BIR: A Method for Selecting the Best Interpretable Multidimensional Scaling Rotation using External Variables

Rebecca Marion, Adrien Bibal, Benoît Frenay

Research output: Contribution to journalArticle


Interpreting nonlinear dimensionality reduction models using external features (or external variables) is crucial in many fields, such as psychology and ecology. Multidimensional scaling (MDS) is one of the most frequently used dimensionality reduction techniques in these fields. However, the rotation invariance of the MDS objective function may make interpretation of the resulting embedding difficult. This paper analyzes how the rotation of MDS embeddings affects sparse regression models used to interpret them and proposes a method, called the Best Interpretable Rotation (BIR) method, which selects the best MDS rotation for interpreting embeddings using external information.
Original languageEnglish
Pages (from-to)83-96
Number of pages14
Publication statusPublished - 4 Feb 2019



  • Machine learning
  • Interpretability
  • Dimensionality reduction
  • Multidimensional scaling
  • Orthogonal transformation
  • Multi-view
  • Sparsity
  • Lasso regularization

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