Improved Convergence Speed of Fully Symmetric Learning Rules for Principal Component Analysis
Fully symmetric learning rules for principal component analysis can be
derived from a novel objective function suggested in our previous work. We
observed that these learning rules suffer from slow convergence for covariance
matrices where some principal eigenvalues are close to each other. Here we
describe a modified objective function with an additional term which mitigates
this convergence problem. We show that the learning rule derived from the
modified objective function inherits all fixed points from the original
learning rule (but may introduce additional ones). Also the stability of the
inherited fixed points remains unchanged. Only the steepness of the objective
function is increased in some directions. Simulations confirm that the
convergence speed can be noticeably improved, depending on the weight factor of
the additional term.