Classifying multidimensional trajectories of neighbourhood change: a self-organizing map andk-means approach

Understanding the dynamic nature of how urban neighbourhoods evolve through time has been a critical issue both in the literature and in public policy practice for decades. Methodological limitations in understanding change across the multiple attribute dimensions that define a neighbourhood, through time and for spatially situated units, have largely reduced empirical analyses to two points in time or for a singular attribute dimension. This paper demonstrates a two-layered approach to classifying neighbourhoods according to their multidimensional, temporal trajectories. The method first projects data onto a two-dimensional output space using a self-organizing map, then constructs temporal trajectories of change across this space and, finally, classifies the resulting trajectories with a k-means algorithm. The resulting typology of neighbourhood trajectories are then mapped in the geographic space to visualize the space–time, multidimensional dynamics. A case study of neighbourhood change from 1970 to 2010 in eight US cities demonstrates the effectiveness approach for grouping neighbourhoods according to the similarity of their temporal pathways of change. Ten processes are uncovered ranging from various forms of suburbanization to revitalization and a suburban densification trend in the newest, rapidly growing cities in the study. Finally, we calculated a join-count statistic to quantify the observed spatial pattern of each of these neighbourhood types in each city.