Fast attribute reduction algorithm based on improved discernibilty matrices

In order to solve the efficiency problem of calculating the attribute reduction based on discernibility matrices,a new algorithm based on counting sorting for computing U/C is provided,and its complexity is cut down to O(|C||U|).Then,the shortcomings of attribution reduction algorithm are analyzed based on discernibility matrices,and the definition of the improved discernibility matrices is presented.Furthermore,core attribute computed by a fast computing core algorithm and an attribute with more frequencies can be used to generate smaller class feature matrices.So a new algorithm based on the improved class feature matrices is proposed,whose worst time complexity and space complexity are cut down to max(O|C|2Σ0≤ij≤K|Di||Dj|)and max(O(|C|Σ0≤ij≤k|Di||Dj|),O(|U|)) respectively.An example is used to illustrate the efficiency of the new algorithm.Experiments show that the new algorithm is efficient for various kinds of data sets.