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Title: Multifractal statistics for characterising two-dimensional spatial distribution of population and stores/facilities Authors:  Mariko Ito - The University of Tokyo (Japan) [presenting]
Takaaki Ohnishi - The University of Tokyo (Japan)
Abstract: The spatial distribution of population and stores/facilities is generally heterogeneous. When we investigate such an object in which the density is heterogeneously distributed, multifractal analysis is a good tool to characterize the structure. In multifractal analysis, for each dimension (singularity strength), we derive the fractal dimension (spectrum) of points in which the local fractal dimension around each of those is the singularity strength. We use Japanese 100-meter estimated mesh data from national censuses and corporate telephone directory database teleport with coordinates, as the data of the spatial distribution of population and stores/facilities respectively. We perform multifractal analysis on these data. Following the frequently used derivation, we calculate the spectrum from the $q$-th generalized dimension, where $q$ is an integer running in a certain region. For two spectrums, for each $q$, we measure the distance between those coordinates of spectrums derived from $q$-th generalized dimension. By using this distance, we further define the distance between the two spectrums. We perform clustering of stores/facilities based on this spectrum distance. We discuss what kind of stores/facilities are in the same cluster as the one of population, and its economic background.