Common principal component subspaces in two groups
本文针对两组数据，开发了一种近似检验方法，判断它们的前m个主成分张成的子空间是否相同，并通过模拟和数值例子验证了方法的有效性。
One important practical application of principal component analysis is to reduce a large number of variables, say p, to a smaller number, m, by making use of the first m principal components. This technique can easily be extended to two or more groups if the subspaces spanned by the first m principal components are the same for all groups. In this paper we develop an approximate procedure for testing such a hypothesis of common subspaces when two groups are involved. The adequacy of the approximation is investigated by a simulation and the method is illustrated by a numerical example.