ICML 2017poster24 citations
Frame-based Data Factorizations
Sebastian Mair, Ahcène Boubekki, Ulf Brefeld
Abstract
Archetypal Analysis is the method of choice to compute interpretable matrix factorizations. Every data point is represented as a convex combination of factors, i.e., points on the boundary of the convex hull of the data. This renders computation inefficient. In this paper, we show that the set of vertices of a convex hull, the so-called frame, can be efficiently computed by a quadratic program. We provide theoretical and empirical results for our proposed approach and make use of the frame to accelerate Archetypal Analysis. The novel method yields similar reconstruction errors as baseline competitors but is much faster to compute.
BibTeX
@InProceedings{pmlr-v70-mair17a,
title = {Frame-based Data Factorizations},
author = {Sebastian Mair and Ahc{\`e}ne Boubekki and Ulf Brefeld},
booktitle = {Proceedings of the 34th International Conference on Machine Learning},
pages = {2305--2313},
year = {2017},
editor = {Precup, Doina and Teh, Yee Whye},
volume = {70},
series = {Proceedings of Machine Learning Research},
month = {06--11 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v70/mair17a/mair17a.pdf},
url = {https://proceedings.mlr.press/v70/mair17a.html},
abstract = {Archetypal Analysis is the method of choice to compute interpretable matrix factorizations. Every data point is represented as a convex combination of factors, i.e., points on the boundary of the convex hull of the data. This renders computation inefficient. In this paper, we show that the set of vertices of a convex hull, the so-called frame, can be efficiently computed by a quadratic program. We provide theoretical and empirical results for our proposed approach and make use of the frame to accelerate Archetypal Analysis. The novel method yields similar reconstruction errors as baseline competitors but is much faster to compute.}
}