On the Mean Accuracy of Hierarchical Classifiers

A performance measure is derived for a multiclass hierarchical classifier under the assumption that a maximum likelihood rule is used at each node and the features at different nodes of the tree are class-conditionally statistically independent. The mean accuracy of an estimated hierarchical classifier is then defined as its performance averaged across all classification problems, when an estimated decision rule is used at every node. For a balanced binary decision tree, it is shown that there exists an optimum number of quantization levels for the features which maximizes the mean accuracy. The optimum quantization level increases with the number of training samples per class available to estimate the node decisions and is a nondecreasing function of the depth of the tree.