A between-cluster approach for clustering skew-symmetric data

Donatella Vicari () and Cinzia Di Nuzzo ()
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Donatella Vicari: Sapienza University of Rome
Cinzia Di Nuzzo: Sapienza University of Rome

Advances in Data Analysis and Classification, 2024, vol. 18, issue 1, No 8, 163-192

Abstract: 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.

Keywords: Clustering; Skew-symmetric data; SVD; Asymmetry; Dimension reduction; 62Hxx; Multivariate; analysis (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11634-023-00566-2

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