Feature selection for multiset-valued data based on fuzzy conditional information entropy using iterative model and matrix operation

Abstract

Multiset-valued data is a powerful tool to deal with missing feature values. Classical rough set theory is sensitive to noise in classification learning due to the stringent condition of equivalence relation. Thus, a class of fuzzy relations can be introduced to describe the similarity between samples in multiset-valued data. However, these fuzzy relations have deficiencies when they are used in the computation of fuzzy conditional information entropy. This paper proposes a new model for multiset-valued data by introducing two variable parameters: one controls the similarity between samples, the other dominates the distance between feature values. This model employs the iterative computation strategy to define fuzzy conditional information entropy that is computing by matrix. The notions of three fuzzy information entropies in a multiset-valued decision information system (MVDIS) are put forward. For measuring any added feature, the significance based on fuzzy conditional information entropy is introduced. Moreover, fuzzy conditional information entropy iterative model (FCIEI-model) is presented. Finally, feature selection in an MVDIS based on FCIEI-model and matrix operation is researched, and the relevant algorithm (denoted as FCIEIM-MO algorithm) is proposed. The experimental results demonstrate that FCIEIM-MO algorithm possesses good robustness and is superior to some feature selection algorithms. The experimental results demonstrate that FCIEIM-MO algorithm possesses good robustness and exhibit better performance compared with some feature selection algorithms.