Fast Algorithm for Neighborhood Entropy and Neighborhood Mutual Information Based on Column Sorting

Abstract

Aiming at the problem that the high computational complexity of calculating information entropy and mutual information of a neighborhood rough set, a fast calculation method based on data sorting was proposed to estimate neighborhood mutual information speedily. This method can reduce the computational complexity of neighborhood entropy from O(n2) to O(nlogn). Under this premise, the method can calculate the approximation of the joint neighborhood entropy by infinite-norm-calculated neighborhood relation, thus to estimate the neighborhood mutual information quickly. For the reason that the method is based on neighborhood entropy, it is also effective for mixed data. Experimental results show that this method can significantly shorten the computational time of neighborhood mutual information and ensure high approximation quality when using large-scale data sets.