Local Manifold Explanations with Tangent Space Regression

Jesse He, Yusu Wang, Gal Mishne
Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), PMLR 334(2):279-297, 2026.

Abstract

Low-dimensional manifold learning is used to embed and visualize high-dimensional data, revealing its underlying geometry. However, identifying which features drive local variation along the manifold remains difficult. Many post-hoc explanation methods target explaining extrinsic embedding coordinates rather than intrinsic manifold structure, or provide only global explanations. In this work, we introduce Local Tangent Space Regression Explanations (LTSREx)), a method to explain the local structure of a manifold in terms of interpretable features by performing sparse linear regression in the tangent space of the manifold at each point, coupled with Tikhonov denoising via the connection Laplacian to ensure that explanations are consistent and vary smoothly across nearby points. We show that our method produces meaningful local explanations on synthetic data, rotated MNIST digits, and two single-cell gene expression datasets. Our code is available at https://github.com/he-jesse/LTSREx.

Cite this Paper

BibTeX
@InProceedings{pmlr-v334-he26a, title = {Local Manifold Explanations with Tangent Space Regression}, author = {He, Jesse and Wang, Yusu and Mishne, Gal}, booktitle = {Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026)}, pages = {279--297}, year = {2026}, editor = {Berman, Eddie and Bernárdez, Guillermo and Chen, Samantha and Cloninger, Alex and Doster, Timothy and Emerson, Tegan and Grigsby, J. Elisenda and Kvinge, Henry and Lawrence, Hannah and Marrinan, Tim and Myers, Audun and Papillon, Mathilde and Tahmasebi, Behrooz and Telyatnikov, Lev and Walters, Robin and Weber, Melanie and Xie, YuQing and Yeats, Eric}, volume = {334}, number = {2}, series = {Proceedings of Machine Learning Research}, month = {18--20 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v334/main/assets/he26a/he26a.pdf}, url = {https://proceedings.mlr.press/v334/he26a.html}, abstract = {Low-dimensional manifold learning is used to embed and visualize high-dimensional data, revealing its underlying geometry. However, identifying which features drive local variation along the manifold remains difficult. Many post-hoc explanation methods target explaining extrinsic embedding coordinates rather than intrinsic manifold structure, or provide only global explanations. In this work, we introduce Local Tangent Space Regression Explanations (LTSREx)), a method to explain the local structure of a manifold in terms of interpretable features by performing sparse linear regression in the tangent space of the manifold at each point, coupled with Tikhonov denoising via the connection Laplacian to ensure that explanations are consistent and vary smoothly across nearby points. We show that our method produces meaningful local explanations on synthetic data, rotated MNIST digits, and two single-cell gene expression datasets. Our code is available at https://github.com/he-jesse/LTSREx.} }
Endnote
%0 Conference Paper %T Local Manifold Explanations with Tangent Space Regression %A Jesse He %A Yusu Wang %A Gal Mishne %B Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026) %C Proceedings of Machine Learning Research %D 2026 %E Eddie Berman %E Guillermo Bernárdez %E Samantha Chen %E Alex Cloninger %E Timothy Doster %E Tegan Emerson %E J. Elisenda Grigsby %E Henry Kvinge %E Hannah Lawrence %E Tim Marrinan %E Audun Myers %E Mathilde Papillon %E Behrooz Tahmasebi %E Lev Telyatnikov %E Robin Walters %E Melanie Weber %E YuQing Xie %E Eric Yeats %F pmlr-v334-he26a %I PMLR %P 279--297 %U https://proceedings.mlr.press/v334/he26a.html %V 334 %N 2 %X Low-dimensional manifold learning is used to embed and visualize high-dimensional data, revealing its underlying geometry. However, identifying which features drive local variation along the manifold remains difficult. Many post-hoc explanation methods target explaining extrinsic embedding coordinates rather than intrinsic manifold structure, or provide only global explanations. In this work, we introduce Local Tangent Space Regression Explanations (LTSREx)), a method to explain the local structure of a manifold in terms of interpretable features by performing sparse linear regression in the tangent space of the manifold at each point, coupled with Tikhonov denoising via the connection Laplacian to ensure that explanations are consistent and vary smoothly across nearby points. We show that our method produces meaningful local explanations on synthetic data, rotated MNIST digits, and two single-cell gene expression datasets. Our code is available at https://github.com/he-jesse/LTSREx.
APA
He, J., Wang, Y. & Mishne, G.. (2026). Local Manifold Explanations with Tangent Space Regression. Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), in Proceedings of Machine Learning Research 334(2):279-297 Available from https://proceedings.mlr.press/v334/he26a.html.

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