Comparison of Traditional and Constrained Recursive Clustering Approaches for Generating Optimal Census Block Group Clusters

Abstract

Census block groups are used in location selection to determine the average drive time for all residents within a given radius to a proposed new store. The United States census uses 220,334 block groups, however the spatial distance between neighboring block groups in densely populated areas is small enough to cluster multiple block groups into a single unit. In this paper, we evaluate the efficiency and accuracy of drive time computations performed on clusters generated by our novel approach of constrained recursive reclustering as run on three traditional clustering algorithms—affinity propagation, k-means, and mean shift. We perform comparisons of our constrained recursive reclustering approach against drive times computed using the original census block group, and using clusters obtained by traditional reclustering. Unlike traditional clustering, where clustering is performed in a single pass, our approach continues reclustering each new cluster until a user specified stopping criteria is reached. We show that traditional clustering techniques generate sub-optimal clusters, with large spatial distances between the cluster centroid and cluster points making them unusable for computing drive times. Our approach provides reductions of 81.2%, 83.4%, and 10.2% for affinity propagation, k-means, and mean shift respectively when run on 220,334 census block groups. Using 200 randomly sampled locations each from Lowe’s, CVS, and Walmart, we show that compared to the original block groups there is no statistically significant difference in drive time computations when using clusters generated by constrained recursive reclustering with affinity propagation for any of the three businesses, and with k-means for CVS and Walmart. While statistically significant differences are obtained with k-means for Lowe’s and with mean shift for all three businesses, the differences are negligible, with the mean difference for each location set being within 30 s.