AN ENHANCEMENT OF GROUP-THEORETIC SPECTRUM ANALYSIS FOR DETECTING SPATIAL AGGLOMERATION

Abstract

 Central place theory¹⁾ 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.²⁾ 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.