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Goodness-of-fit filtering in classical metric multidimensional scaling with large datasets

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  • Jan Graffelman

Abstract

Metric multidimensional scaling (MDS) is a widely used multivariate method with applications in almost all scientific disciplines. Eigenvalues obtained in the analysis are usually reported in order to calculate the overall goodness-of-fit of the distance matrix. In this paper, we refine MDS goodness-of-fit calculations, proposing additional point and pairwise goodness-of-fit statistics that can be used to filter poorly represented observations in MDS maps. The proposed statistics are especially relevant for large data sets that contain outliers, with typically many poorly fitted observations, and are helpful for improving MDS output and emphasizing the most important features of the dataset. Several goodness-of-fit statistics are considered, and both Euclidean and non-Euclidean distance matrices are considered. Some examples with data from demographic, genetic and geographic studies are shown.

Suggested Citation

  • Jan Graffelman, 2020. "Goodness-of-fit filtering in classical metric multidimensional scaling with large datasets," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(11), pages 2011-2024, August.
  • Handle: RePEc:taf:japsta:v:47:y:2020:i:11:p:2011-2024
    DOI: 10.1080/02664763.2019.1702929
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    Cited by:

    1. Percy K. Mistry & Anthony Strock & Ruizhe Liu & Griffin Young & Vinod Menon, 2023. "Learning-induced reorganization of number neurons and emergence of numerical representations in a biologically inspired neural network," Nature Communications, Nature, vol. 14(1), pages 1-21, December.

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