Partial common principal component subspaces

Abstract

SUMMARY We consider the principal components analysis of g groups of m variables for those situations in which, for each group, the first k principal components account for most of the total variability of observations in that group. If the set of these gk principal component vectors spans a space of dimension r, where r is less than m, then it will be possible simultaneously to reduce the dimensionality, for all groups, from m to r while retaining most of the within-group variability. Methods are already available for determining if r = k, in which case the g groups have a common principal component subspace. In this paper, we develop a general procedure for determining if r = s for arbitrary s. This can then be used repeatedly to determine r when r > k.