On principal subspace analysis

This paper is concerned with asymptotic behavior of the so-called subspace learning algorithm for extracting principal components of an input covariance matrix. The subspace spanned by the columns of the limiting solution is explicitly computed for any given initial condition. Moreover, the eigenvalue distribution of the covariance matrix is found relevant to the extraction of a dominant eigenspace of the covariance matrix. The dependence of the subspace on the initial weight matrix is examined in detail. The class of initial weight matrices leading to the extraction of any prespecified eigenspace of the covariance matrix is completely characterized.