A Geometric Approach to Archetypal Analysis via Sparse Projections

Vinayak Abrol, Pulkit Sharma
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:42-51, 2020.

Abstract

Archetypal analysis (AA) aims to extract patterns using self-expressive decomposition of data as convex combinations of extremal points (on the convex hull) of the data. This work presents a computationally efficient greedy AA (GAA) algorithm. GAA leverages the underlying geometry of AA, is scalable to larger datasets, and has significantly faster convergence rate. To achieve this, archetypes are learned via sparse projection of data. In the transformed space, GAA employs an iterative subset selection approach to identify archetypes based on the sparsity of convex representations. The work further presents the use of GAA algorithm for extended AA models such as robust and kernel AA. Experimental results show that GAA is considerably faster while performing comparable to existing methods for tasks such as classification, data visualization/categorization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-abrol20a, title = {A Geometric Approach to Archetypal Analysis via Sparse Projections}, author = {Abrol, Vinayak and Sharma, Pulkit}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {42--51}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/abrol20a/abrol20a.pdf}, url = {https://proceedings.mlr.press/v119/abrol20a.html}, abstract = {Archetypal analysis (AA) aims to extract patterns using self-expressive decomposition of data as convex combinations of extremal points (on the convex hull) of the data. This work presents a computationally efficient greedy AA (GAA) algorithm. GAA leverages the underlying geometry of AA, is scalable to larger datasets, and has significantly faster convergence rate. To achieve this, archetypes are learned via sparse projection of data. In the transformed space, GAA employs an iterative subset selection approach to identify archetypes based on the sparsity of convex representations. The work further presents the use of GAA algorithm for extended AA models such as robust and kernel AA. Experimental results show that GAA is considerably faster while performing comparable to existing methods for tasks such as classification, data visualization/categorization.} }
Endnote
%0 Conference Paper %T A Geometric Approach to Archetypal Analysis via Sparse Projections %A Vinayak Abrol %A Pulkit Sharma %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-abrol20a %I PMLR %P 42--51 %U https://proceedings.mlr.press/v119/abrol20a.html %V 119 %X Archetypal analysis (AA) aims to extract patterns using self-expressive decomposition of data as convex combinations of extremal points (on the convex hull) of the data. This work presents a computationally efficient greedy AA (GAA) algorithm. GAA leverages the underlying geometry of AA, is scalable to larger datasets, and has significantly faster convergence rate. To achieve this, archetypes are learned via sparse projection of data. In the transformed space, GAA employs an iterative subset selection approach to identify archetypes based on the sparsity of convex representations. The work further presents the use of GAA algorithm for extended AA models such as robust and kernel AA. Experimental results show that GAA is considerably faster while performing comparable to existing methods for tasks such as classification, data visualization/categorization.
APA
Abrol, V. & Sharma, P.. (2020). A Geometric Approach to Archetypal Analysis via Sparse Projections. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:42-51 Available from https://proceedings.mlr.press/v119/abrol20a.html.

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