Novel criterion function for minor subspace tracking based on Rayleigh quotient

Aiming at the lack of information criterion functions of sub subspace,a novel criterion function was proposed by adding a penalty term to the Rayleigh quotient.Through analyzing the properties of all the stable points,it was proven that the criterion function exhibited the global maximum attained if and only if the weight matrices span the minor subspace.A minor subspace tracking algorithm was derived by gradient ascending method and its global convergence analysis was also accomplished.Numerical simulations and real application verifies the correctness of the criterion function and derived algorithm.