Simultaneous higher-order relation prediction via collective incidence matrix embedding

Abstract

We propose a prediction method for higher-order relational data from multiple sources. The high-dimensional property of higher-order relations causes problems associated with sparse observations. To cope with this problem, we propose a method to integrate higher-order relational data from multiple sources. Our target task is the simultaneous decomposition of higher-order, multi-relational data, which corresponds to the simultaneous decomposition of multiple tensors. However, we transform each tensor into an incidence matrix for the corresponding hypergraph and apply a nonlinear dimensionality reduction technique that results in a generalized eigenvalue problem guaranteeing global optimal solutions. We also extend our method to incorporate objects’ attribute information to improve prediction for unseen/unobserved objects. To the best of our knowledge, this is the first reported method that can make predictions for (1) higher-order relations (2) with multi-relational data (3) with object attribute information and which (4) guarantees global optimal solutions. Using real-world datasets from social web services, we demonstrate that our proposed method is more robust against data sparsity than state-of-the-art methods for higher-order, single/multi-relational data including nonnegative multiple tensor factorization.