BIOT: Explaining multidimensional nonlinear MDS embeddings using the Best Interpretable Orthogonal Transformation

Adrien Bibal; Rebecca Marion; Rainer von Sachs; Benoît Frénay

doi:10.1016/j.neucom.2021.04.088

BIOT: Explaining multidimensional nonlinear MDS embeddings using the Best Interpretable Orthogonal Transformation

Adrien Bibal, Rebecca Marion, Rainer von Sachs, Benoît Frénay

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Résumé

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.

langue originale	Anglais
Pages (de - à)	109-118
Nombre de pages	10
journal	Neurocomputing
Volume	453
Les DOIs	https://doi.org/10.1016/j.neucom.2021.04.088
Etat de la publication	Publié - 17 sept. 2021

Financement

The authors would like to thank Alex Koch, assistant professor at the University of Chicago, for his feedback on the application of BIOT to his dataset. We also thank Reviewer 2 for proposing the proof in Eq. (9). The work of R. Marion was supported by the Belgian Fund for Scientific Research (F.R.S.-FNRS, FRIA grant). The authors would like to thank Alex Koch, assistant professor at the University of Chicago, for his feedback on the application of BIOT to his dataset. We also thank Reviewer 2 for proposing the proof in Eq. (9) . The work of R. Marion was supported by the Belgian Fund for Scientific Research (F.R.S.-FNRS, FRIA grant).

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title = "BIOT: Explaining multidimensional nonlinear MDS embeddings using the Best Interpretable Orthogonal Transformation",

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.",

keywords = "Explainability, Lasso, Multidimensional scaling, Orthogonal transformations",

author = "Adrien Bibal and Rebecca Marion and \{von Sachs\}, Rainer and Beno{\^i}t Fr{\'e}nay",

note = "Funding Information: The authors would like to thank Alex Koch, assistant professor at the University of Chicago, for his feedback on the application of BIOT to his dataset. We also thank Reviewer 2 for proposing the proof in Eq. (9). The work of R. Marion was supported by the Belgian Fund for Scientific Research (F.R.S.-FNRS, FRIA grant). Funding Information: The authors would like to thank Alex Koch, assistant professor at the University of Chicago, for his feedback on the application of BIOT to his dataset. We also thank Reviewer 2 for proposing the proof in Eq. (9) . The work of R. Marion was supported by the Belgian Fund for Scientific Research (F.R.S.-FNRS, FRIA grant). Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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doi = "10.1016/j.neucom.2021.04.088",

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AU - von Sachs, Rainer

AU - Frénay, Benoît

N1 - Funding Information: The authors would like to thank Alex Koch, assistant professor at the University of Chicago, for his feedback on the application of BIOT to his dataset. We also thank Reviewer 2 for proposing the proof in Eq. (9). The work of R. Marion was supported by the Belgian Fund for Scientific Research (F.R.S.-FNRS, FRIA grant). Funding Information: The authors would like to thank Alex Koch, assistant professor at the University of Chicago, for his feedback on the application of BIOT to his dataset. We also thank Reviewer 2 for proposing the proof in Eq. (9) . The work of R. Marion was supported by the Belgian Fund for Scientific Research (F.R.S.-FNRS, FRIA grant). Publisher Copyright: © 2021 Elsevier B.V.

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BIOT: Explaining multidimensional nonlinear MDS embeddings using the Best Interpretable Orthogonal Transformation

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