Probabilistic principal surfaces

A modification to the current probabilistic formulations of the principal curve and principal surface is proposed. The modification involves orienting and clipping the covariances at each of the manifold nodes such that variance in directions tangential to the manifold are minimized. The motivation behind this modification lies in the desire to recover and approximate the projection step of the original principal curve algorithm in current probabilistic principal surface formulations. Experiments on artificial and real datasets suggest that this modification does indeed lead to a vast improvement in convergence speed and better generalization properties for principal surfaces