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Classification of Asymmetric Proximity Data

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  • Donatella Vicari

Abstract

When clustering asymmetric proximity data, only the average amounts are often considered by assuming that the asymmetry is due to noise. But when the asymmetry is structural, as typically may happen for exchange flows, migration data or confusion data, this may strongly affect the search for the groups because the directions of the exchanges are ignored and not integrated in the clustering process. The clustering model proposed here relies on the decomposition of the asymmetric dissimilarity matrix into symmetric and skew-symmetric effects both decomposed in within and between cluster effects. The classification structures used here are generally based on two different partitions of the objects fitted to the symmetric and the skew-symmetric part of the data, respectively; the restricted case is also presented where the partition fits jointly both of them allowing for clusters of objects similar with respect to the average amounts and directions of the data. Parsimonious models are presented which allow for effective and simple graphical representations of the results. Copyright Classification Society of North America 2014

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  • Donatella Vicari, 2014. "Classification of Asymmetric Proximity Data," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 386-420, October.
    • Handle: RePEc:spr:jclass:v:31:y:2014:i:3:p:386-420
    DOI: 10.1007/s00357-014-9159-6
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    References listed on IDEAS

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    Cited by:

    1. Giuseppe Bove & Akinori Okada, 2018. "Methods for the analysis of asymmetric pairwise relationships," 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 5-31, March.
    2. Donatella Vicari, 2018. "CLUSKEXT: CLUstering model for SKew-symmetric data including EXTernal information," 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 43-64, March.
    3. 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.
    4. Ioan I. Gâf-Deac & Mohammad Jaradat & Florina Bran & Raluca Florentina Crețu & Daniel Moise & Svetlana Platagea Gombos & Teodora Odett Breaz, 2022. "Similarities and Proximity Symmetries for Decisions of Complex Valuation of Mining Resources in Anthropically Affected Areas," Sustainability, MDPI, vol. 14(16), pages 1-22, August.

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