Knowledge reduction is a key issue in data mining. In order to simplify the covering approximation space and mining rules from it, Zhu proposed a reduction of covering approximation space which does not rely on any prior given concept or decision. Unfortunately, it could only reduce absolutely redundant knowledge. To reduce relatively redundant knowledge with respect to a given concept or decision, the problem of relative reduction is studied in this paper. The condition in which an element of a covering is relatively reducible is discussed. By deleting all relatively reducible elements of a covering approximation space, one can get the relative reduction of the original covering approximation space. Moreover, one can find that the covering lower and upper approximations in the reduced space are the same as in the original covering space. That is to say, it does not decrease the classification ability of a covering approximation space to reduce the relatively reducible elements in it. In addition, combining absolute reduction and relative reduction, an algorithm for knowledge reduction of covering approximation space is developed. It can reduce not only absolutely redundant knowledge, but also relatively redundant knowledge. It is significant for the following-up steps of data mining.
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- Knowledge Reduction of Covering Approximation Space
- Springer Berlin Heidelberg
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