Spatial Weights: Constructing Weight-Compatible Exchange Matrices from Proximity Matrices

  • François Bavaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8728)


Exchange matrices represent spatial weights as symmetric probability distributions on pairs of regions, whose margins yield regional weights, generally well-specified and known in most contexts. This contribution proposes a mechanism for constructing exchange matrices, derived from quite general symmetric proximity matrices, in such a way that the margin of the exchange matrix coincides with the regional weights. Exchange matrices generate in turn diffusive squared Euclidean dissimilarities, measuring spatial remoteness between pairs of regions. Unweighted and weighted spatial frameworks are reviewed and compared, regarding in particular their impact on permutation and normal tests of spatial autocorrelation. Applications include tests of spatial autocorrelation with diagonal weights, factorial visualization of the network of regions, multivariate generalizations of Moran’s I, as well as “landscape clustering,” aimed at creating regional aggregates both spatially contiguous and endowed with similar features.


Spatial Autocorrelation Spatial Weight Regional Weight Voter Weight Exchange Matrix 
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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • François Bavaud
    • 1
  1. 1.University of LausanneSwitzerland

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