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Generalized Reduced K–Means

Author

Listed:
  • Mariaelena Bottazzi Schenone

    (Sapienza University of Rome: Universita degli Studi di Roma La Sapienza)

  • Roberto Rocci

    (Sapienza University of Rome: Universita degli Studi di Roma La Sapienza)

  • Maurizio Vichi

    (Sapienza University of Rome: Universita degli Studi di Roma La Sapienza)

Abstract

In the context of sports analytics, the evaluation of players’ performance has traditionally been a complex endeavor, given the multidimensional nature of the data involved. This paper introduces a novel approach for multivariate analyses of complex data sets, with a focus on professional basketball data. The proposed model simultaneously performs unsupervised classification of units into K clusters and their optimal low-dimensional reconstruction. This is done considering variables’ dimensionality representation into Q components for each group of clusters that can be identified by the same latent dimensions. Consequently, we refer to the new model as Generalized Reduced K-Means (GRKM), which includes RKM as a special case when a unique lower rank reconstruction of the variables is needed. Before the application on real data, the effectiveness of the proposal is shown by means of an extended simulation study. By applying this innovative method to a comprehensive set of National Basketball Association (NBA) statistics, we demonstrate its efficacy in distinguishing player profiles across offensive and defensive spectrums, simultaneously grouping them into coherent clusters.

Suggested Citation

  • Mariaelena Bottazzi Schenone & Roberto Rocci & Maurizio Vichi, 2025. "Generalized Reduced K–Means," Computational Statistics, Springer, vol. 40(4), pages 1753-1778, April.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:4:d:10.1007_s00180-024-01592-0
    DOI: 10.1007/s00180-024-01592-0
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    References listed on IDEAS

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    1. Rocci, Roberto & Vichi, Maurizio, 2008. "Two-mode multi-partitioning," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1984-2003, January.
    2. Cooper, W.W. & Ruiz, José L. & Sirvent, Inmaculada, 2009. "Selecting non-zero weights to evaluate effectiveness of basketball players with DEA," European Journal of Operational Research, Elsevier, vol. 195(2), pages 563-574, June.
    3. Jos Berge, 2006. "The rigid orthogonal Procrustes rotation problem," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 201-205, March.
    4. Henk Kiers & Donatella Vicari & Maurizio Vichi, 2005. "Simultaneous classification and multidimensional scaling with external information," Psychometrika, Springer;The Psychometric Society, vol. 70(3), pages 433-460, September.
    5. Roberto Rocci & Stefano Gattone & Maurizio Vichi, 2011. "A New Dimension Reduction Method: Factor Discriminant K-means," Journal of Classification, Springer;The Classification Society, vol. 28(2), pages 210-226, July.
    6. Michio Yamamoto & Heungsun Hwang, 2017. "Dimension-Reduced Clustering of Functional Data via Subspace Separation," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 294-326, July.
    7. Heungsun Hwang & Hec Montréal & William Dillon & Yoshio Takane, 2006. "An Extension of Multiple Correspondence Analysis for Identifying Heterogeneous Subgroups of Respondents," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 161-171, March.
    8. Vichi, Maurizio & Kiers, Henk A. L., 2001. "Factorial k-means analysis for two-way data," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 49-64, July.
    9. M. Velden & A. Iodice D’Enza & F. Palumbo, 2017. "Cluster Correspondence Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 158-185, March.
    10. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    11. Roberto Rocci & Maurizio Vichi, 2005. "Three-Mode Component Analysis with Crisp or Fuzzy Partition of Units," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 715-736, December.
    12. Hornik, Kurt, 2005. "A CLUE for CLUster Ensembles," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i12).
    13. Maurizio Vichi & Roberto Rocci & Henk A.L. Kiers, 2007. "Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches," Journal of Classification, Springer;The Classification Society, vol. 24(1), pages 71-98, June.
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