TY - GEN
T1 - Structured low-rank matrix factorization
T2 - 31st International Conference on Machine Learning, ICML 2014
AU - Haeffele, Benjamin D.
AU - Young, Eric D.
AU - Vidal, René
N1 - Publisher Copyright:
Copyright 2014 by the author(s).
PY - 2014
Y1 - 2014
N2 - Recently, convex solutions to low-rank matrix factorization problems have received increasing attention in machine learning. However, in many applications the data can display other structures beyond simply being low-rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current low-rank methods. In this paper we explore a matrix factorization technique suitable for large datasets that captures additional structure in the factors by using a projective tensor norm, which includes classical image regularizers such as total variation and the nuclear norm as particular cases. Although the resulting optimization problem is not convex, we show that under certain conditions on the factors, any local mini-mizer for the factors yields a global minimizer for their product. Examples in biomedical video segmentation and hyperspectral compressed recovery show the advantages of our approach on high-dimensional datasets.
AB - Recently, convex solutions to low-rank matrix factorization problems have received increasing attention in machine learning. However, in many applications the data can display other structures beyond simply being low-rank. For example, images and videos present complex spatio-temporal structures, which are largely ignored by current low-rank methods. In this paper we explore a matrix factorization technique suitable for large datasets that captures additional structure in the factors by using a projective tensor norm, which includes classical image regularizers such as total variation and the nuclear norm as particular cases. Although the resulting optimization problem is not convex, we show that under certain conditions on the factors, any local mini-mizer for the factors yields a global minimizer for their product. Examples in biomedical video segmentation and hyperspectral compressed recovery show the advantages of our approach on high-dimensional datasets.
UR - http://www.scopus.com/inward/record.url?scp=84919830640&partnerID=8YFLogxK
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M3 - Conference contribution
AN - SCOPUS:84919830640
T3 - 31st International Conference on Machine Learning, ICML 2014
SP - 4108
EP - 4117
BT - 31st International Conference on Machine Learning, ICML 2014
PB - International Machine Learning Society (IMLS)
Y2 - 21 June 2014 through 26 June 2014
ER -