Figure 3.

Example ROC curves to assess cluster overlap. An ROC curve (B and D, left side) is drawn as a function of moving outward from a cluster center and counting the proportion of cluster members (blue points) encountered along the y-axis versus the proportion of non-cluster members (red points) encountered along the x-axis. The collection of distances from every point within a cluster and every point outside a cluster is binned and used to create the distance histograms (B and D, right side). Shown in red is the distance histogram for cluster members and cluster non-members are shown in blue. Two extreme cases are exemplified in this figure. (A) Example expression data falling into two completely discrete clusters highlighted in red and blue. (B) The corresponding ROC curve (left) and distance histograms (right) for the sample data shown in (A). Note that since all cluster members are encountered before any non-cluster members the area under the ROC curve is 1.0. The distance histograms also show this perfect separation. (C) Example expression data falling into two completely overlapping clusters highlighted in red and blue. (D) The corresponding ROC curve (left) and distance histograms (right) for sample data shown in (B). Note that since cluster members and non-cluster members are encountered at an equal rate as a function of distance from the cluster center, the ROC curve approximates the line x = y and the area under the ROC curve is 0.5. This overlap is also highlighted in the distance histograms because the distributions of distances for cluster members completely overlap with that of the distribution of distances for non-cluster members.