TY - JOUR
T1 - BIOT
T2 - Explaining multidimensional nonlinear MDS embeddings using the Best Interpretable Orthogonal Transformation
AU - Bibal, Adrien
AU - Marion, Rebecca
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.
PY - 2021/9/17
Y1 - 2021/9/17
N2 - 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.
AB - 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.
KW - Explainability
KW - Lasso
KW - Multidimensional scaling
KW - Orthogonal transformations
UR - http://www.scopus.com/inward/record.url?scp=85106318384&partnerID=8YFLogxK
U2 - 10.1016/j.neucom.2021.04.088
DO - 10.1016/j.neucom.2021.04.088
M3 - Article
AN - SCOPUS:85106318384
SN - 0925-2312
VL - 453
SP - 109
EP - 118
JO - Neurocomputing
JF - Neurocomputing
ER -