Relational learning via collective matrix factorization

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 would then encode users' ratings of movies, movies' genres, and actors' roles in movies. A common prediction technique given one pairwise relation, for example a #users × #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.

Reasoning about Object Affordances in a Knowledge Base Representation

“…In this work, we choose to express our data structure and inference in a Markov Logic Network (MLN). A number of recent advances in database and machine learning [30,32,4] also point ways to different inference algorithms.…”

Một Tiếp Cận Đa Quan Hệ Cho Hệ Thống Gợi Ý

“…Trước tiên chúng tôi tóm tắt ngắn gọn kỹ thuật phân rã ma trận trên quan hệ đơn (MF) (xem thêm trong bài viết [4]) và kỹ thuật phân rã ma trận đa quan hệ (MRMF) (xem thêm trong bài viết [5], [11]) để làm cơ sở cho việc đề xuất một hướng tiếp cận đa quan hệ mới.…”

Bayesian Matrix Co-Factorization: Variational Algorithm and Cramér-Rao Bound

“…Matrix co-factorization has been used to improve the performance of matrix factorization by incorporating knowledge in the additional matrices, such as label information [16], link information [17], and inter-subject variations [3]. One of the advantages of the matrix co-factorization is that it can be applied for the general entity-relationship models of the target data and the additional data [9,14], where the factor matrices correspond to the entities and the input matrices correspond to the relationships of the model. Since the entity-relationship model is a fundamental tool to model the relational data, this simple mapping between the entity-relationship model and the co-factorization model enables the straight-forward use of various kind of side information, especially for the cold-start problems where both the user side information and the item side information are required.…”