A Bound on Kappa-Error Diagrams for Analysis of Classifier Ensembles

Kappa-error diagrams are used to gain insights about why an ensemble method is better than another on a given data set. A point on the diagram corresponds to a pair of classifiers. The x-axis is the pairwise diversity (kappa), and the y-axis is the averaged individual error. In this study, kappa is calculated from the 2 × 2 correct/wrong contingency matrix. We derive a lower bound on kappa which determines the feasible part of the kappa-error diagram. Simulations and experiments with real data show that there is unoccupied feasible space on the diagram corresponding to (hypothetical) better ensembles, and that individual accuracy is the leading factor in improving the ensemble accuracy.