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A non-parametric method to determine basic probability assignment for classification problems

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Abstract

As an important tool for knowledge representation and decision-making under uncertainty, Dempster-Shafer evidence theory (D-S theory) has been used in many fields. The application of D-S theory is critically dependent on the availability of the basic probability assignment (BPA). The determination of BPA is still an open issue. A non-parametric method to obtain BPA is proposed in this paper. This method can handle multi-attribute datasets in classification problems. Each attribute value of the dataset sample is treated as a stochastic quantity. Its non-parametric probability density function (PDF) is calculated using the training data, which can be regarded as the probability model for the corresponding attribute. The BPA function is then constructed based on the relationship between the test sample and the probability models. The missing attribute values in datasets are treated as ignorance in the framework of the evidence theory. This method does not have the assumption of any particular distribution. As a result, it can be flexibly used in many engineering applications. The obtained BPA can avoid high conflict between evidence, which is desired in data fusion. Several benchmark classification problems are used to demonstrate the proposed method and to compare against existing methods. The constructed classifier based on the proposed method compares well to the state-of-the-art algorithms.

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Notes

  1. UCI Machine Learning Repository: http://archive.ics.uci.edu/ml/datasets/Iris

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Acknowledgments

The author greatly appreciate the reviews’ suggestions. The work is partially supported by National Natural Science Foundation of China (Grant No. 61174022), Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20131102130002), National High Technology Research and Development Program of China (863 Program) (Grant No. 2013AA013801), the open funding project of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University (Grant No. BUAA-VR-14KF-02),General Motors R & D (Project No. ND0044200) and Joint PhD Student Scholarship of SJTU. The support is gratefully acknowledged.

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Authors and Affiliations

  1. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Peida Xu & Xiaoyan Su

  2. Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN, 37235, USA

    Sankaran Mahadevan & Chenzhao Li

  3. School of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Yong Deng

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  1. Peida Xu
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  4. Chenzhao Li
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Correspondence to Yong Deng.

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Xu, P., Su, X., Mahadevan, S. et al. A non-parametric method to determine basic probability assignment for classification problems. Appl Intell 41, 681–693 (2014). https://doi.org/10.1007/s10489-014-0546-9

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