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Multifractal theory with its applications in data management

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Abstract

The extraction of interesting information from enormous and irregular datasets has always been a significant research topic. For the datasets with irregular distribution and self-similarity, multifractal theory is the most appreciated approach and has been successfully applied in many fields, such as financial analysis, image processing, medical diagnosis, earthquake study, etc. In this paper, we make a detailed analysis and summary on three main functions, namely multifractal structure diagnosis, tendency and singularity analysis. Finally, some experiments based on oil prices data and spatial physical data are carried out to validate its performance effectively.

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Acknowledgments

This research was partially supported by the National Natural Science Foundation of China (Nos. 51379049), the Fundamental Research Funds for the Central Universities of China (Nos. HEUCFX41302) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Heilongjiang Province (Nos. LC2013C21). The authors would like to thank the anonymous reviewers for improving the quality of this article.

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  1. College of Automation, Harbin Engineering University, Harbin , 150001, China

    Yuxin Zhao, Shuai Chang & Chang Liu

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  1. Yuxin Zhao
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Correspondence to Yuxin Zhao.

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Zhao, Y., Chang, S. & Liu, C. Multifractal theory with its applications in data management. Ann Oper Res 234, 133–150 (2015). https://doi.org/10.1007/s10479-014-1599-1

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