Unsupervised Hierarchical Classification Approach for Imprecise Data in the Breast Cancer Detection

(1) Background: in recent years, a lot of the research of statistical methods focused on the classification problem in presence of imprecise data. A particular case of imprecise data is the interval-valued data. Following this research line, in this work a new hierarchical classification technique for multivariate interval-valued data is suggested for diagnosis of the breast cancer; (2) Methods: an unsupervised hierarchical classification method for imprecise multivariate data (called HC-ID) is performed for diagnosis of breast cancer (i.e., to discriminate between benign or malignant masses) and the results have been compared with the conventional (unsupervised) hierarchical classification approach (HC); (3) Results: the application on real data shows that the HC-ID procedure performs better HC procedure in terms of accuracy (HC-ID = 0.80, HC = 0.66) and sensitivity (HC-ID = 0.61, HC = 0.08). In the results obtained by the usual procedure, there is a high degree of false-negative (i.e., benign cancer diagnosis in malignant status) affected by the high degree of variability (i.e., uncertainty) characterizing the worst data.