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Mapping the evolution of cities

A challenging part of developing evolutionary models of cities is their dynamism. We must find ways to treat change rather than static states as our topic of interest. That is, we often want to understand what something is by how it becomes. Two neighbourhoods might be very similar in terms of their characteristics right now, but have very different propensities to change. Likewise, two neighbourhoods might be quite different at the present moment, but change in similar ways. However, standard methods have a hard time identifying these sorts of similarities grounded in shared propensities to change in response to varying conditions. 

“Classification and Regression via Integer Optimization for Neighborhood Change” proposes a new method designed to do just that, through a method we term “predictive clustering.” As the paper notes, the predictive clustering approach makes three key contributions to neighbourhood change research more broadly:

• Conceptually, predictive clustering is highly distinct from traditional methods—in particu-lar, LR. Because it relies on a predictive model, it can uncover how specific characteristics influence an outcome researchers are interested in studying. We can then observe heteroge-neity in those influences and use it to cluster observations. This perspective makes neigh-borhood dynamics fundamental to the definition of urban space.

• Methodologically, in contrast to traditional neighborhood classifications, predictive cluster-ing is based on a specific outcome to which areas similarly “respond.” In other words, our proposal can be considered model-based clustering (Fraley and Raftery 2002). This frame-work defines the current state of a neighborhood as a set of variables thought to influence trajectories of change. In this article, following a long tradition of research, we use income change to illustrate the potential of this methodological feature of our approach (for a recent example, see Hochstenbach and Van Gent 2015).

• Practically, predictive clustering has clear implications that differentiate it from the tradi-tional K-Means approach. Our approach can identify neighborhoods that exhibit different processes of change even if they look similar at any given point in time, and similar dynam-ics even when they look different. Not only is this potentially useful for urban policymakers when designing interventions, it cannot be readily examined when one only considers char-acteristics of the neighborhood, as in the traditional K-Means approach.

Below is the abstract, and here is a link to the paper. 

Abstract: 

This article applies a method we term “predictive clustering” to cluster neighborhoods. Much of the literature in this direction is based on groupings built using intrinsic characteristics of each observation. Our approach departs from this framework by delineating clusters based on how the neighborhood’s features respond to a particular outcome of interest (e.g., income change). To do so, we leverage a classification and regression via integer optimization (CRIO) method that groups neighborhoods according to their predictive characteristics and consistently outperforms traditional clustering methods along several metrics. The CRIO methodology contributes a novel methodological and conceptual capability to the literature on neighborhood dynamics that can provide useful insights for policymaking.