Spatially constrained clustering locates the edges of homogeneous regions, resulting in closed, areal boundaries (see the figure in What are boundaries).
BoundarySeer implements an adaptation of multivariate clustering that groups locations that are both similar and spatially adjacent. Adjacency occurs when clusters share an edge (raster and polygon data) or neighbor each other in a Delaunay triangulation (for point data in vector format). Similarity is determined by the selection of an appropriate dissimilarity metric.
Based on the adjacency and similarity values, clusters are generated using the chosen algorithm (here either centroid or linkage clustering), but formation is constrained so that clusters form contiguous areas. With agglomerative clustering, each location begins as its own cluster, and then an iterative procedure 'agglomerates' the clusters. At each step, the most similar of all spatially adjacent clusters are merged, and coalescing continues until the stopping criterion is met. In BoundarySeer, the stopping criterion is a user-defined number of clusters. Finally, borders of the clusters are drawn as crisp, closed boundaries.
Clusters created with agglomerative techniques can be refined through k-means clustering. With k-means clustering, cluster membership is refined through shifting individual locations into spatially adjacent clusters in order to minimize the within-cluster sum of squares error. Finally, borders of the clusters are drawn as boundaries. Areal boundaries defined in this fashion are crisp and closed.
Applications include the identification of boundaries between tree community types (Legendre and Fortin 1989, Fortin and Drapeau 1995), and soil zone classification to determine agricultural land suitability (Burrough 1989), among others.
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