/unsupervised-methods
1st May, 2021Gareth Simons

## Untangling urban data signatures: Unsupervised machine learning methods for detection of urban archetypes

### Abstract

Urban morphological measures applied at a high-resolution of analysis may yield a wealth of data describing varied characteristics of the urban environment in a substantial degree of detail; however, these forms of high-dimensional datasets are not immediately relatable to wider constructs rooted in conventional conceptions of urbanism. Data science and machine learning methods provide an opportunity to explore such forms of data through use of unsupervised machine learning methods through which the dimensionality of the data can be reduced while recovering latent themes and identifying characteristic patterns which may resonate with urbanist discourse more generally.

Dimensionality reduction and clustering methods including Principal Component Analysis (PCA), Variational Autoencoders ($\beta$-VAE), and an Autoencoder based Guassian Mixture Model (VaDE) are discussed and demonstrated for purposes of ‘untangling’ data: unveiling themes which may be used to bridge quantitative and qualitative descriptions of urbanism. The methods are applied to a morphological dataset for Greater London consisting of a combination of centrality, landuse accessibility, mixed-uses, and population density measures which have been computed at pedestrian walking thresholds ranging from 100m to 800m. The spatial aggregations and morphological measures are computed at a 20m network resolution using the cityseer-apiPython package which utilises a local windowing-methodology with distances computed directly over the network and with aggregations performed dynamically and with respect to the direction of approach, thus preserving the relationships between the variables and retaining contextual precision.

Whereas the demonstrated methods hold tremendous potential, their power is difficult to convey or fully exploit using conventional lower-dimensional visualisation methods. This underscores the need for subsequent research into how such methods may be coupled to interactive visualisation methods to further elucidate the richness of the data and its potential implications.

### Introduction: Detection of urban archetypes with unsupervised machine learning methods

Vibrant pedestrian districts manifest an affinity for complexity and its requisite diversity, as do complex systems more generally1. Yet, urban masterplans have historically demonstrated a proclivity towards reductionism. Cities were increasingly rearranged around motor-vehicles and were reconceived in the abstract on drawings boards: the more granular, dense, mixed-use, and visually ‘messy’ artefacts of evolved cities were steamrolled to make way for grandiose compositions that were ultimately too large, too homogenous, and too resistant towards change for pedestrian-based forms of urbanism to thrive2|3. Though initially associated with high-modernism, aspects of these patterns are still prevalent in various forms of contemporary urbanism manifesting across the spectrum from suburbia to romanticised smart city masterplans, explicitly or implicitly emphasising idealised efficiencies at the expense of complexity4|5|6. This paradigm can stifle the oft unpredictable and chaotic forms of interaction aiding processes of discovery and diffusion within complex adaptive systems7|8.

The complex systems interpretation of cities, replete with dynamics from emergence to non-linearities to phase-changes9|10|11|12, resists simple averages and crude models13. This presents a challenge: architects, urban designers, and planners are faced with the dilemma of how to plan for inherently unpredictable processes at the urban scale14|15. Whereas it is not possible to anticipate every last action of city citizens — and how these chains of interaction might bifurcate or coalesce through space — it is possible to gauge, more generally, how that certain forms of urbanism may be more conducive to large numbers of permutations of complex interactions16. Complex systems derived methods, including network centralities and landuse diversity measures, are proxies for urban complexity: they foreshadow networks of potential interactions available to city citizens. Whereas our ability to model the full complexity of urban systems will always be constrained — not least by sensitivity to initial conditions — it remains possible to explore the spatial manifestations of complex processes present in historical cities and to compare these to new forms of development. The question then arises: if we apply localised centrality and mixed-use measures at a sufficiently precise and high resolution of analysis, then are emerging forms of data analysis and unsupervised machine learning methods useful for purposes of ‘untangling’ and ‘sifting-out’ signature patterns from the mass of ensuing data? These terms are used in the literal sense because large and high-dimensional datasets require teasing apart to reveal latent themes which may ultimately help bridge the gap from quantitative forms of urban analytics to qualitatively framed conceptions of cities (@Portugali2012.

A knee-jerk reaction may be to reject machine learning out-of-hand for for its links to mathematics and statistics more generally; however, on closer scrutiny the synthesis of locally precise urban morphological measures combined with machine learning methods affords the use of highly detailed datasets capable of capturing and preserving contextual particularities; facilitates use of high-dimensional datasets with significant assortments of variables and potentially complex and varied non-linear relationships between them; and, in the form of unsupervised methods combined with deep neural networks, allows for structures to be unearthed directly from within the data without the imposition of externally held theories or formulas. Compared to traditional statistical methods applied to larger spatial aggregations, the application of machine learning to high resolution spatial data resembles an approach that is more akin to proceeding from the particular to the general: in spite of the large volumes of information the data-space is (in effect) explored ‘line-by-line’ with model losses computed and updated over comparatively small batches of data. Patterns are ‘sniffed-out’ using exploratory and bottom-up-like procedures with the more prevalent of these congealing over successive iterations to reveal thematic patterns that have emerged from within the data. It must be emphasised that this reasoning only holds true if working with localised metrics gathered at a sufficiently high resolution of analysis and with the measures processed directly from each location. The use of intervening levels of spatial aggregation, interpolation from larger to smaller units of scale, or overly large units of analysis needs to be eschewed because these would otherwise result in the attrition of information and, critically, discard or otherwise mask local-scale inter-relationships between the variables.

Traditional forms of urban morphological analysis have been difficult apply at scale because of reliance on manually collated observations and wearisome calculations. Geographic Information Systems (GIS) have permitted larger scales of quantitative analysis, but the lack of large and granular data sources combined with computational constraints meant that these methods have tended to be applied against larger units of spatial aggregation and relied on simplified distance metrics19|20. More recently, however, the increased availability of detailed datasets has facilitated a finer scale of analysis while retaining the ability to process larger areal extents21, thus prompting the adoption of multi-variable and multi-scalar workflows. The ensuing large and high-dimensional datasets can be combined with unsupervised exploratory methods, and has engendered interest in how urban morphological analysis can be applied not only to the exposition of existing cities, but also in the capacity of a rigorous design-aid for newly planned forms of development22|23|24|25.

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