Euclidean distances, soft and spectral clustering on weighted graphs

Authors:
François Bavaud
Affiliations:
University of Lausanne, Department of Geography, Department of Computer Science and Mathematical Methods, Lausanne, Switzerland
Venue:
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
Year:
2010

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Abstract

We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means of higher-dimensional embeddings (Schoenberg transformations). Geographical flow data, properly conditioned, illustrate the procedure as well as visualization aspects.