A logarithmic cost function for principal singular component analysis

An un-unconstrained optimization problem involving logarithmic cost function that incorporates a diagonal matrix is utilized for deriving gradient dynamical systems that converge to the principal singular components of arbitrary matrix. The equilibrium points of the resulting gradient systems are determined and their stability is thoroughly analyzed. Qualitative properties of the proposed systems are analyzed in detail including the limit of solutions as time approaches infinity. The performance of this system is also examined.