@article{oai:nagoya.repo.nii.ac.jp:00020689,
author = {鈴木, 啓央 and 山本, 裕二 and SUZUKI, Hiroo and YAMAMOTO, Yuji},
issue = {1},
journal = {総合保健体育科学},
month = {Sep},
note = {In this study, we examined the validity of a calculation method that estimates the scaling region in fractal dimension analysis for empirical data. The most probable dimension value (MPDV) method was proposed to estimate the scaling region for smaller data sets, and to evaluate correlation dimension using the Grassberger-Procaccia (GP) method. The MPDV method was applied to Hénon maps, which consisted of 1,000 and 189 data points. This method proved to be somewhat effective in its ability to estimate the scaling region in the GP method for both data sets. However, when the MPDV method was applied to empirical data that were observed in the experiment of human movement, the histogram of the slopes had two peaks that depended on the number of bins. In this case, the scaling region could not be estimated as a unique value. Thus, we developed a new algorithm, which we refer to as the difference slope method, for estimating the scaling region in fractal dimensional analysis as a function of the change in the slope of a log-log graph. In the difference slope method, the estimated scaling regions are dependent on the threshold of variances of the slopes. If stricter threshold values are adopted, then the proposed calculation method for estimating the scaling region would give valid values for the correlation dimension, even in the empirical data.},
pages = {7--19},
title = {実データに対するGP法を用いたフラクタル次元解析における推定領域の検討},
volume = {36},
year = {2013}
}