Reduct Generation by Formation of Directed Minimal Spanning Tree Using Rough Set Theory

Abstract

In recent years, dimension of datasets has increased rapidly in many applications which bring great difficulty to data mining and pattern recognition. Also, all the measured variables of these high-dimensional datasets are not relevant for understanding the underlying phenomena of interest. In this paper, firstly, similarities among the attributes are measured by computing similarity factors based on relative indiscernibility relation, a concept of rough set theory. Based on the similarity factors, attribute similarity set AS = {(A $\overset{k}{\rightarrow}$ B) / A, B are attributes and B similar to A with similarity factor k} is formed which helps to construct a directed weighted graph with weights as the inverse of similarity factor k. Then a minimal spanning tree of the graph is generated, from which iteratively most important vertex is selected in reduct set. The iteration completes when the edge set is empty. Thus the selected attributes, from which edges emanate, are the most relevant attributes and are known as reduct. The proposed method has been applied on some benchmark datasets and the classification accuracy is calculated by various classifiers to demonstrate the effectiveness of the method.