  Many real-world data mining applications need varying cost for different
types of classification errors and thus call for cost-sensitive classification
algorithms. Existing algorithms for cost-sensitive classification are
successful in terms of minimizing the cost, but can result in a high error rate
as the trade-off. The high error rate holds back the practical use of those
algorithms. In this paper, we propose a novel cost-sensitive classification
methodology that takes both the cost and the error rate into account. The
methodology, called soft cost-sensitive classification, is established from a
multicriteria optimization problem of the cost and the error rate, and can be
viewed as regularizing cost-sensitive classification with the error rate. The
simple methodology allows immediate improvements of existing cost-sensitive
classification algorithms. Experiments on the benchmark and the real-world data
sets show that our proposed methodology indeed achieves lower test error rates
and similar (sometimes lower) test costs than existing cost-sensitive
classification algorithms. We also demonstrate that the methodology can be
extended for considering the weighted error rate instead of the original error
rate. This extension is useful for tackling unbalanced classification problems.
