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Detrended partial cross-correlation analysis-random matrix theory for denoising network construction

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Abstract

A denoised complex network framework employing a detrended partial cross-correlation analysis-based coefficient for achieving the intrinsic scale-dependent correlations between each pair of variables is developed to explore the interrelatedness of multiple nonstationary variables in the real-world. In doing this, we start with introducing the detrended partial cross-correlation coefficient into random matrix theory, and executing a denoising process through correlation matrix reconfiguration, which is followed by utilizing the denoised correlation matrix to construct a planar maximally filtered graph network. It allows us assess the interactions among complex objects more accurately. The effectiveness of our proposed method is validated through the numerical experiments simulating the eigenvalue distribution, and the results show that our method accurately locates the maximum eigenvalue at a specific scale, but existing methods fail to achieve. As a practical application, we also apply the proposed denoising network framework to investigate the co-movement behavior of PM\(_{2.5}\) air pollution of North China and the linkage of commodity futures prices in China. The results show that the denoising process significantly enhances the information content of the network, revealing several interesting insights regarding network properties.

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Availability of data and materials

The PM\(_{2.5}\) data and China’s commodity futures data used in this study are available from the corresponding author on reasonable request.

Code Availability

The code is available from the corresponding author on reasonable request.

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Acknowledgements

The author wishes to thank the anonymous reviewers and the handling editor for their constructive comments and suggestions, which led to a great improvement to the presentation of this work.

Funding

This work was partially supported by the National Natural Science Foundation of China (Grant nos. 12371088, 12471489) and the Key Research Project of the Department of Education of Hunan Province (CN) (Grant no. 22A0135).

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Contributions

All authors contributed to the study conception and design. Material preparation and data collection were performed by Z Zhang and M Wang. Visualization and analysis were performed by F Wang and Z Zhang. Method design were partially performed by F Wang and G Ling. The first draft of the manuscript was written by F Wang and all authors commented on previous versions of the manuscript. The revision was made by F Wang and Z Zhang. All authors read and approved the final manuscript.

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Correspondence to Fang Wang.

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Appendix A: 42 China’s commodity futures

Appendix A: 42 China’s commodity futures

Table 6 42 China’s commodity futures. All contracts are continuous main contracts

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Wang, F., Zhang, Z., Wang, M. et al. Detrended partial cross-correlation analysis-random matrix theory for denoising network construction. Appl Intell 55, 16 (2025). https://doi.org/10.1007/s10489-024-05975-0

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