Spectral Clustering and Integration: The Inner Dynamics of Computational Geometry and Spatial Morphology

Abstract

Deviating from common evaluation strategies of spatial networks that are realised through numerical comparison of single floating-point numbers such as global and local space syntax measures (centralities, connectivity, etc.) we aim to present a new computational methodology for creating detailed topo-geometric encodings of spaces that encapsulate some of the fundamental ideas about spatial morphology by Hillier (Space is the Machine: A Configurational Theory of Architecture, London, UK, Space Syntax, 2007 [1]). In most cases, space syntax measures try to capture a particular quality of the space for comparison but they lose much of the detail of the spatial topo-geometry and morphology by mainly aggregating graph path traversals and not retaining any other information. This research explores the use of weighted graph spectra, in a composite form, for the purpose of characterising the spatial structure as a whole. The new methodology focuses on the three primary space syntax graph modelling concepts, ‘angular’, ‘metric’ and ‘topological’, from the point of view of the resulting spatial geometries and develops new computational innovations in order to map spatial penetration of local neighbourhood spectra in different scales, dimensions and built environment densities in a continues way. The result is a new composite vector of high dimensionality that can be easily measured against others for detailed comparison. The proposed methodology is then demonstrated with the complete road-network dataset of Great Britain. The main dataset together with subsets is then used in a series of unsupervised machine learning analyses, including clustering and a form of Euclidian ‘spectral integration’.