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BIOT: Explaining Multidimensional Nonlinear MDS Embeddings using the Best Interpretable Orthogonal Transformation

Author

Listed:
  • Bibal, Adrien
  • Marion, Rebecca

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • von Sachs, Rainer
  • Frénay, Benoît

Abstract

Dimensionality reduction (DR) is a popular approach to data exploration in which instances in a given dataset are mapped to a lower-dimensional representation or “embedding.” For nonlinear dimensionality reduction (NLDR), the dimensions of the embedding may be difficult to understand. In such cases, it may be useful to learn how the different dimensions relate to a set of external features (i.e., relevant features that were not used for the DR). A variety of methods (e.g., PROFIT and BIR) use external features to explain embeddings generated by NLDR methods with rotation-invariant objective functions, such as multidimensional scaling (MDS). However, these methods are restricted to two-dimensional embeddings. In this paper, we propose BIOT, which makes it possible to explain an MDS embedding with any number of dimensions without requiring visualization.

Suggested Citation

  • Bibal, Adrien & Marion, Rebecca & von Sachs, Rainer & Frénay, Benoît, 2021. "BIOT: Explaining Multidimensional Nonlinear MDS Embeddings using the Best Interpretable Orthogonal Transformation," LIDAM Reprints ISBA 2021016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2021016
    DOI: https://doi.org/10.1016/j.neucom.2021.04.088
    Note: In: Neurocomputing, Vol. 453, p. 109-118 (2021)
    as

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