centroid method has two optimality properties. It yields loadings with the highest sum of absolute values, even in absence of the constraint that the squared component weights be equal. In addition, it yields scores with maximum variance, subject to the constraint that none of the squared component weights be larger than 1.This research is financed by NSERC of Canada. The author is grateful to Michel Tenenhaus for pointing the similarity of the procedures in the centroid method and Q-mode PCA in L₁. The author also thanks the editor and associate editor for providing shorter proofs of the theorems, along with the referees for their helpful comments.