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Spectral comparison of large urban graphs

Hanna, S.; (2009) Spectral comparison of large urban graphs. In: Koch, D. and Marcus, L. and Steen, J., (eds.) Proceedings of the 7th International Space Syntax Symposium. (pp. p. 39). Royal Institute of Technology (KTH): Stockholm, Sweden. Green open access

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Abstract

The spectrum of an axial graph is proposed as a means for comparison between spaces, particularly for measuring between very large and complex graphs. A number of methods have been used in recent years for comparative analysis within large sets of urban areas, both to investigate properties of specific known types of street network or to propose a taxonomy of urban morphology based on an analytical technique. In many cases, a single or small range of predefined, scalar measures such as metric distance, integration, control or clustering coefficient have been used to compare the graphs. While these measures are well understood theoretically, their low dimensionality determines the range of observations that can ultimately be drawn from the data. Spectral analysis consists of a high dimensional vector representing each space, between which metric distance may be measured to indicate the overall difference between two spaces, or subspaces may be extracted to correspond to certain features. It is used for comparison of entire urban graphs, to determine similarities (and differences) in their overall structure. Results are shown of a comparison of 152 cities distributed around the world. The clustering of cities of similar properties in a high dimensional space is discussed. Principal and nonlinear components of the data set indicate significant correlations in the graph similarities between cities and their proximity to one another, suggesting that cultural features based on location are evident in the city form and that these can be quantified by the proposed method. Results of classification tests show that a city’s location can be estimated based purely on its form. The high dimensionality of the spectra is beneficial for its utility in data-mining applications that can draw correlations with other data sets such as land use information. It is shown how further processing by supervised learning allows the extraction of relevant features. A methodological comparison is also drawn with statistical studies that use a strong correlation between human genetic markers and geographical location of populations to derive detailed reconstructions of prehistoric migration. Thus, it is suggested that the method may be utilised for mapping the transfer of cultural memes by measuring comparison between cities.

Type: Proceedings paper
Title: Spectral comparison of large urban graphs
Open access status: An open access version is available from UCL Discovery
Publisher version: http://www.sss7.org/Proceedings_list.html
Language: English
Additional information: Part of the 7th International Space Syntax Symposium, School of Architecture and the Built Environment, The Royal Institute of Technology (KTH), Stockholm, Sweden, 8-11 June 2009. Please see http://eprints.ucl.ac.uk/15021, http://eprints.ucl.ac.uk/15294, http://eprints.ucl.ac.uk/15301/, http://eprints.ucl.ac.uk/15302/, http://eprints.ucl.ac.uk/15303/, http://eprints.ucl.ac.uk/16184/, and http://eprints.ucl.ac.uk/16411 for other proceedings from this symposium
Keywords: Graphs, graph spectra, comparative analysis, cities, memes
UCL classification:
URI: https://discovery.ucl.ac.uk/id/eprint/16409
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