Input dependent misclassification costs for cost-sensitive classifiers

In data mining and in classification specifically, cost issues have been undervalued for a long time, although they are of crucial importance in real-world applications. Recently, however, cost issues have received growing attention, see for example [1,2,3]. Cost-sensitive classifiers are usually based on the assumption of constant misclassification costs between given classes, that is, the cost incurred when an object of class j is erroneously classified as belonging to class i. In many domains, the same type of error may have differing costs due to particular characteristics of objects to be classified. For example, loss caused by misclassifying credit card abuse as normal usage is dependent on the amount of uncollectible credit involved. In this paper, we extend the concept of misclassification costs to include the influence of the input data to be classified. Instead of a fixed misclassification cost matrix, we now have a misclassification cost matrix of functions, separately evaluated for each object to be classified. We formulate the conditional risk for this new approach and relate it to the fixed misclassification cost case. As an illustration, experiments in the telecommunications fraud domain are used, where the costs are naturally data-dependent due to the connection-based nature of telephone tariffs. Posterior probabilities from a hidden Markov model are used in classification, although the described cost model is applicable with other methods such as neural networks or probabilistic networks.