Spectral Clustering for Urban Networks

Abstract

As planetary urbanization accelerates, the significance of developing better methods for analyzing and making sense of complex urban networks also increases. The complexity and heterogeneity of contemporary urban space poses a challenge to conventional descriptive tools. In recent years, the emergence of urban network analysis and the widespread availability of GIS data has brought network analysis methods into the discussion of urban form. This paper describes a method for computationally identifying clusters within urban and other spatial networks using spectral analysis techniques. While spectral clustering has been employed in some limited urban studies, on large spatialized datasets (particularly in identifying land use from orthoimages), it has not yet been thoroughly studied in relation to the space of the urban network itself. We present the construction of a weighted graph Laplacian matrix representation of the network and the processing of the network by eigen decomposition and subsequent clustering of eigenvalues in 4d-space.In this implementation, the algorithm computes a cross-comparison for different numbers of clusters and recommends the best option based on either the 'elbow method,' or by "eigen gap"criteria. The results of the clustering operation are immediately visualized on the original map and can also be validated numerically according to a selection of cluster metrics. Cohesion and separation values are calculated simultaneously for all nodes. After presenting these, the paper also expands on the 'silhouette' value, which is a composite measure that seems especially suited to urban network clustering.This research is undertaken with the aim of informing the design process and so the visualization of results within the active 3d model is essential. Within the paper, we illustrate the process as applied to formal grids and also historic, vernacular urban fabric; first on small, extract urban fragments and then over an entire city networks to indicate the scalability.