The paper "Relational Learning via Collective Matrix Factorization" by Ajit P. Singh and Geoffrey J. Gordon introduces a method for relational learning that predicts unknown values of relations given a database of entities and observed relations among them. The authors propose a collective matrix factorization model that simultaneously factors multiple matrices, sharing parameters when an entity participates in multiple relations. This approach leverages information from one relation to improve predictions in another, enhancing the accuracy of the model. The model can handle various error models and relational schemas, and it generalizes several existing matrix factorization methods. The paper also discusses the use of Bregman divergences to measure error and extends standard alternating projection algorithms to the collective matrix factorization model. Additionally, it introduces stochastic optimization methods to handle large, sparse matrices. The authors demonstrate the efficiency and effectiveness of their model through experiments on movie rating prediction tasks, showing that it outperforms single-matrix factorization methods in both dense and sparse data scenarios.The paper "Relational Learning via Collective Matrix Factorization" by Ajit P. Singh and Geoffrey J. Gordon introduces a method for relational learning that predicts unknown values of relations given a database of entities and observed relations among them. The authors propose a collective matrix factorization model that simultaneously factors multiple matrices, sharing parameters when an entity participates in multiple relations. This approach leverages information from one relation to improve predictions in another, enhancing the accuracy of the model. The model can handle various error models and relational schemas, and it generalizes several existing matrix factorization methods. The paper also discusses the use of Bregman divergences to measure error and extends standard alternating projection algorithms to the collective matrix factorization model. Additionally, it introduces stochastic optimization methods to handle large, sparse matrices. The authors demonstrate the efficiency and effectiveness of their model through experiments on movie rating prediction tasks, showing that it outperforms single-matrix factorization methods in both dense and sparse data scenarios.