Research on dependent evidence combination based on principal component analysis

Xiaoyan Su; Shuwen Shang; Leihui Xiong; Ziying Hong; Jian Zhong; Xiaoyan Su; Shuwen Shang; Leihui Xiong; Ziying Hong; Jian Zhong

doi:10.3934/mbe.2024214

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 4: 4853-4873. doi: 10.3934/mbe.2024214

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Research on dependent evidence combination based on principal component analysis

1.
School of Automation Engineering, Shanghai University of Electric Power, Shanghai 200090, China
2.
State Grid Nanchang Electric Power Supply Company, Nanchang 330069, China

Received: 09 December 2023 Revised: 30 January 2024 Accepted: 13 February 2024 Published: 29 February 2024

Dempster-Shafer evidence theory, as a generalization of probability theory, is a powerful tool for dealing with a variety of uncertainties, such as incompleteness, ambiguity, and conflict. Because of its advantages in information fusion compared with traditional probability theory, it is widely used in various fields. However, the classic Dempster's combination rule assumes that evidences are independent of each other, which is difficult to satisfy in real life. Ignoring the dependence among the evidences will lead to unreasonable fusion results, and even wrong conclusions. Considering the limitations of D-S evidence theory, this paper proposed a new evidence fusion model based on principal component analysis (PCA) to deal with the dependence among evidences. First, the approximate independent principal components of each information source were obtained based on principal component analysis. Second, the principal component data set was used as a new information source for evidence theory. Third, the basic belief assignments (BBAs) were constructed. As the fundamental construct of evidence theory, a BBA is a probabilistic function corresponding to each hypothesis, quantifying the belief assigned based on the evidence at hand. This function facilitates the synthesis of disparate evidence sources into a mathematically coherent and unified belief structure. After constructing the BBAs, the BBAs were fused and a conclusion was drawn. The case study verified that the proposed method is more robust than several traditional methods and can deal with redundant information effectively to obtain more stable results.
- information fusion,
- evidence theory,
- dependence,
- basic belief assignment,
- principal component analysis
Citation: Xiaoyan Su, Shuwen Shang, Leihui Xiong, Ziying Hong, Jian Zhong. Research on dependent evidence combination based on principal component analysis[J]. Mathematical Biosciences and Engineering, 2024, 21(4): 4853-4873. doi: 10.3934/mbe.2024214

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Abstract

Dempster-Shafer evidence theory, as a generalization of probability theory, is a powerful tool for dealing with a variety of uncertainties, such as incompleteness, ambiguity, and conflict. Because of its advantages in information fusion compared with traditional probability theory, it is widely used in various fields. However, the classic Dempster's combination rule assumes that evidences are independent of each other, which is difficult to satisfy in real life. Ignoring the dependence among the evidences will lead to unreasonable fusion results, and even wrong conclusions. Considering the limitations of D-S evidence theory, this paper proposed a new evidence fusion model based on principal component analysis (PCA) to deal with the dependence among evidences. First, the approximate independent principal components of each information source were obtained based on principal component analysis. Second, the principal component data set was used as a new information source for evidence theory. Third, the basic belief assignments (BBAs) were constructed. As the fundamental construct of evidence theory, a BBA is a probabilistic function corresponding to each hypothesis, quantifying the belief assigned based on the evidence at hand. This function facilitates the synthesis of disparate evidence sources into a mathematically coherent and unified belief structure. After constructing the BBAs, the BBAs were fused and a conclusion was drawn. The case study verified that the proposed method is more robust than several traditional methods and can deal with redundant information effectively to obtain more stable results.

References

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