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A novel approach to simplifying dynamic data through multi-scale decision systems

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Abstract

Optimal scale selection of multi-scale decision system (MDS) is an effective method to reduce data complexity, and there are a series of detailed analysis methods. However, the optimal scale combination (OSC) of MDS is often not unique, and there is no comparison method between OSCs. Meanwhile, multi-scale data is difficult to obtain, there is no effective method to convert single-scale data into MDS. Therefore, we propose a method for simplifying dynamic data by converting it to MDS and selecting the best OSC of it. Firstly, we propose the concepts of classes number vector and classes number matrix from the perspective of the number of equivalence classes. And we further introduce the generation methods of MDS and generalized MDS using clustering methods, respectively. Secondly, for the problem where the OSC cannot be compared in MDS, we transform it into a multi-attribute decision making problem and use relevant decision methods to obtain the best OSC, which is remembered as global OSC. Subsequently, we propose the concepts of local OSC and global OSC and design corresponding algorithms to find the global OSC. Furthermore, we combine the above two types of algorithms to propose a method for simplifying dynamic single scale data and consider the impact of dynamic data on the model. Finally, we validate the effectiveness of the proposed method through numerical experiments.

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Acknowledgements

The authors are extremely grateful to the editor and anonymous referees for their valuable comments and helpful suggestions which helped to improve the presentation of this paper.

Funding

This research was supported by the National Natural Science Foundation of China (Grant no. 12101500) and the Natural Science Foundation of Shaanxi Province (Grant no. 2023-JC-QN-0062) and the Chinese Universities Scientific Fund (Grant nos. 2452018054 and 2452022370).

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Authors and Affiliations

  1. College of Science, Northwest A& F University, YangLing, 712100, People’s Republic of China

    Tianyu Wang, Shuai Liu & Bin Yang

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  1. Tianyu Wang
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  2. Shuai Liu
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  3. Bin Yang
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Contributions

Tianyu Wang: Conceptualization, Writing—original draft. Shuai Liu: Methodology, Investigation, Writing—review & editing. Bin Yang: Methodology, Investigation, Writing—review & editing.

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Correspondence to Shuai Liu or Bin Yang.

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Wang, T., Liu, S. & Yang, B. A novel approach to simplifying dynamic data through multi-scale decision systems. Comp. Appl. Math. 43, 254 (2024). https://doi.org/10.1007/s40314-024-02760-0

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