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Comparison between Two Algorithms for Computing the Weighted Generalized Affinity Coefficient in the Case of Interval Data

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  • Áurea Sousa

    (Faculty of Sciences and Technology, CEEAplA and OSEAN, Universidade dos Açores, 9500-321 Ponta Delgada, Portugal)

  • Osvaldo Silva

    (Faculty of Sciences and Technology, CICSNOVA.UAc, Universidade dos Açores, 9500-321 Ponta Delgada, Portugal)

  • Leonor Bacelar-Nicolau

    (Faculty of Medicine, Institute of Preventive Medicine and Public Health & ISAMB/FM-UL, Universidade de Lisboa, 1649-028 Lisboa, Portugal)

  • João Cabral

    (Faculty of Sciences and Technology, Universidade dos Açores, 9500-321 Ponta Delgada, Portugal
    CIMA-Research Centre, Mathematics and Applications & Azores University, 9500-321 Ponta Delgada, Portugal)

  • Helena Bacelar-Nicolau

    (Faculty of Psychology, Institute of Environmental Health (ISAMB/FM-UL), Universidade de Lisboa, 1649-013 Lisboa, Portugal)

Abstract

From the affinity coefficient between two discrete probability distributions proposed by Matusita, Bacelar-Nicolau introduced the affinity coefficient in a cluster analysis context and extended it to different types of data, including for the case of complex and heterogeneous data within the scope of symbolic data analysis (SDA). In this study, we refer to the most significant partitions obtained using the hierarchical cluster analysis (h.c.a.) of two well-known datasets that were taken from the literature on complex (symbolic) data analysis. h.c.a. is based on the weighted generalized affinity coefficient for the case of interval data and on probabilistic aggregation criteria from a VL parametric family. To calculate the values of this coefficient, two alternative algorithms were used and compared. Both algorithms were able to detect clusters of macrodata (aggregated data into groups of interest) that were consistent and consonant with those reported in the literature, but one performed better than the other in some specific cases. Moreover, both approaches allow for the treatment of large microdatabases (non-aggregated data) after their transformation into macrodata from the huge microdata.

Suggested Citation

  • Áurea Sousa & Osvaldo Silva & Leonor Bacelar-Nicolau & João Cabral & Helena Bacelar-Nicolau, 2023. "Comparison between Two Algorithms for Computing the Weighted Generalized Affinity Coefficient in the Case of Interval Data," Stats, MDPI, vol. 6(4), pages 1-13, October.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:4:p:68-1094:d:1259033
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    References listed on IDEAS

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    1. Francisco Carvalho & Paula Brito & Hans-Hermann Bock, 2006. "Dynamic clustering for interval data based on L 2 distance," Computational Statistics, Springer, vol. 21(2), pages 231-250, June.
    2. Marie Chavent & Francisco Carvalho & Yves Lechevallier & Rosanna Verde, 2006. "New clustering methods for interval data," Computational Statistics, Springer, vol. 21(2), pages 211-229, June.
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