Connectivity-Optimized Representation Learning via Persistent Homology

Christoph Hofer, Roland Kwitt, Marc Niethammer, Mandar Dixit
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:2751-2760, 2019.

Abstract

We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an autoencoder’s latent space via a novel type of loss, operating on information from persistent homology. Under mild conditions, this loss is differentiable and we present a theoretical analysis of the properties induced by the loss. We choose one-class learning as our upstream task and demonstrate that the imposed structure enables informed parameter selection for modeling the in-class distribution via kernel density estimators. Evaluated on computer vision data, these one-class models exhibit competitive performance and, in a low sample size regime, outperform other methods by a large margin. Notably, our results indicate that a single autoencoder, trained on auxiliary (unlabeled) data, yields a mapping into latent space that can be reused across datasets for one-class learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-hofer19a, title = {Connectivity-Optimized Representation Learning via Persistent Homology}, author = {Hofer, Christoph and Kwitt, Roland and Niethammer, Marc and Dixit, Mandar}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {2751--2760}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/hofer19a/hofer19a.pdf}, url = {https://proceedings.mlr.press/v97/hofer19a.html}, abstract = {We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an autoencoder’s latent space via a novel type of loss, operating on information from persistent homology. Under mild conditions, this loss is differentiable and we present a theoretical analysis of the properties induced by the loss. We choose one-class learning as our upstream task and demonstrate that the imposed structure enables informed parameter selection for modeling the in-class distribution via kernel density estimators. Evaluated on computer vision data, these one-class models exhibit competitive performance and, in a low sample size regime, outperform other methods by a large margin. Notably, our results indicate that a single autoencoder, trained on auxiliary (unlabeled) data, yields a mapping into latent space that can be reused across datasets for one-class learning.} }
Endnote
%0 Conference Paper %T Connectivity-Optimized Representation Learning via Persistent Homology %A Christoph Hofer %A Roland Kwitt %A Marc Niethammer %A Mandar Dixit %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-hofer19a %I PMLR %P 2751--2760 %U https://proceedings.mlr.press/v97/hofer19a.html %V 97 %X We study the problem of learning representations with controllable connectivity properties. This is beneficial in situations when the imposed structure can be leveraged upstream. In particular, we control the connectivity of an autoencoder’s latent space via a novel type of loss, operating on information from persistent homology. Under mild conditions, this loss is differentiable and we present a theoretical analysis of the properties induced by the loss. We choose one-class learning as our upstream task and demonstrate that the imposed structure enables informed parameter selection for modeling the in-class distribution via kernel density estimators. Evaluated on computer vision data, these one-class models exhibit competitive performance and, in a low sample size regime, outperform other methods by a large margin. Notably, our results indicate that a single autoencoder, trained on auxiliary (unlabeled) data, yields a mapping into latent space that can be reused across datasets for one-class learning.
APA
Hofer, C., Kwitt, R., Niethammer, M. & Dixit, M.. (2019). Connectivity-Optimized Representation Learning via Persistent Homology. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:2751-2760 Available from https://proceedings.mlr.press/v97/hofer19a.html.

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