Semi-Supervised Bipartite Ranking with the Normalized Rayleigh Coefficient
We propose a new algorithm for semi-supervised learning in the bipartite ranking framework. It is based on the maximization of a so-called normalized Rayleigh coefficient, which differs from the usual Rayleigh coefficient of Fisher's linear discriminant in that the actual covariance matrices are used instead of the scatter matrices. We show that if the class conditional distributions are Gaussian, then the ranking function produced by our algorithm is the optimal linear ranking function. A kernelized version of the proposed algorithm and a semi-supervised formulation are provided. Preliminary numerical results are promising.