TransH 论文笔记

- Abstract

TransH在TransE的基础上的改进，将关系映射到超平面，在超平面上进行平行操作。并提出更好的负例样本设计方式。

- Background

最开始的传统逻辑推理方式，不易于处理，也不具有健壮性。后发展到，将知识图谱嵌入到向量空间，关系r则是向量空间中的操作。

其中，TransE并不能很好的处理“reflexive, one-to-many, many-to-one, and many-to-many”。

- ALgorithm

In TransH, each relation is characterized by two vectors, the norm vector (wr) of the hyperplane, and the translation vector (dr ) on the hyperplane. For a golden triplet (h, r, t), that it is correct in terms of worldly facts, the projections of h and t on the hyperplane are expected to be connected by the translation vector dr with low error.
不是是实体的相同嵌入空间内操作，而是映射到超平面。

Wr.T * h = h · Wr( 点积)，是h在单位向量Wr上的投影。再乘上Wr，则为hwr。
打分函数：

最小化损失函数的限制：

非受限损失函数：

同时采用随机梯度下降算法。

降低错误的负例：
We tend to give more chance to replacing the head entity if the relation is one-to-many and give more chance to replacing the tail entity if the relation is many-to-one. In this way, the chance of generating false negative labels is reduced.
tph -> 每头实体所对应的尾实体个数；
hpt -> 每尾实体所对应的头实体个数。

- Experiment

link prediction:
this task is to complete a triplet (h, r, t) with h or t missing, i.e., predict t given (h,r) or predict h given (r,t). Rather than requiring one best answer, this task emphasizes more on ranking a set of candidate entities from the knowledge graph.
Regarding the strategy of constructing negative labels, we use “unif” to denote the tra- ditional way of replacing head or tail with equal probability, and use “bern.” to denote reducing false negative labels by replacing head or tail with different probabilities.

even the naive baseline Unstructured (i.e., TransE without translation) outperform other approaches on WN18 in terms of the Mean metric. This may be because the number of relations in WN18 is quite small so that it is acceptable to ignore the different types of relations.



triplets classification:
This task is to confirm whether a given triplet (h, r, t) is cor- rect or not, i.e., binary classification on a triplet.

NTN：张量神经网络模型
FB13是稠密的图谱，具有强关连性。

relational fact extraction:
knowledge graph embedding is able to score a candidate fact, without observing any evidence from ex- ternal text corpus.
精确率和召回率的关系：https://www.zhihu.com/question/19645541


图a：结合Sm2r（文本侧提取法）的得分规则，计算出TransE、TransH的得分
图b：体现TransE、TransH的独立预测能力，以矢量嵌入为得分规则
Sm2r on this subset of candidates. TransH performs much better than TransE when recall is higher than 0.6.

- Conclusion

TransH overcomes the flaws of TransE concerning the reflexive/one-to-many/many-to-one/many-to-many rela- tions while inheriting its efficiency. Extensive experiments on the tasks of link prediction, triplet classification, and rela- tional fact extraction show that TransH brings promising im- provements to TransE. The trick of reducing false negative labels proposed in this paper is also proven to be effective.