Convex Collective Matrix Factorization

Guillaume Bouchard, Dawei Yin, Shengbo Guo
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:144-152, 2013.

Abstract

In many applications, multiple interlinked sources of data are available and they cannot be represented by a single adjacency matrix, to which large scale factorization method could be applied. Collective matrix factorization is a simple yet powerful approach to jointly factorize multiple matrices, each of which represents a relation between two entity types. Existing algorithms to estimate parameters of collective matrix factorization models are based on non-convex formulations of the problem; in this paper, a convex formulation of this approach is proposed. This enables the derivation of large scale algorithms to estimate the parameters, including an iterative eigenvalue thresholding algorithm. Numerical experiments illustrate the benefits of this new approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v31-bouchard13a, title = {Convex Collective Matrix Factorization}, author = {Bouchard, Guillaume and Yin, Dawei and Guo, Shengbo}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {144--152}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/bouchard13a.pdf}, url = {https://proceedings.mlr.press/v31/bouchard13a.html}, abstract = {In many applications, multiple interlinked sources of data are available and they cannot be represented by a single adjacency matrix, to which large scale factorization method could be applied. Collective matrix factorization is a simple yet powerful approach to jointly factorize multiple matrices, each of which represents a relation between two entity types. Existing algorithms to estimate parameters of collective matrix factorization models are based on non-convex formulations of the problem; in this paper, a convex formulation of this approach is proposed. This enables the derivation of large scale algorithms to estimate the parameters, including an iterative eigenvalue thresholding algorithm. Numerical experiments illustrate the benefits of this new approach.} }
Endnote
%0 Conference Paper %T Convex Collective Matrix Factorization %A Guillaume Bouchard %A Dawei Yin %A Shengbo Guo %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-bouchard13a %I PMLR %P 144--152 %U https://proceedings.mlr.press/v31/bouchard13a.html %V 31 %X In many applications, multiple interlinked sources of data are available and they cannot be represented by a single adjacency matrix, to which large scale factorization method could be applied. Collective matrix factorization is a simple yet powerful approach to jointly factorize multiple matrices, each of which represents a relation between two entity types. Existing algorithms to estimate parameters of collective matrix factorization models are based on non-convex formulations of the problem; in this paper, a convex formulation of this approach is proposed. This enables the derivation of large scale algorithms to estimate the parameters, including an iterative eigenvalue thresholding algorithm. Numerical experiments illustrate the benefits of this new approach.
RIS
TY - CPAPER TI - Convex Collective Matrix Factorization AU - Guillaume Bouchard AU - Dawei Yin AU - Shengbo Guo BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-bouchard13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 144 EP - 152 L1 - http://proceedings.mlr.press/v31/bouchard13a.pdf UR - https://proceedings.mlr.press/v31/bouchard13a.html AB - In many applications, multiple interlinked sources of data are available and they cannot be represented by a single adjacency matrix, to which large scale factorization method could be applied. Collective matrix factorization is a simple yet powerful approach to jointly factorize multiple matrices, each of which represents a relation between two entity types. Existing algorithms to estimate parameters of collective matrix factorization models are based on non-convex formulations of the problem; in this paper, a convex formulation of this approach is proposed. This enables the derivation of large scale algorithms to estimate the parameters, including an iterative eigenvalue thresholding algorithm. Numerical experiments illustrate the benefits of this new approach. ER -
APA
Bouchard, G., Yin, D. & Guo, S.. (2013). Convex Collective Matrix Factorization. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:144-152 Available from https://proceedings.mlr.press/v31/bouchard13a.html.

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