RESCAL 论文笔记

- 预备知识

克罗内克积（Kronecker product）
https://baike.baidu.com/item/%E5%85%8B%E7%BD%97%E5%86%85%E5%85%8B%E7%A7%AF/6282573?fr=aladdin

- Abstract

we present a novel approach to relational learning based on the factorization of a three-way tensor.

method is able to perform collective learning via the latent components of the model and provide an efficient algorithm to compute the factoriza- tion.

- Background

最开始的张量分解法，无法实现集体学习（捕捉相关实体的属性、关系或类别）；随后的DEDICOM可以实现，但是有约束条件，无法合理的关系学习。

well-known tensor factorization approaches such as CANDECOMP/PARAFAC (CP) (Harshman & Lundy, 1994) or Tucker (Tucker, 1966) cannot model this collective learning effect sufficiently. The DEDICOM de- composition (Harshman, 1978) is capable of detecting this type of correlations, but unfortunately, it puts constraints on the model that are not reasonable for relational learning in general and thus leads to suboptimal results.

对比现有的关系学习的方法，会有更好或者相似的实验结果，但是耗时更少。

- Algorithm

语义网中的RDF模型由(subject, predicate, object) 组成的。在张量中，1、0代表实体之间的关系是否存在。
参数说明：

打分函数：

是非对称矩阵，这样可以建模非对称关系，在同一个实体作为头实体或尾实体时会得到不同的 latent component representation。

损失函数：

- Experment

• Collective Classification（集合分类）

属于集合学习，一组实例可能是相关的，应该对这个集体进行分类推断。为了获得这些依赖关系，不能只得到简单的关系特征，还需要从实例中挖掘到更深层次的依赖关系。

对实体进行预测，通过准确度判断。

• Collective Entity Resolution（集合实体解析）
  可视为一个link predition，通过预测三元组（x，isEqual，y）的概率，从实体-潜在成分空间A中进行推导两个实体的相似程度。

• Kinships, Nations and UMLS
  

• Runtime Performance and Technical Considerations

- Conclusion

our approach is able to perform collective learning via the latent compo- nents of the factorization. The results on various datasets as well as the runtime performance are very competiive and show that tensors in general and RESCAL specifically are promising new approaches to relational learning.