Feature selection in a discrete feature space based on fuzzy conditional information entropy iterative model and matrix operation

Abstract

A discrete feature space consists of the set of samples, the set of categorical attributes (features) describing the samples and a decision attribute. Generally, many feature selection algorithms for a discrete feature space are based on the lower approximation or information entropy. However, the calculation of the lower approximation is more cumbersome, and information entropy may result based on equivalence class in a poor selection of features. This paper proposes feature selection algorithm for a discrete feature space by using fuzzy conditional information entropy iterative strategy and matrix operation. Firstly, the fuzzy symmetry relation induced by a discrete feature space is defined. Then, fuzzy conditional and joint information entropy for a discrete feature space are presented, and some properties are obtained. Subsequently, fuzzy conditional information entropy iterative model (FCIEI-model) is proposed. Moreover, difference, block diagonal, and decision block diagonal matrices are introduced. Next, a feature selection algorithm (denoted as FDM-algorithm) on account of FCIEI-model and matrix operations is designed and its time complexity is analyzed. Finally, the performance of the algorithm is evaluated through a series of experiments. The results show that the given algorithm is better than the existing algorithms.