A mathematical programming based procedure for breast cancer classification

In this paper we propose a new procedure for classification based on a hybrid approach. The classification problem is solved by minimizing the distance between the components of each clusters and the centers of the clusters. The determination of the cluster centers is therefore a critical step in our approach and was addressed used the k-means algorithm. Once the centers of each class are determined, the rule of center neighbourhood is applied to assign an element to a class using mathematical programming. The implementation of our hybrid approach was validated on benchmark datasets and applied to an original biological dataset on 84 breast cancer tumours. Each tumour was measured for five parameters corresponding to the expression of five biomarkers (proteins). The obtained classification was discussed using biological knowledge and classical clinical experts' classification of breast tumors.