TY - CHAP

T1 - Frame-based Data Factorizations

AU - Mair, Sebastian

AU - Boubekki, Ahcène

AU - Brefeld, Ulf

N1 - Conference code: 34

PY - 2017/7/25

Y1 - 2017/7/25

N2 - 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.

AB - 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.

KW - Business informatics

UR - http://proceedings.mlr.press/v70/mair17a.html

UR - http://www.scopus.com/inward/record.url?scp=85048477893&partnerID=8YFLogxK

M3 - Article in conference proceedings

T3 - Proceedings of Machine Learning Research

SP - 2305

EP - 2313

BT - 34th International Conference on Machine Learning, ICML 2017

A2 - Precup, Doina

A2 - Teh, Yee Whye

PB - Curran Associates

CY - Red Hook

T2 - International Conference on Machine Learning - ICML 2017

Y2 - 6 August 2017 through 11 August 2017

ER -