Revisiting weighted inverse rayleigh quotient for minor component extraction

A framework for classes of minor component learning rides is presented. In the proposed rules, eigenvectors of a covariance matrix are simultaneously estimated. The derivation of MCA rules is based on optimizing a weighted inverse Rayleigh quotient so that the optimum weights at equilibrium points are exactly the desired eigenvectors of a covariance matrix instead of an arbitrary orthonormal basis of the minor subspace. Variations of the derived MCA learning rules are obtained by imposing orthogonal and quadratic constraints and change of variables. Some of the proposed algorithms can also perform PCA by merely changing the sign of the step-size.