Random Filters for Enriching the Discriminatory power of Topological Representations

Grayson Jorgenson, Henry Kvinge, Tegan Emerson, Colin Olson
Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, PMLR 196:183-188, 2022.

Abstract

Topological representations of data are inherently coarse summaries which endows them with certain desirable properties like stability but also potentially inhibits their discriminatory power relative to fine-scale learned features. In this work we present a novel framework for enriching the discriminatory power of topological representations based on random filters and capturing “interferencetopology” rather than direct topology. We show that our random filters outperform previously explored structured image filters while requiring orders of magnitude less computational time. The approach is demonstrated on the MNIST dataset but is broadly applicable across data sets and modalities. This work is concluded with a discussion of the mathematical intuition underlying the approach and identification of future directions to enable deeper understanding and theoretical results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v196-jorgenson22a, title = {Random Filters for Enriching the Discriminatory Power of Topological Representations}, author = {Jorgenson, Grayson and Kvinge, Henry and Emerson, Tegan and Olson, Colin}, booktitle = {Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022}, pages = {183--188}, year = {2022}, editor = {Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Kaul, Manohar and Ktena, Ira and Kvinge, Henry and Miolane, Nina and Rieck, Bastian and Tymochko, Sarah and Wolf, Guy}, volume = {196}, series = {Proceedings of Machine Learning Research}, month = {25 Feb--22 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v196/jorgenson22a/jorgenson22a.pdf}, url = {https://proceedings.mlr.press/v196/jorgenson22a.html}, abstract = {Topological representations of data are inherently coarse summaries which endows them with certain desirable properties like stability but also potentially inhibits their discriminatory power relative to fine-scale learned features. In this work we present a novel framework for enriching the discriminatory power of topological representations based on random filters and capturing “interferencetopology” rather than direct topology. We show that our random filters outperform previously explored structured image filters while requiring orders of magnitude less computational time. The approach is demonstrated on the MNIST dataset but is broadly applicable across data sets and modalities. This work is concluded with a discussion of the mathematical intuition underlying the approach and identification of future directions to enable deeper understanding and theoretical results.} }
Endnote
%0 Conference Paper %T Random Filters for Enriching the Discriminatory power of Topological Representations %A Grayson Jorgenson %A Henry Kvinge %A Tegan Emerson %A Colin Olson %B Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022 %C Proceedings of Machine Learning Research %D 2022 %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Manohar Kaul %E Ira Ktena %E Henry Kvinge %E Nina Miolane %E Bastian Rieck %E Sarah Tymochko %E Guy Wolf %F pmlr-v196-jorgenson22a %I PMLR %P 183--188 %U https://proceedings.mlr.press/v196/jorgenson22a.html %V 196 %X Topological representations of data are inherently coarse summaries which endows them with certain desirable properties like stability but also potentially inhibits their discriminatory power relative to fine-scale learned features. In this work we present a novel framework for enriching the discriminatory power of topological representations based on random filters and capturing “interferencetopology” rather than direct topology. We show that our random filters outperform previously explored structured image filters while requiring orders of magnitude less computational time. The approach is demonstrated on the MNIST dataset but is broadly applicable across data sets and modalities. This work is concluded with a discussion of the mathematical intuition underlying the approach and identification of future directions to enable deeper understanding and theoretical results.
APA
Jorgenson, G., Kvinge, H., Emerson, T. & Olson, C.. (2022). Random Filters for Enriching the Discriminatory power of Topological Representations. Proceedings of Topological, Algebraic, and Geometric Learning Workshops 2022, in Proceedings of Machine Learning Research 196:183-188 Available from https://proceedings.mlr.press/v196/jorgenson22a.html.

Related Material