群論的スペクトル解析による空間集積抽出手法の高度化  [in Japanese] AN ENHANCEMENT OF GROUP-THEORETIC SPECTRUM ANALYSIS FOR DETECTING SPATIAL AGGLOMERATION  [in Japanese]

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Abstract

Christaller<sup>1)</sup>の中心地理論は古くから知られるが,実データから正六角形状の空間集積パターンを定量化し,妥当性を検討する手法は確立されていない.Ikeda 他<sup>2)</sup>は正六角形状の空間集積パターンを抽出しうる手法を開発したが,次の課題が残されている:(i) 対象領域の客観的な選定法が存在しない点,(ii) 抽出したパターンの有意性が不明である点.本稿では,課題(i),(ii)に対処し,中心地理論に則した空間集積パターンをより客観的に抽出する手法を開発する.(i)のために,対象領域を探索する最適化問題を作成する.(ii)のために,permutation testによる統計的な検定法を導入する.提案手法を人口データに適用した結果,統計的に有意な2種類の空間集積パターンが検出され,中心地理論の妥当性が示唆された.

 Central place theory<sup>1)</sup> envisaged that economic agglomerations form regular hexagonal patterns. A long-standing issue is a lack of quantitative method for assessing emergence of such regularities in the actual data. Ikeda et al.<sup>2)</sup> introduced a group-theoretic spectrum analysis as the first attempt to develop a quantitative approach to detect hexagonal patterns. However, there has been several technical issues to be settled in their method: (i) How to select domain that crucially affect the result? (ii) How to select predominant spectrum? To settle these issues, we employ several methodologies: an optimization formulation for the choice of a domain, an eigenvector-based criterion for noise reduction, and a permutation test for a significance test of spectrum. The effectiveness of the proposed method is demonstrated by an analysis of the actual population data of Southern Germany and Eastern USA.

Journal

  • Journal of Japan Society of Civil Engineers, Ser. D3 (Infrastructure Planning and Management)

    Journal of Japan Society of Civil Engineers, Ser. D3 (Infrastructure Planning and Management) 74(4), 398-410, 2018

    Japan Society of Civil Engineers

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