Feature selection for set-valued data based on D–S evidence theory

Feature selection is one basic and critical technology for data mining, especially in current “big data era”. Rough set theory is sensitive to noise in feature selection due the stringent condition of an equivalence relation. However, D–S evidence theory is flexible to measure uncertainty of information. In this paper, we introduce robust feature evaluation metrics “belief function” and “plausibility function” into feature selection algorithm to avoid the defect that classification effect is affected by noise such as missing values, confusing data, etc. Firstly, similarity between information values in a set-valued information system (SVIS) is introduced and a variable parameter to control the similarity of samples is given. Secondly, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}-lower and θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}-upper approximations in an SVIS are put forward. Then, the concepts of θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}-belief function, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}-plausibility function, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}-belief reduction and θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}-plausibility reduction are given. Moreover, several feature selection algorithms based on the D–S evidence theory in an SVIS are proposed. Experimental results and statistical test show that the proposed metric is insensitive to noise because it comprehensively considers the evidence at all levels, and the proposed algorithms are more robust than several state-of-the-art feature selection algorithms.