The intersection of location-allocation and clustering

Location-allocation and partitional spatial clustering both deal with spatial data, seemingly from different viewpoints. Partitional clustering analyses datasets by partitioning them into separate groups, while location-allocation places facilities in locations that best meet the needs of demand points. However, both partitional clustering and location-allocation can be formulated as optimization problems minimizing the distances of (demand) points from their associated centers (facilities). Further, both techniques consider certain extensions such as weighted data points, different distance metrics, capacity constraints, different membership types, outliers, and selecting the number of clusters or facilities. In this article, we highlight and review the similarities and differences of these techniques, compare them with model-placed clustering, and provide a unified theoretical framework covering both approaches. We look at a number of extensions common for both approaches, propose a new spatial clustering method, PACK, which combines and adjusts those extensions, and provide software tools (rpack) for conducting spatial analysis with the new method.