Note: This is a package under development.

BIOT

This package implements Best Interpretable Orthogonal Transformation (BIOT), which is a method that can be used to explain the dimensions of embeddings generated by Multidimensional Scaling (MDS).

BIOT is a generalization of the method Best Interpretable Rotation (BIR) (for more information about BIR, see https://github.com/AdrienBibal/BIR). BIOT is different from BIR with respect to 3 main points:

• BIOT can be applied to embeddings with more than two dimensions;
• Orthogonal transformations are used instead of rotations;
• Iterative optimization is used instead of performing an exhaustive search in a highly non-convex space.

This results in a method that converges automatically, that performs more general transformations and, most importantly, that can explain MDS embeddings with any number of dimensions (instead of only two, which is the case for BIR).

TO DO

This package is currently under development, and there are several items left on the to-do list:

• Write instructions for use with an example
• Write unit tests
• ...

Author(s)

This code was written by Rebecca Marion.

References

Bibal, Adrien, Rebecca Marion, Rainer von Sachs, and Benoît Frénay. "BIOT: Explaining multidimensional nonlinear MDS embeddings using the Best Interpretable Orthogonal Transformation." Neurocomputing 453 (2021): 109-118.

Bibal, Adrien, Rebecca Marion, and Benoît Frénay. "Finding the most interpretable MDS rotation for sparse linear models based on external features." In ESANN. 2018.

Marion, Rebecca, Adrien Bibal, and Benoît Frénay. "BIR: A method for selecting the best interpretable multidimensional scaling rotation using external variables." Neurocomputing 342 (2019): 83-96.