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Multidimensional fractal scaling analysis using higher order moving average polynomials and its fast algorithm

Ju, Hanqiu Honda, Naoki Yoshimura, Shige H. Kaneko, Miki Shigematsu, Taiki Kiyono, Ken 京都大学 DOI:10.1016/j.sigpro.2023.108997

2023.07

概要

The detrending moving average (DMA) analysis demonstrates excellent performance for the characterization of long-range correlations and fractal scaling and is performed in various research fields. The conventional DMA with a simple moving average can remove linear trends embedded in the observed time series. To improve the detrending ability of the DMA, higher-order DMA including a higher order polynomial detrending was also introduced using the Savitzky-Golay filter and its fast implementation algorithm was developed. However, the higher-order DMA applicable to higher dimensional data is yet to be well established. As the data dimension increases, an increase in the computational cost becomes a problem that needs to be resolved. Further, the implementation of the higher order DMA is a time-consuming procedure. To resolve this problem, we here proposed a fast algorithm for multidimensional DMA with higher order polynomial detrending. In the proposed algorithm, to reduce the computational complexity, parallel translation and recurrence techniques are introduced. Monte Carlo experiments for two-dimensional data show that the computational time of the proposed algorithm is approximately proportional to the cubic of the data length, whereas the computational time of the conventional implementation is approximately proportional to the quartic of the data length. Moreover, we evaluate the estimation accuracy of the Hurst exponent of the proposed method. Finally, we demonstrate the possible application of the proposed method by estimating the Hurst exponent of images.

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参考文献

[27]

[1] M. Kobayashi, T. Musha, 1/F fluctuation of heartbeat period, IEEE Trans.

Biomed. Eng. 6 (1982) 456–457.

[2] C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger,

Mosaic organization of dna nucleotides, Phys. Rev. E 49 (2) (1994) 1685.

[3] C.-K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, Quantification of scaling

exponents and crossover phenomena in nonstationary heartbeat time series,

Chaos 5 (1) (1995) 82–87.

[4] K. Kiyono, Z.R. Struzik, N. Aoyagi, F. Togo, Y. Yamamoto, Phase transition in

a healthy human heart rate, Phys. Rev. Lett. 95 (2005) 058101, doi:10.1103/

PhysRevLett.95.058101.

[5] R.N. Mantegna, H.E. Stanley, Introduction to Econophysics: Correlations and

Complexity in Finance, Cambridge university press, 1999.

[6] J. Alvarez-Ramirez, E. Rodriguez, J.C. Echeverría, Detrending fluctuation analysis

based on moving average filtering, Physica A 354 (2005) 199–219.

[7] Y. Wang, Y. Wei, C. Wu, Detrended fluctuation analysis on spot and futures markets of west texas intermediate crude oil, Physica A 390 (5) (2011)

864–875.

[8] D. Rybski, S.V. Buldyrev, S. Havlin, F. Liljeros, H.A. Makse, Scaling laws of human interaction activity, Proc. Natl. Acad. Sci. 106 (31) (2009) 12640–12645.

[9] C. Fan, J.-L. Guo, Y.L. Zha, Fractal analysis on human dynamics of library loans,

Physica A 391 (24) (2012) 6617–6625.

[10] B.B. Mandelbrot, J.W.V. Ness, Fractional Brownian motions, fractional noises

and applications, SIAM Rev. 10 (4) (1968) 422–437.

[11] T. Nakamura, K. Kiyono, H. Wendt, P. Abry, Y. Yamamoto, Multiscale analysis

of intensive longitudinal biomedical signals and its clinical applications, Proc.

IEEE 104 (2) (2016) 242–261.

[12] R. Sassi, S. Cerutti, F. Lombardi, M. Malik, H.V. Huikuri, C.-K. Peng, G. Schmidt,

Y. Yamamoto, D. Reviewers, B. Gorenek, et al., Advances in heart rate variability signal analysis: joint position statement by the e-cardiology ESC working

[28]

[29]

[30]

[31]

[32]

[33]

[34]

[35]

[36]

[37]

[38]

10

group and the European heart rhythm association co-endorsed by the Asia pacific heart rhythm society, Ep Europace 17 (9) (2015) 1341–1353.

Y. Tsujimoto, Y. Miki, S. Shimatani, K. Kiyono, Fast algorithm for scaling analysis with higher-order detrending moving average method, Phys. Rev. E 93 (5)

(2016) 053304.

L. Ponson, D. Bonamy, E. Bouchaud, Two-dimensional scaling properties of experimental fracture surfaces, Phys. Rev. Lett. 96 (3) (2006) 035506.

