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A between-cluster approach for clustering skew-symmetric data

Author

Listed:
  • Donatella Vicari

    (Sapienza University of Rome)

  • Cinzia Di Nuzzo

    (Sapienza University of Rome
    University of Catania)

Abstract

In order to investigate exchanges between objects, a clustering model for skew-symmetric data is proposed, which relies on the between-cluster effects of the skew-symmetries that represent the imbalances of the observed exchanges between pairs of objects. The aim is to detect clusters of objects that share the same behaviour of exchange so that origin and destination clusters are identified. The proposed model is based on the decomposition of the skew-symmetric matrix pertaining to the imbalances between clusters into a sum of a number of off-diagonal block matrices. Each matrix can be approximated by a skew-symmetric matrix by using a truncated Singular Value Decomposition (SVD) which exploits the properties of the skew-symmetric matrices. The model is fitted in a least-squares framework and an efficient Alternating Least Squares algorithm is provided. Finally, in order to show the potentiality of the model and the features of the resulting clusters, an extensive simulation study and an illustrative application to real data are presented.

Suggested Citation

  • Donatella Vicari & Cinzia Di Nuzzo, 2024. "A between-cluster approach for clustering skew-symmetric data," 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. 18(1), pages 163-192, March.
    • Handle: RePEc:spr:advdac:v:18:y:2024:i:1:d:10.1007_s11634-023-00566-2
    DOI: 10.1007/s11634-023-00566-2
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