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Advances in Artificial Intelligence
Volume 2009 (2009), Article ID 134807, 13 pages
Research Article

A New Information Measure Based on Example-Dependent Misclassification Costs and Its Application in Decision Tree Learning

Faculty of Electrical Engineering and Computer Science, University of Technology Berlin, Sekr. FR 5-8, Franklinstraße 28/29, D-10587 Berlin, Germany

Received 29 December 2008; Revised 2 June 2009; Accepted 21 July 2009

Academic Editor: Rattikorn Hewett

Copyright © 2009 Fritz Wysotzki and Peter Geibel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This article describes how the costs of misclassification given with the individual training objects for classification learning can be used in the construction of decision trees for minimal cost instead of minimal error class decisions. This is demonstrated by defining modified, cost-dependent probabilities, a new, cost-dependent information measure, and using a cost-sensitive extension of the CAL5 algorithm for learning decision trees. The cost-dependent information measure ensures the selection of the (local) next best, that is, cost-minimizing, discriminating attribute in the sequential construction of the classification trees. This is shown to be a cost-dependent generalization of the classical information measure introduced by Shannon, which only depends on classical probabilities. It is therefore of general importance and extends classic information theory, knowledge processing, and cognitive science, since subjective evaluations of decision alternatives can be included in entropy and the transferred information. Decision trees can then be viewed as cost-minimizing decoders for class symbols emitted by a source and coded by feature vectors. Experiments with two artificial datasets and one application example show that this approach is more accurate than a method which uses class dependent costs given by experts a priori.