Abstract: Using the same topology as that of Oja-Brockett-Xu parallel neural network, a novel dual purpose adaptive algorithm for principal and minor component extraction was proposed by the optimization framework of a weighted Rayleigh quotient on the compact Stiefel manifold. By taking the right translation invariant Killing metric on orthogonal matrix group and search along the geodesic emanating from identity by means of exponential map, a novel dual learning algorithm for principal and minor component analysis was proposed. The proposed algorithm could switch from PCA (Principal Component Analysis) to MCA (Minor Component Analysis) with a simple sign change of its stepsize parameter. Moreover, orthonormality of the weight matrix was guaranteed at any iteration step. The effectiveness of the proposed algorithm was further verified in the section of numerical simulation.

Key words: compact Stiefel manifold, dual learning, minor component analysis, principal component analysis