Computer-Aided Breast Cancer Diagnosis with Optimal Feature Sets: Reduction Rules and Optimization Techniques

Abstract

This chapter introduces a new method for knowledge extraction from databases for the purpose of finding a discriminative set of features that is also a robust set for within-class classification. Our method is generic and we introduce it here in the field of breast cancer diagnosis from digital mammography data. The mathematical formalism is based on a generalization of the k-Feature Set problem called (α, β)-k-Feature Set problem, introduced by Cotta and Moscato (J Comput Syst Sci 67(4):686-690, 2003). This method proceeds in two steps: first, an optimal (α, β)-k-feature set of minimum cardinality is identified and then, a set of classification rules using these features is obtained. We obtain the (α, β)-k-feature set in two phases; first a series of extremely powerful reduction techniques, which do not lose the optimal solution, are employed; and second, a metaheuristic search to identify the remaining features to be considered or disregarded. Two algorithms were tested with a public domain digital mammography dataset composed of 71 malignant and 75 benign cases. Based on the results provided by the algorithms, we obtain classification rules that employ only a subset of these features.

Serial and parallel kernelization of Multiple Hitting Set parameterized by the Dilworth number, implemented on the GPU

“…Generalization. Motivated by problems in feature selection, optimal cancer medication, and genome-wide association studies, attempts have been undertaken to generalize Weihe's data reduction algorithm to Multiple Hitting Set [19,40,41]. However, Cotta et al [19] only generalize the hyperedge deletion rule (W2).…”