Pairwise Rayleigh Quotient Classifier with Application to the Analysis of Breast Tumors

T. Mu, A.K. Nandi (UK), and R.M. Rangayyan (Canada)


Supervised learning, pairwise constraints, Rayleigh quotient, generalized eigenvalue problem, breast cancer, breast tumors


In this paper, we propose a new supervised learning method for binary classification, named the pairwise Rayleigh quotient (PRQ) classifier, in which the nonlinearity is achieved by employing kernel functions. The PRQ classifier generates a Rayleigh quotient based on a set of pairwise constraints, which consequently leads to a generalized eigenvalue problem with low complexity of implementation. The PRQ classifier is applied in the original feature space for linear classification, as well as in a transformed feature space by employing the triangle kernel for nonlinear classification, to discriminate malignant breast tumors from a set of 57 regions in mammograms, of which 20 are related to malignant tumors and 37 to benign masses. Nine different feature combinations are studied. Experimental results demonstrate that the proposed linear PRQ classifier provides results comparable to those obtained with Fisher linear discriminant analysis (FLDA). In the case of nonlinear classification, the PRQ classifier with the triangle kernel provides a perfect performance of 1.0 for all of the nine feature combinations evaluated in terms of the area under the receiver operating characteristics curve, but with good robustness limited to the setting of the kernel parameter in a certain range. We propose a measure of robustness to evaluate the PRQ classifier.

Important Links:

Go Back