Clustering of the interlocking rings dataset by AutoSOME with a statistical confidence metric. The classic and challenging dataset consisting of two orthogonal interlocking rings  was analyzed using AutoSOME. (A) Clustering of the rings dataset with increasing ensemble runs, where different colors represent output clusters. Complete resolution of the two rings was achieved following 25 ensemble iterations. (B) A cluster confidence metric projected onto the rings dataset after 25 ensemble runs. The confidence metric for cluster membership is based on the fuzzy clustering ensemble produced by AutoSOME, with conf(x, j) = 100 (blue) representing the case where data point x is always in cluster j, and conf(x, j) = 0 (red) representing the case where data point x is never placed in cluster j. See Ensemble averaging in Methods for details of the AutoSOME cluster confidence procedure.