Risk Estimation for Hierarchical Classifier

We describe the Hierarchical Classifier (HC), which is a hybrid architecture [1] built with the help of supervised training and unsu-pervised problem clustering. We prove a theorem giving the estimationˆR of HC risk. The proof works because of an improved way of computing cluster weights, introduced in this paper. Experiments show thatˆR is correlated with HC real error. This allows us to usê R as the approximation of HC risk without evaluating HC subclusters. We also show howˆR can be used in efficient clustering algorithms by comparing HC architectures with different methods of clustering.