New research for detecting complex associations between variables with randomness

Yuwen Du; Bin Nie; Jianqiang Du; Xuepeng Zheng; Haike Jin; Yuchao Zhang; Yuwen Du; Bin Nie; Jianqiang Du; Xuepeng Zheng; Haike Jin; Yuchao Zhang

doi:10.3934/mbe.2024059

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 1356-1393. doi: 10.3934/mbe.2024059

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Research article

New research for detecting complex associations between variables with randomness

School of Computer, Jiangxi University of Chinese Medicine, Nanchang 330004, China

Academic Editor: Vladimir Mityushev

Received: 16 July 2023 Revised: 30 October 2023 Accepted: 23 November 2023 Published: 27 December 2023

Many correlation analysis methods can capture a wide range of functional types of variables. However, the influence of uncertainty and distribution status in data is not considered, which leads to the neglect of the regularity information between variables, so that the correlation of variables that contain functional relationship but subject to specific distributions cannot be well identified. Therefore, a novel correlation analysis framework for detecting associations between variables with randomness (RVCR-CA) is proposed. The new method calculates the normalized RMSE to evaluate the degree of functional relationship between variables, calculates entropy difference to measure the degree of uncertainty in variables and constructs the copula function to evaluate the degree of dependence on random variables with distributions. Then, the weighted sum method is performed to the above three indicators to obtain the final correlation coefficient R. In the study, which considers the degree of functional relationship between variables, the uncertainty in variables and the degree of dependence on the variables containing distributions, cannot only measure the correlation of functional relationship variables with specific distributions, but also can better evaluate the correlation of variables without clear functional relationships. In experiments on the data with functional relationship between variables that contain specific distributions, UCI data and synthetic data, the results show that the proposed method has more comprehensive evaluation ability and better evaluation effect than the traditional method of correlation analysis.
- correlation analysis,
- information entropy,
- cubic B-spline,
- copula function,
- analytic hierarchy process
Citation: Yuwen Du, Bin Nie, Jianqiang Du, Xuepeng Zheng, Haike Jin, Yuchao Zhang. New research for detecting complex associations between variables with randomness[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 1356-1393. doi: 10.3934/mbe.2024059

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Abstract

Many correlation analysis methods can capture a wide range of functional types of variables. However, the influence of uncertainty and distribution status in data is not considered, which leads to the neglect of the regularity information between variables, so that the correlation of variables that contain functional relationship but subject to specific distributions cannot be well identified. Therefore, a novel correlation analysis framework for detecting associations between variables with randomness (RVCR-CA) is proposed. The new method calculates the normalized RMSE to evaluate the degree of functional relationship between variables, calculates entropy difference to measure the degree of uncertainty in variables and constructs the copula function to evaluate the degree of dependence on random variables with distributions. Then, the weighted sum method is performed to the above three indicators to obtain the final correlation coefficient R. In the study, which considers the degree of functional relationship between variables, the uncertainty in variables and the degree of dependence on the variables containing distributions, cannot only measure the correlation of functional relationship variables with specific distributions, but also can better evaluate the correlation of variables without clear functional relationships. In experiments on the data with functional relationship between variables that contain specific distributions, UCI data and synthetic data, the results show that the proposed method has more comprehensive evaluation ability and better evaluation effect than the traditional method of correlation analysis.

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