Comparative Analysis of Multi-fractal Data Missing Processing Methods

Lai Simin; Wan Li; Zeng Xiangjian

doi:doi:10.11648/j.acm.20190802.14

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Comparative Analysis of Multi-fractal Data Missing Processing Methods

Lai Simin, Wan Li, Zeng Xiangjian

Published in Applied and Computational Mathematics (Volume 8, Issue 2)

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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[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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[17]	Mali P, Mukhopadhyay A. Multifractal characterization of gold market: A multifractal detrended fluctuation analysis [J]. Physica A: Statistical Mechanics and its Applications, 2014, 413: 361-372.
[18]	Xie W J, Han R Q, Jiang Z Q, et al. Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures [J]. EPL (Europhysics Letters), 2017, 119 (4): 48008.

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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

Lai Simin

School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
Wan Li

School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
Zeng Xiangjian

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

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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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download