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Visualizing Profiles of Large Datasets of Weighted and Mixed Data

Author

Listed:
  • Aurea Grané

    (Statistics Department, Universidad Carlos III de Madrid, 28903 Getafe, Spain)

  • Alpha A. Sow-Barry

    (Statistics Department, Universidad Carlos III de Madrid, 28903 Getafe, Spain)

Abstract

This work provides a procedure with which to construct and visualize profiles, i.e., groups of individuals with similar characteristics, for weighted and mixed data by combining two classical multivariate techniques, multidimensional scaling (MDS) and the k -prototypes clustering algorithm. The well-known drawback of classical MDS in large datasets is circumvented by selecting a small random sample of the dataset, whose individuals are clustered by means of an adapted version of the k -prototypes algorithm and mapped via classical MDS. Gower’s interpolation formula is used to project remaining individuals onto the previous configuration. In all the process, Gower’s distance is used to measure the proximity between individuals. The methodology is illustrated on a real dataset, obtained from the Survey of Health, Ageing and Retirement in Europe (SHARE), which was carried out in 19 countries and represents over 124 million aged individuals in Europe. The performance of the method was evaluated through a simulation study, whose results point out that the new proposal solves the high computational cost of the classical MDS with low error.

Suggested Citation

  • Aurea Grané & Alpha A. Sow-Barry, 2021. "Visualizing Profiles of Large Datasets of Weighted and Mixed Data," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:891-:d:537881
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    References listed on IDEAS

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    1. Irene Albarrán & Pablo Alonso & Aurea Grané, 2015. "Profile identification via weighted related metric scaling: an application to dependent Spanish children," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 593-618, June.
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    4. Grané, Aurea & Salini, Silvia & Verdolini, Elena, 2021. "Robust multivariate analysis for mixed-type data: Novel algorithm and its practical application in socio-economic research," Socio-Economic Planning Sciences, Elsevier, vol. 73(C).
    5. Ziqi Jia & Ling Song, 2020. "Weighted k-Prototypes Clustering Algorithm Based on the Hybrid Dissimilarity Coefficient," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, July.
    6. Dray, Stéphane & Dufour, Anne-Béatrice, 2007. "The ade4 Package: Implementing the Duality Diagram for Ecologists," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 22(i04).
    7. Alonso, Pablo J., 2011. "Profile identification via weighted related metric scaling : an application to dependent Spanish children," DES - Working Papers. Statistics and Econometrics. WS ws113628, Universidad Carlos III de Madrid. Departamento de Estadística.
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    1. Aurea Grané & Giancarlo Manzi & Silvia Salini, 2021. "Smart Visualization of Mixed Data," Stats, MDPI, vol. 4(2), pages 1-14, June.

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