Adaptive minor component extraction with modular structure

An information criterion for adaptively estimating multiple minor eigencomponents of a covariance matrix is proposed. It is proved that the proposed criterion has a unique global minimum at the minor subspace and that all other equilibrium points are saddle points. Based on the gradient search approach of the proposed information criterion, an adaptive algorithm called adaptive minor component extraction (AMEX) is developed. The proposed algorithm automatically performs the multiple minor component extraction in parallel without the inflation procedure. Similar to the adaptive lattice filter structure, the AMEX algorithm also has the flexibility wherein increasing the number of the desired minor component does not affect the previously extracted minor components. The AMEX algorithm has a highly modular structure and the various modules operate completely in parallel without any delay. Simulation results are given to demonstrate the effectiveness of the AMEX algorithm for both the minor component analysis (MCA) and the minor subspace analysis (MSA).