Hierarchical nature of breast cancer progression: Consensus ensemble k-clustering tree reveals the recursive splitting of breast cancer subtypes. At k = 2, the ensemble clustering split the normal samples from the disease samples. At k = 3, the normal cluster remained unchanged and the disease samples split into low grade (pathological grades 1 and 2) and high grade (pathological grades 2 and 3). The optimum number of clusters in the data was seven corresponding to one normal cluster, two low grade clusters and four high grade clusters. Between two k values, the samples did not switch clusters, indicating that the hierarchical structure in the figure is a strong property of the data. In the final disease clusters, samples from the same patient microdissected from DCIS and IDC lesions were found in the same cluster, indicating that the disease subtypes are more heterogeneous than disease progression within a subtype.