Computational Statistics

, Volume 33, Issue 4, pp 1799–1822 | Cite as

ClustGeo: an R package for hierarchical clustering with spatial constraints

  • Marie ChaventEmail author
  • Vanessa Kuentz-Simonet
  • Amaury Labenne
  • Jérôme Saracco
Original Paper


In this paper, we propose a Ward-like hierarchical clustering algorithm including spatial/geographical constraints. Two dissimilarity matrices \(D_0\) and \(D_1\) are inputted, along with a mixing parameter \(\alpha \in [0,1]\). The dissimilarities can be non-Euclidean and the weights of the observations can be non-uniform. The first matrix gives the dissimilarities in the “feature space” and the second matrix gives the dissimilarities in the “constraint space”. The criterion minimized at each stage is a convex combination of the homogeneity criterion calculated with \(D_0\) and the homogeneity criterion calculated with \(D_1\). The idea is then to determine a value of \(\alpha \) which increases the spatial contiguity without deteriorating too much the quality of the solution based on the variables of interest i.e. those of the feature space. This procedure is illustrated on a real dataset using the R package ClustGeo.


Ward-like hierarchical clustering Soft contiguity constraints Pseudo-inertia Non-Euclidean dissimilarities Geographical distances 



The authors are grateful to the editor and the anonymous referees for their valuable comments that lead to several improvements of this article.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IMB, UMR CNRS 5251, Inria Bordeaux Sud Ouest, CQFD TeamUniversité de BordeauxTalenceFrance
  2. 2.UR ETBX, Centre de BordeauxIRSTEACestas CedexFrance
  3. 3.IMB, UMR CNRS 5251, Inria Bordeaux Sud Ouest, CQFD TeamENSC - Bordeaux INPTalenceFrance

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