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Relational Learning via Collective Matrix Factorization (2008)

By: Ajit P. Singh and Geoffrey J. Gordon

Abstract: Relational learning is concerned with predicting unknown values of a relation, given a database of entities and observed relations among entities. An example of relational learning is movie rating prediction, where entities could include users, movies, genres, and actors. Relations encode users' ratings of movies, movies' genres, and actors' roles in movies. A common prediction technique given one pairwise relation, for example a \#users TIMES \#movies ratings matrix, is low-rank matrix factorization. In domains with multiple relations, represented as multiple matrices, we may improve predictive accuracy by exploiting information from one relation while predicting another. To this end, we propose a collective matrix factorization model: we simultaneously factor several matrices, sharing parameters among factors when an entity participates in multiple relations. Each relation can have a different value type and error distribution; so, we allow nonlinear relationships between the parameters and outputs, using Bregman divergences to measure error. We extend standard alternating projection algorithms to our model, and derive an efficient Newton update for the projection. Furthermore, we propose stochastic optimization methods to deal with large, sparse matrices. Our model generalizes several existing matrix factorization methods, and therefore yields new large-scale optimization algorithms for these problems. Our model can handle any pairwise relational schema and a wide variety of error models. We demonstrate its efficiency, as well as the benefit of sharing parameters among relations.

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Ajit P. Singh and Geoffrey J. Gordon (2008). "Relational Learning via Collective Matrix Factorization." Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD). pdf long          
BibTeX citation

@inproceedings{Singh+Gordon:kdd08cmf,
author = {Ajit P. Singh and Geoffrey J. Gordon},
title = {Relational Learning via Collective Matrix Factorization},
booktitle = {Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD)},
year = 2008,
wwwfilebase = {kdd2008-singh-gordon},
wwwtopic = {Relational Learning}
}



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