Test-cost-sensitive attribute reduction based on neighborhood rough set

Recent research in machine learning and data mining has produced a wide variety of algorithms for cost-sensitive learning. Most existing rough set methods on this issue deal with nominal attributes. This is because that nominal attributes produce equivalent relations and therefore are easy to process. However, in real applications, datasets often contain numerical attributes. As we know, numerical attributes are more complex than nominal ones and require more computational resources. Consequently, respective learning tasks are more challenging. This paper deals with test-cost-sensitive attribute reduction for numerical valued decision systems. Neighborhood rough set achieved success in numerical data processing, hence we adopt the model to define the minimal test cost reduct problem. Due to the complexity of the new problem, heuristic algorithms are needed to find a sub-optimal solution. We propose one kind of heuristic information, which is the sum of the positive region and weighted test cost. When the test cost is not considered, the information degrades to the positive region, which is the most commonly used one in classical rough set. Three metrics are adopted to evaluate the performance of reduction algorithms from a statistical viewpoint. Experimental results show that the proposed method takes advantages of test costs and therefore produces satisfactory results.