Transactions of the Japanese Society for Artificial Intelligence
Online ISSN : 1346-8030
Print ISSN : 1346-0714
Short Paper
Simultaneous Higher-order Relation Prediction via Collective Incidence Matrix Embedding
Nozomi NoriDanushka BollegalaHisashi Kashima
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Volume 30 (2015) Issue 2 Pages 459-465

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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.

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© The Japanese Society for Artificial Intelligence 2015
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