Strict 2-Surface Proximal Classifier with Application to Breast Cancer Detection in Mammograms

We propose a 2-plane learning method for binary classification, named as the strict 2-surface proximal (S2SP) classifier, by seeking two cross proximal planes based on two strict optimization objectives with a "square of sum" optimization factor, of which the nonlinearity is achieved by employing kernel functions. We apply the S2SP classifier for both linear and nonlinear classification to recognize malignant tumors from a set of 57 regions in mammograms, of which 20 are related to malignant tumors and 37 to benign masses. Ten different feature combinations are studied. Experimental results demonstrate that the linear S2SP classifier provides results comparable to those obtained by Fisher linear discriminant analysis (FLDA). For one feature set (FSs), the linear classification performance was significantly improved to 0.97 by using the S2SP classifier, as compared to the FLDA performance of 0.82, in terms of the area under the receiver operating characteristics (ROC) curve. In the case of nonlinear classification, the S2SP classifier with the triangle kernel provided a perfect performance of 1.0 for all of the ten feature combinations, also evaluated in terms of the area under the ROC curve, but with good robustness limited to the setting of the kernel parameter in a certain range.