Dual subspace learning via geodesic search on Stiefel manifold

Abstract

Oja’s principal subspace algorithm is a well-known and powerful technique for learning and tracking principal information of time series. However, Oja’s algorithm is divergent when performing the task of minor subspace analysis. In the present paper, we transform Oja’s algorithm into a dual learning algorithm in the sense of fulfilling principal subspace analysis as well as minor subspace analysis via geodesic search on Stiefel manifold. Also inherent stability is guaranteed for the proposed geodesic based algorithm due to the fact the weight matrix rigourously evolves on the compact Stiefel manifold. The effectiveness of the proposed algorithm is further verified in the section of numerical simulation.