KGE-HousE
huyi / August 2022
Abstract
model evaluation
The effectiveness of KGE largely depends on the ability to model intrinsic relation patterns and mapping properties.
work of this paper
- HousE
两种 Householder transformations:
- (1) Householder rotations to achieve superior capacity of modeling relation patterns;
- (2) Householder projections to handle sophisticated relation mapping properties.
- rotation –> modeling relation patterns
- projection –> relation mapping properties
Introduction
overview
KGE 是一种 graph completion 的手段，learns low-dimensional representations for entities and relations, excels as an effective tool for predicting missing links.
problem
none of the existing methods is capable of modeling all the relation patterns and RMPs
contribution
- 提出了一个 general model 叫 HousE.
- 提出了一种 model 高维旋转的方法 ———— householder parameterization
- vanilla Householder reflections –> Householder projections
- By combining the Householder projections and rotations, HousE is able to model all the relation patterns and RMPs in Table 1.
- experiment
- We conduct extensive experiments over five benchmarks and our proposal consistently outperforms SOTA baselines over all the datasets.
Problem Setup
学习目标
we define the score function as a distance function $d_r(h, t)$. The distance of the positive triple $(h, r, t) \in D$ is expected to be smaller than the corrupted negative triples $(h′, r, t)$ or $(h, r, t′)$, which can be generated by randomly replacing the entity $h$ or $t$ with other entities.
是否需要多一个检查步骤，即coruppted triples不在dataset当中loss function
用相对损失函数
Methodology
3.1 HousE-r: Relational Householder Rotations
-
naive strategy 随便初始化一个k*k维的旋转矩阵，然后通过每一次gradient descent来更新参数
- complicated optimization process
- cannot fully cover the set of all k × k rotation matrices 为什么不能cover全部的rotation？
-
elegant parameterization based on Householder reflections
- any k-dimensional rotations can be represented as $2[\frac{k}{2}]$ Householder reflections
- 这种参数化方式的优势在于：model k-dimensional rotations without any special optimizing procedure
- 反射矩阵 Householder matrix H
-
Based on the Householder matrices, we can design a mapping to represent rotations
- Theorem 3.1. When n = $\frac{k}{2}$, the image of Rot-H is the set of all k × k rotation matrices, i.e., Image(Rot-H) = SO(k), SO(k) is the k-dimensional special orthogonal group. 那k是奇数的时候怎么办？
- any k-dimensional rotations can be represented as $2[\frac{k}{2}]$ Householder reflections
