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Comparative Analysis of Multi-fractal Data Missing Processing Methods

Received: 4 July 2019     Published: 29 July 2019
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Abstract

Data missing often affects the characteristics of the sequence. Using appropriate methods to process the missing data is the premise and guarantee to obtain high quality information. In this study, a fractal interpolation method is proposed to fill the missing data with self-similar feature sequences. Two sets of binomial multifractal sequences with parameters of 0.25 and 0.35 are taken as the research objects, and the Hurst index value of the sequence after filling processing is calculated by MF-DMA, which verifies the practicability of the fractal interpolation filling method. At the same time, the method is applied to multi-fractal sequences with missing rates of 10%, 15% and 20% respectively, and compared with the filling effects of deletion method and random filling method, then, the applicability of the three methods is obtained. The results show that, for binomial multifractal sequences with different missing ratios, the Hurst index of the sequence processed by fractal interpolation has the highest degree of fitting with the theoretical value, its effect of repairing the fractal sequence is better than the other two methods, and has a good application prospect.

Published in Applied and Computational Mathematics (Volume 8, Issue 2)
DOI 10.11648/j.acm.20190802.14
Page(s) 44-49
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Multi-fractal, Fractal Interpolation Filling, MF-DMA, Hurst Index

References
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[7] Chen Peng, Zheng Manxian. Multifractal Characteristics and Conduction Effect of International Commodity Price Fluctuation [J]. Price Theory and Practice, 2018 (10): 81-84.
[8] Zhang Yong, Guan Wei. Multifractal Analysis of Traffic Flow Time Series [J]. Computer Engineering and Applications, 2010, 46 (29): 23-25.
[9] Chen Y, Xiang Z, Dong Y, et al. Multi-Fractal Characteristics of Mobile Node’s Traffic in Wireless Mesh Network with AODV and DSDV Routing Protocols [J]. Wireless Personal Communications, 2011, 58 (4): 741-757.
[10] Gu G F, Zhou W X. Detrending moving average algorithm for multifractals [J]. Physical Review E. 2010, 82 (1): 011136.
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[12] Li Q, Cao G, Xu W. Relationship research between meteorological disasters and stock markets based on a multifractal detrending moving average algorithm [J]. International Journal of Modern Physics B, 2018, 32 (01): 1.
[13] Amo E D, Carrillo M D, Sánchez J F. PCF self-similar sets and fractal interpolation [J]. Mathematics & Computers in Simulation, 2013, 92 (6): 28-39.
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  • APA Style

    Lai Simin, Wan Li, Zeng Xiangjian. (2019). Comparative Analysis of Multi-fractal Data Missing Processing Methods. Applied and Computational Mathematics, 8(2), 44-49. https://doi.org/10.11648/j.acm.20190802.14

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    ACS Style

    Lai Simin; Wan Li; Zeng Xiangjian. Comparative Analysis of Multi-fractal Data Missing Processing Methods. Appl. Comput. Math. 2019, 8(2), 44-49. doi: 10.11648/j.acm.20190802.14

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    AMA Style

    Lai Simin, Wan Li, Zeng Xiangjian. Comparative Analysis of Multi-fractal Data Missing Processing Methods. Appl Comput Math. 2019;8(2):44-49. doi: 10.11648/j.acm.20190802.14

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  • @article{10.11648/j.acm.20190802.14,
      author = {Lai Simin and Wan Li and Zeng Xiangjian},
      title = {Comparative Analysis of Multi-fractal Data Missing Processing Methods},
      journal = {Applied and Computational Mathematics},
      volume = {8},
      number = {2},
      pages = {44-49},
      doi = {10.11648/j.acm.20190802.14},
      url = {https://doi.org/10.11648/j.acm.20190802.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20190802.14},
      abstract = {Data missing often affects the characteristics of the sequence. Using appropriate methods to process the missing data is the premise and guarantee to obtain high quality information. In this study, a fractal interpolation method is proposed to fill the missing data with self-similar feature sequences. Two sets of binomial multifractal sequences with parameters of 0.25 and 0.35 are taken as the research objects, and the Hurst index value of the sequence after filling processing is calculated by MF-DMA, which verifies the practicability of the fractal interpolation filling method. At the same time, the method is applied to multi-fractal sequences with missing rates of 10%, 15% and 20% respectively, and compared with the filling effects of deletion method and random filling method, then, the applicability of the three methods is obtained. The results show that, for binomial multifractal sequences with different missing ratios, the Hurst index of the sequence processed by fractal interpolation has the highest degree of fitting with the theoretical value, its effect of repairing the fractal sequence is better than the other two methods, and has a good application prospect.},
     year = {2019}
    }
    

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  • TY  - JOUR
    T1  - Comparative Analysis of Multi-fractal Data Missing Processing Methods
    AU  - Lai Simin
    AU  - Wan Li
    AU  - Zeng Xiangjian
    Y1  - 2019/07/29
    PY  - 2019
    N1  - https://doi.org/10.11648/j.acm.20190802.14
    DO  - 10.11648/j.acm.20190802.14
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 44
    EP  - 49
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20190802.14
    AB  - Data missing often affects the characteristics of the sequence. Using appropriate methods to process the missing data is the premise and guarantee to obtain high quality information. In this study, a fractal interpolation method is proposed to fill the missing data with self-similar feature sequences. Two sets of binomial multifractal sequences with parameters of 0.25 and 0.35 are taken as the research objects, and the Hurst index value of the sequence after filling processing is calculated by MF-DMA, which verifies the practicability of the fractal interpolation filling method. At the same time, the method is applied to multi-fractal sequences with missing rates of 10%, 15% and 20% respectively, and compared with the filling effects of deletion method and random filling method, then, the applicability of the three methods is obtained. The results show that, for binomial multifractal sequences with different missing ratios, the Hurst index of the sequence processed by fractal interpolation has the highest degree of fitting with the theoretical value, its effect of repairing the fractal sequence is better than the other two methods, and has a good application prospect.
    VL  - 8
    IS  - 2
    ER  - 

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Author Information
  • School of Mathematics and Information Science, Guangzhou University, Guangzhou, China

  • School of Mathematics and Information Science, Guangzhou University, Guangzhou, China

  • School of Mathematics and Information Science, Guangzhou University, Guangzhou, China

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