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Hierarchical clustering of asymmetric networks

Author

Listed:
  • Gunnar Carlsson

    (Stanford University)

  • Facundo Mémoli

    (Ohio State University)

  • Alejandro Ribeiro

    (University of Pennsylvania)

  • Santiago Segarra

    (Massachusetts Institute of Technology)

Abstract

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods that, based on the dissimilarity structure, output hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter. Our construction of hierarchical clustering methods is built around the concept of admissible methods, which are those that abide by the axioms of value—nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them—and transformation—when dissimilarities are reduced, the network may become more clustered but not less. Two particular methods, termed reciprocal and nonreciprocal clustering, are shown to provide upper and lower bounds in the space of admissible methods. Furthermore, alternative clustering methodologies and axioms are considered. In particular, modifying the axiom of value such that clustering in two-node networks occurs at the minimum of the two dissimilarities entails the existence of a unique admissible clustering method. Finally, the developed clustering methods are implemented to analyze the internal migration in the United States.

Suggested Citation

  • Gunnar Carlsson & Facundo Mémoli & Alejandro Ribeiro & Santiago Segarra, 2018. "Hierarchical clustering of asymmetric networks," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(1), pages 65-105, March.
    • Handle: RePEc:spr:advdac:v:12:y:2018:i:1:d:10.1007_s11634-017-0299-5
    DOI: 10.1007/s11634-017-0299-5
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    References listed on IDEAS

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    1. T. C. Hu, 1961. "Letter to the Editor---The Maximum Capacity Route Problem," Operations Research, INFORMS, vol. 9(6), pages 898-900, December.
    2. Donatella Vicari, 2014. "Classification of Asymmetric Proximity Data," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 386-420, October.
    3. P B Slater, 1984. "A Partial Hierarchical Regionalization of 3140 US Counties on the Basis of 1965–1970 Intercounty Migration," Environment and Planning A, , vol. 16(4), pages 545-550, April.
    4. Lawrence Hubert, 1973. "Min and max hierarchical clustering using asymmetric similarity measures," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 63-72, March.
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