Multi-objective cost-sensitive attribute reduction

Cost-sensitive learning is both hot and difficult in data mining and machine learning applications. Some research considers only one type of cost. Others convert two or more types of cost into the same unit, and then deal with a single-objective optimization problem. However, in many cases different types of cost cannot be converted. In this paper, we define and tackle multi-objective attribute reduct problem with multiple types of test cost. First, we compute all reducts of a decision system. Then, we separately calculate the money cost and time cost of these reducts and compare them according to the two kinds of test cost. Finally, the worse ones are removed. The remaining reducts form a Pareto optimal solution set. We tested our algorithm with three representative cost distributions on four UCI datasets. Experimental results indicate that a Pareto optimal solution set is usually very small compared with the size of all reducts. Hence our approach is effective in filtering out worse solutions and helping users in scheme selection.