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Measures of uncertainty for partially labeled categorical data based on an indiscernibility relation: an application in semi-supervised attribute reduction

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Abstract

In many practical applications of machine learning, only part of data is labeled because the cost of assessing class label is relatively high. This paper concentrates on measures of uncertainty for a partial label categorical decision information system (p-CDIS), and considers an application to semi-supervised attribute reduction. Firstly, two decision information systems (DISs) can be induced by a p-CDIS (U, C, d): one is for a decision information system for labeled categorical data \((U^l,C,d)\) and the other one is a decision information system for unlabeled categorical data \((U^u,C,d)\), and the missing rate of labels in (U, C, d) is introduced. In view of partial label data, the existential research did not take into account the missing rate of labels and only considered one importance of each attribute subset. Then, four importance of an attribute subset \(P\subseteq C\) in (U, C, d) are defined based on an indiscernibility relation. They are the weighted sum of the importance of P in \((U^l,C,d)\) and \((U^u,C,d)\) determined by the missing rate of labels. These four importance can be regarded as four uncertainty measurements (UMs) for (U, P, d). Next, numerical experiments and statistical tests are carried out on 15 datasets of UCI to demonstrate four UMs’ advantages and disadvantages. Finally, as an application for UM in p-CDIS, two better UMs are used as semi-supervised attribute reduction and two corresponding algorithms are designed that can automatically adapt to different missing rates of labels. The experimental results show the feasibility and superiority of the designed algorithms.

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Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for their valuable comments and suggestions, which have helped immensely in improving the quality of the paper. This work is supported by Natural Science Foundation of Guangxi Province (2021GXNSFAA220114, 2020GXNSFAA159155) and Guangxi First-class Discipline Statistics Construction Project Fund.

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Authors and Affiliations

  1. Center for Applied Mathematics of Guangxi, Yulin Normal University, Yulin, Guangxi, 537000, P.R. China

    Jiali He & Pei Wang

  2. School of Artificial Intelligence, Guangxi Minzu University, Nanning, Guangxi, 530006, P.R. China

    Gangqiang Zhang

  3. School of Computer Science and Engineering, Yulin Normal University, Yulin, Guangxi, 537000, P.R. China

    Dan Huang

  4. School of Big Data and Artificial Intelligence, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, P.R. China

    Guangji Yu

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  1. Jiali He
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  2. Gangqiang Zhang
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  4. Pei Wang
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  5. Guangji Yu
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Contributions

Jiali He: Methodology, Writing-Original draft; Gangqiang Zhang: Software, Editing, Investigation; Dan Huang: Data curation; Pei Wang: Validation; Guangji Yu: Software, Investigation.

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Correspondence to Gangqiang Zhang or Guangji Yu.

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He, J., Zhang, G., Huang, D. et al. Measures of uncertainty for partially labeled categorical data based on an indiscernibility relation: an application in semi-supervised attribute reduction. Appl Intell 53, 29486–29513 (2023). https://doi.org/10.1007/s10489-023-05078-2

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