Outcomepurity

Outcomepurity is a metric used in data analysis to quantify the homogeneity of outcomes within predefined groups, such as clusters, bins, or leaves of a decision tree. The premise is that a group with a single dominant outcome is more predictable, whereas mixed outcomes reduce reliability.

Definition and calculation: For a dataset partitioned into K groups G1 to GK, and m possible outcome classes, let p_{i,c} be the proportion of items in group i with outcome c. The group purity is max_c p_{i,c}. Outcomepurity is defined as OC = sum_{i=1}^K (|Gi|/N) * max_c p_{i,c}, where N is the total number of items. The value ranges from 1/m (completely mixed within every group) up to 1 (each group contains only one outcome).

Interpretation and relation to other measures: OC reflects the average probability that a randomly chosen item from a group belongs to the group’s majority outcome. Higher values indicate greater within-group predictability. Outcomepurity is related to traditional purity measures used in clustering and classification, but it emphasizes outcome homogeneity within partitions rather than overall error rates.

Applications and limitations: It is used to evaluate and compare partitions produced by clustering, binning, or decision-tree pruning. It can guide feature engineering by favoring splits that increase within-group outcome consistency. Limitations include sensitivity to group size, potential bias with imbalanced classes, and a focus on within-group homogeneity that may ignore global performance. The metric also depends on how the data are partitioned, so it should be used alongside other performance indicators.

Related metrics: purity, Gini impurity, and entropy. Outcomepurity is a conceptual measure with varying informal definitions in practice.