J. Schmittbuhl, F. Renard, J.-P. Gratier, R. Toussaint, Roughness of stylolites: implications of 3D high resolution topography measurements, Phys. Rev. Lett. 93

(23) (2004) 238501.

G. Rangarajan, M. Ding, Integrated approach to the assessment of long range

correlation in time series data, Phys. Rev. E 61 (5) (20 0 0) 4991.

Q. Wang, W. Zhao, Z. Liang, X. Wang, T. Zhou, Y. Wu, L. Jiao, Investigation

of diamond wheel topography in elliptical ultrasonic assisted grinding (EUAG)

of monocrystal sapphire using fractal analysis method, Ultrasonics 84 (2018)

87–95.

M. Holschneider, On the wavelet transformation of fractal objects, J. Stat. Phys.

50 (5–6) (1988) 963–993.

D. Veitch, P. Abry, A wavelet-based joint estimator of the parameters of

long-range dependence, IEEE Trans. Inf. Theory 45 (3) (1999) 878–897.

A. Arneodo, N. Decoster, S. Roux, A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic

random rough surfaces, Eur. Phys. J. B 15 (3) (20 0 0) 567–60 0.

G. Li, K. Zhang, J. Gong, X. Jin, Calculation method for fractal characteristics of

machining topography surface based on wavelet transform, Procedia CIRP 79

(2019) 500–504.

G.-F. Gu, W.X. Zhou, Detrended fluctuation analysis for fractals and multifractals in higher dimensions, Phys. Rev. E 74 (6) (2006) 061104.

A. Carbone, Algorithm to estimate the hurst exponent of high-dimensional

fractals, Phys. Rev. E 76 (5) (2007) 056703.

S. Arianos, A. Carbone, C. Türk, Self-similarity of higher-order moving averages,

Phys. Rev. E 84 (4) (2011) 046113.

A. Carbone, K. Kiyono, Detrending moving average algorithm: frequency response and scaling performances, Phys. Rev. E 93 (6) (2016) 063309.

K. Kiyono, Y. Tsujimoto, Nonlinear filtering properties of detrended fluctuation

analysis, Physica A 462 (2016) 807–815.

J.E. Kuo, H. Wang, S. Pickup, Multidimensional least-squares smoothing using

orthogonal polynomials, Anal. Chem. 63 (6) (1991) 630–635.

D.J. Thornley, Novel anisotropic multidimensional convolutional filters for

derivative estimation and reconstruction, in: 2007 IEEE International Conference on Signal Processing and Communications, IEEE, 2007, pp. 253–256.

C. Shekhar, On simplified application of multidimensional Savitzky-Golay filters and differentiators, in: AIP Conference Proceedings, Vol. 1705, AIP Publishing LLC, 2016, p. 020014.

A. Fournier, D. Fussell, L. Carpenter, Computer rendering of stochastic models,

Commun. ACM 25 (6) (1982) 371–384.

R.F. Voss, Random fractal forgeries, in: Fundamental Algorithms for Computer

Graphics, Springer, 1985, pp. 805–835.

T. Blachowicz, A. Ehrmann, K. Domino, Statistical analysis of digital images

of periodic fibrous structures using generalized hurst exponent distributions,

Physica A 452 (2016) 167–177.

T. Blachowicz, K. Domino, M. Koruszowic, J. Grzybowski, T. Böhm, A. Ehrmann,

Statistical analysis of nanofiber mat AFM images by gray-scale-resolved hurst

exponent distributions, Appl. Sci. 11 (5) (2021) 2436.

Y. Zhang, A. Yoshida, N. Sakai, Y. Uekusa, M. Kumeta, S.H. Yoshimura, In vivo

dynamics of the cortical actin network revealed by fast-scanning atomic force

microscopy, Microscopy 66 (4) (2017) 272–282.

J. Wang, W. Shao, J. Kim, Combining MF-DFA and LSSVM for retina images classification, Biomed. Signal Process. Control 60 (2020) 101943.

F. Wang, L. Wang, R.B. Zou, Multifractal detrended moving average analysis for

texture representation, Chaos 24 (3) (2014) 033127.

F. Wang, Z.-S. Li, G.P. Liao, Multifractal detrended fluctuation analysis for image texture feature representation, Int. J. Pattern Recognit. Artif. Intell. 28 (03)

(2014) 1455005.

Y.-H. Shao, G.-F. Gu, Z.-Q. Jiang, W.X. Zhou, Effects of polynomial trends on

detrending moving average analysis, Fractals 23 (03) (2015) 1550034.

...

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