Principal components: A descent algorithm

A descent procedure is proposed for the search of low-dimensional subspaces of a high-dimensional space that satisfy an optimality criterion. Specifically, the procedure is applied to finding the subspace spanned by the first m singular components of an n-dimensional dataset. The procedure minimizes the associated cost function through a series of orthogonal transformations, each represented economically as the exponential of a skew-symmetric matrix drawn from a low-dimensional space.