A new reduction algorithm - difference-similitude matrix

In this paper, we present a new reduction algorithm. The main idea comes from showroom\´s discernibility matrix. Discernibility matrix only takes advantage of the difference of the condition attributes of the objects. But we also take the similitude of the condition attributes into account. By analyzing the difference and similitude of the conditional attributes of IS, the DSM (difference-similitude matrix) is formed. By defining the significance of the attributes and the uniformity of the objects, and analyzing the elements m_ij^d & m_ij^sin DSM, a new data reduction algorithm is put forward. The algorithm can obtain as minimal rules as possible while preserving the consistency of classifications. This reduction algorithm based on DSM is employed to analyze databases from UCI. Through comparing the reduction result of DSM algorithm and the discernibility matrix algorithm, it shows that DSM algorithm can obtain higher reduction rate of objects. Tested by "leave-one-out", DSM algorithm is proved to have higher correctness.