Error correction of semantic mathematical expressions based on bayesian algorithm

Xue Wang; Fang Yang; Hongyuan Liu; Qingxuan Shi; Xue Wang; Fang Yang; Hongyuan Liu; Qingxuan Shi

doi:10.3934/mbe.2022255

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 6: 5428-5445. doi: 10.3934/mbe.2022255

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Error correction of semantic mathematical expressions based on bayesian algorithm

1.
School of Cyber Security and Computer, Hebei University, Baoding 071002, China
2.
Institute of Intelligent Image and Document Information Processing, Hebei University, Baoding 071002, China

Academic Editor: Runzhang Xu

Received: 16 November 2021 Revised: 04 March 2022 Accepted: 16 March 2022 Published: 25 March 2022

The semantic information of mathematical expressions plays an important role in information retrieval and similarity calculation. However, a large number of presentational expressions in the presentation MathML format contained in electronic scientific documents do not reflect semantic information. It is a shortcut to extract semantic information using the rule mapping method to convert presentational expressions in presentation MathML format into semantic expressions in the content MathML format. However, the conversion result is prone to semantic errors because the expressions in the two formats do not have exact correspondences in grammatical structures and markups. In this study, a Bayesian error correction algorithm is proposed to correct the semantic errors in the conversion results of mathematical expressions based on the rule mapping method. In this study, the expressions in presentation MathML and content MathML in the NTCIR data set are used as the training set to optimize the parameters of the Bayesian model. The expressions in presentation MathML in the documents collected by the laboratory from the CNKI website are used as the test set to test the error correction results. The experimental results show that the average $ {F_1} $ value is 0.239 with the rule mapping method, and the average $ {F_1} $ value is 0.881 with the Bayesian error correction method, with the average error correction rate is 0.853.
- error correction,
- mathematical expressions,
- Bayesian algorithm,
- presentation MathML,
- content MathML
Citation: Xue Wang, Fang Yang, Hongyuan Liu, Qingxuan Shi. Error correction of semantic mathematical expressions based on bayesian algorithm[J]. Mathematical Biosciences and Engineering, 2022, 19(6): 5428-5445. doi: 10.3934/mbe.2022255

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Abstract

The semantic information of mathematical expressions plays an important role in information retrieval and similarity calculation. However, a large number of presentational expressions in the presentation MathML format contained in electronic scientific documents do not reflect semantic information. It is a shortcut to extract semantic information using the rule mapping method to convert presentational expressions in presentation MathML format into semantic expressions in the content MathML format. However, the conversion result is prone to semantic errors because the expressions in the two formats do not have exact correspondences in grammatical structures and markups. In this study, a Bayesian error correction algorithm is proposed to correct the semantic errors in the conversion results of mathematical expressions based on the rule mapping method. In this study, the expressions in presentation MathML and content MathML in the NTCIR data set are used as the training set to optimize the parameters of the Bayesian model. The expressions in presentation MathML in the documents collected by the laboratory from the CNKI website are used as the test set to test the error correction results. The experimental results show that the average $ {F_1} $ value is 0.239 with the rule mapping method, and the average $ {F_1} $ value is 0.881 with the Bayesian error correction method, with the average error correction rate is 0.853.

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