A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs
A Non-commutative Bilinear Model for Answering Path Queries in Knowledge Graphs
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DOI：
10.18653/v1/d19-1246
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
K. Hayashi;M. Shimbo
中科院分区：
文献类型：
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作者：
K. Hayashi;M. Shimbo
知识图嵌入（KGE）的双线性对角模型，如DistMult和ComplEx，通过将关系表示为对角矩阵来平衡表达性和计算效率。虽然它们在预测原子关系方面表现良好，但复合关系（关系路径）不能通过关系矩阵的乘积自然地建模，因为对角矩阵的乘积是交换的，因此与关系的顺序不变。本文提出了一种新的基于块循环矩阵的双线性KGE模型BlockHolE。在BlockHolE中，关系矩阵可以是非交换的，允许用矩阵乘积来建模复合关系。该模型的参数化方式涵盖了从对角关系矩阵到全关系矩阵的范围。基于循环矩阵傅里叶变换的对偶性，可以发展出一种快速计算技术。
Bilinear diagonal models for knowledge graph embedding (KGE), such as DistMult and ComplEx, balance expressiveness and computational efficiency by representing relations as diagonal matrices. Although they perform well in predicting atomic relations, composite relations (relation paths) cannot be modeled naturally by the product of relation matrices, as the product of diagonal matrices is commutative and hence invariant with the order of relations. In this paper, we propose a new bilinear KGE model, called BlockHolE, based on block circulant matrices. In BlockHolE, relation matrices can be non-commutative, allowing composite relations to be modeled by matrix product. The model is parameterized in a way that covers a spectrum ranging from diagonal to full relation matrices. A fast computation technique can be developed on the basis of the duality of the Fourier transform of circulant matrices.