Grouping by Mixture of Normals for Breast Cancer in Two Groups, Benign and Malignant

The diagnosis of cancer cells from biopsies is mainly based on the analysis of the morphological changes of the nuclear structure as the increase in nuclear size, which probably occurs due to the deregulation of cell cycle, as well as the cell growth. The increase of the nuclear size is observed in biopsies of patients with benign and malignant diagnosis. A radius_mean variable (mean of distances from the center to points on the perimeter), related with the increase of nuclear size in patients with benign and malignant diagnosis, is studied in this work. An analysis of this variable proves, by the algorithm of unsupervised learning, Expectation–maximization (EM). That said variable has a mixture of normals with two components type behavior. Such an algorithm is able to discriminate the data in two groups (malignant and benign), the model shows a 97.8% of coincidence for benign cases and 66.5% for malignant cases.