A COMPARISON BETWEEN TWO OLS-BASED APPROACHES TO ESTIMATING URBAN MULTIFRACTAL PARAMETERS

作者：Huang, Lin-Shan; Chen, Yan-Guang^*

来源：Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 2018, 26(1): 1850019.

DOI：10.1142/S0218348X18500196

• Multifractal Spectrum
• Fractal Cities
• Urban Form
• Least Squares Method
• Scaling Range
• Beijing City

Multifractal theory provides a new spatial analytical tool for urban studies, but many basic problems remain to be solved. Among various pending issues, the most significant one is how to obtain proper multifractal dimension spectrums. If an algorithm is improperly used, the parameter spectrums will be abnormal. This paper is devoted to investigating two ordinary least squares (OLS)-based approaches for estimating urban multifractal parameters. Using empirical study and comparative analysis, we demonstrate how to utilize the adequate linear regression to calculate multifractal parameters. The OLS regression analysis has two different approaches. One is that the intercept is fixed to zero, and the other is that the intercept is not limited. The results of comparative study show that the zero-intercept regression yields proper multifractal parameter spectrums within certain scale range of moment order, while the common regression method often leads to abnormal multifractal parameter values. A conclusion can be reached that fixing the intercept to zero is a more advisable regression method for multifractal parameters estimation, and the shapes of spectral curves and value ranges of fractal parameters can be employed to diagnose urban problems. This research is helpful for scientists to understand multifractal models and apply a more reasonable technique to multifractal parameter calculations.

• 出版日期2018-2
• 单位北京大学