A weighted rough set approach for cost-sensitive learning

In many real-world applications, the costs of different errors are often unequal. Therefore, the inclusion of costs into learning, also named costsensitive learning, has been regarded as one of the most relevant topics of future machine learning research. Rough set theory is a powerful mathematic tool dealing with inconsistent information for attribute dependence analysis, knowledge reduction and decision rule extraction. However, it is insensitive to the costs of misclassification due to the absence of a mechanism of considering the subjective knowledge. This paper discusses problems connected with introducing the subjective knowledge into rough set learning and proposes a weighted rough set approach for cost-sensitive learning. In this method, weights are employed to represent the subjective knowledge of costs and a weighted information system is defined firstly. With the introduction of weights, weighted attribute dependence analysis is carried out and an index of weighted approximate quality is given. Furthermore, weighted attribute reduction algorithm and weighted rule extraction algorithm are designed to find the reducts and rules with the consideration of weights. Based on the proposed weighted rough set, a series of comparing experimentations with several familiar general techniques on cost-sensitive learning are constructed. The results show that the approach of weighted rough set produces averagely the minimum misclassification costs and the lowest high cost errors.