A closed-form reduction of multi-class cost-sensitive learning to weighted multi-class learning

Authors:
Fen Xia;Yan-wu Yang;Liang Zhou;Fuxin Li;Min Cai;Daniel D. Zeng
Affiliations:
The Key Lab of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, China;The Key Lab of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, China;The Key Lab of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, China;The Key Lab of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, China;Department of Computer Science, Beijing Jiaotong University, China;The Key Lab of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, China and Department of Management Information Systems, The University of Arizona, US ...
Venue:
Pattern Recognition
Year:
2009

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Abstract

In cost-sensitive learning, misclassification costs can vary for different classes. This paper investigates an approach reducing a multi-class cost-sensitive learning to a standard classification task based on the data space expansion technique developed by Abe et al., which coincides with Elkan's reduction with respect to binary classification tasks. Using this proposed reduction approach, a cost-sensitive learning problem can be solved by considering a standard 0/1 loss classification problem on a new distribution determined by the cost matrix. We also propose a new weighting mechanism to solve the reduced standard classification problem, based on a theorem stating that the empirical loss on independently identically distributed samples from the new distribution is essentially the same as the loss on the expanded weighted training set. Experimental results on several synthetic and benchmark datasets show that our weighting approach is more effective than existing representative approaches for cost-sensitive learning.