# A Review of Knowledge Graph Completion

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Conventional Knowledge Graph Completion

#### 2.1. Translational Models

#### 2.2. Tensor Dompositional Models

^{2}). Additionally, RESCAL has never been tested on data with many relation types [27]. RESCAL has a large number of parameters, and this makes it prone to overfitting.

#### 2.3. Neural Network Models

#### 2.4. Convolutional-Based Models

## 3. Graph Neural Networks

#### 3.1. Graph Convolution Network Models

#### 3.2. Attention Neural Network Models

#### 3.3. Pre-Trained Neural Network Models in Knowledge Graphs

## 4. Challenges in Knowledge Graphs

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Notation | Description |
---|---|

d | Vector |

W_{r} | The normal vector of hyperplane |

r | Embedding vector of relation |

h, t | Embedding vectors of head and tail |

M | Projection matrix |

〈 〉 | Diagonal matrices |

d | The dimensionality of an entity in embedding space |

k | The dimensionality of relation in embedding space |

Re | The real part of a complex value |

⨂ | Hamilton product |

**Table 2.**Scoring functions of state-of-the-art translational-based knowledge graph embedding models.

Model | Score Function | Memory Complexity |
---|---|---|

TransE | ${\left|\left|h+r-t\right|\right|}_{\raisebox{1ex}{${l}_{1}$}\!\left/ \!\raisebox{-1ex}{${l}_{2}$}\right.}$ | $O\left({N}_{e}d+{N}_{r}d\right)$ |

TransH | ${\left|\left|\left(h-{w}_{r}^{T}h{w}_{r}\right)+{d}_{r}-\left(t-{w}_{r}^{T}t{w}_{r}\right)\right|\right|}_{2}^{2}$ | $O\left({N}_{e}d+{N}_{r}d\right)$ |

TransR | ${\left|\left|{M}_{r}h+{M}_{r}t\right|\right|}_{2}^{2}$ | $O\left({N}_{e}d+{N}_{r}({d}^{2}+d)\right)$ |

TransD | ${\left|\right|({r}_{p}{h}_{p}^{T}+I)h+r-\left({r}_{p}{r}_{p}^{T}+I\right)t\left|\right|}_{2}^{2}$ | $O\left(2{N}_{e}d+2{N}_{r}d\right)$ |

TransM | ${w}_{r}{\left|\left|h+r-t\right|\right|}_{\raisebox{1ex}{${l}_{1}$}\!\left/ \!\raisebox{-1ex}{${l}_{2}$}\right.}$ | $O\left({N}_{e}d+{N}_{r}k\right)$ |

TransW | $\begin{array}{cc}\left|\right|(\sum {h}_{i}\otimes {w}_{hi}+& {b}_{h})+\sum {r}_{i}\otimes {w}_{ri}\hfill \\ & -\left(\sum {r}_{i}\otimes {w}_{ti}+{b}_{t}\right){\left|\right|}_{1/2}^{2}\end{array}$ | |

RotatE | $-\left|\left|h\odot r-t\right|\right|$ | $O\left(2{N}_{e}d+2{N}_{r}d\right)$ |

HAKE | ${\left|\left|{h}_{m}\circ {r}_{m}-{t}_{m}\right|\right|}_{2}+\lambda {\left|\left|\mathrm{sin}\left(\left({h}_{p}+{r}_{p}-{t}_{p}\right)/2\right)\right|\right|}_{1}$ | $O\left(2{N}_{e}d+2{N}_{r}d\right)$ |

**Table 3.**Scoring functions of state-of-the-art tensor decompositional-based knowledge graph embedding models.

Model | Score Function | Memory Complexity |
---|---|---|

RESCAL | $h.{W}_{r}.t$ | $O\left({N}_{e}d+{N}_{r}{d}^{2}\right)$ |

DistMult | $\langle h,r,t\rangle $ | $O\left({N}_{e}d+{N}_{r}d\right)$ |

ComplEx | $Re\left(\langle h,r,\overline{t}\rangle \right)$ | $O\left(2{N}_{e}d+2{N}_{r}d\right)$ |

Quaternion | $h\otimes {r}^{\u22b2}.t$ | $O\left({N}_{e}d+{N}_{r}d\right)$ |

DualE | $h\otimes {r}^{\u22b2}.t$ | $O\left({N}_{e}d+{N}_{r}d\right)$ |

Tucker | $W{\times}_{1}{h}^{T}{\times}_{2}{M}_{r}{\times}_{3}t$ | $O\left({N}_{e}d+{N}_{r}d+{d}_{e}{d}_{r}{d}_{e}\right)$ |

**Table 4.**Scoring functions of state-of-the-art tensor decompositional-based knowledge graph embedding models.

Model | Score Function | Memory Complexity |
---|---|---|

SME | ${g}_{left}{\left(h,r\right)}^{T}{g}_{right}\left(r,t\right)$ | $O\left({N}_{e}d+{N}_{r}d\right)$ |

NTN | ${r}^{T}\mathrm{tanh}\left({h}^{T}\widehat{M}t+{M}_{r1}h+{M}_{r2}t+{b}_{r}\right)$ | $O\left({N}_{e}d+{N}_{r}{d}^{2}d\right)$ |

**Table 5.**Scoring functions of state-of-the-art convolutional-based knowledge graph embedding models.

Model | Score Function | Memory Complexity |
---|---|---|

ConvE | $f\left(vec\left(f(\left[\overline{h};\overline{r}]\right)\star \mathsf{\Omega}\right)W\right)t$ | $\begin{array}{cc}\hfill O({N}_{e}d+{N}_{r}d+& T{m}_{\mathsf{\Omega}}{n}_{\mathsf{\Omega}}+Td(2{d}_{m}-{m}_{\mathsf{\Omega}}\hfill \\ & +1)\left({d}_{n}-{n}_{\mathsf{\Omega}}+1\right)\end{array}$ |

ConvKB | $concat\left(f(\left[h,r,t]\right)\star \mathsf{\Omega}\right)w$ | $O\left({N}_{e}d+{N}_{r}k+4T\right)$ |

HypER | $f\left(vec\left(h\star ve{c}^{-1}({w}_{r}H\right)\right)W)t$ | $O\left({N}_{e}d+{N}_{r}d\right)$ |

InteractE | $f(f\left(perm\left(\left[h;r\right])\u229bw\right)W+b\right)t$ | $O\left({N}_{e}d+{N}_{r}d+T{m}_{\mathsf{\Omega}}{n}_{\mathsf{\Omega}}+2Tp{d}^{2}\right)$ |

ConEx | $Re\left(\langle conv\left(h,r\right),h,r,\overline{t}\rangle \right)$ |

Model | Relation Update | Entity Update |

R-GCN | - | ${h}_{i}^{\left(l+1\right)}=\sigma \left({h}_{i}^{\left(l\right)}{W}_{0}^{\left(l\right)}+{\displaystyle {\displaystyle \sum}_{j\in {N}_{i}^{r}}}{\displaystyle {\displaystyle \sum}_{r\in R}}\frac{1}{{c}_{i,r}}{h}_{j}^{\left(l\right)}{W}_{r}^{\left(l\right)}\right)$ |

RA-GCN | - | ${h}_{i}^{\left(l+1\right)}=\sigma \left({h}_{i}^{\left(l\right)}{W}_{0}^{\left(l\right)}+{\displaystyle {\displaystyle \sum}_{j\in {N}_{i}^{r}}}{\displaystyle {\displaystyle \sum}_{r\in R}}{h}_{j}^{\left(l\right)}{W}_{r}^{\left(l\right)}\right)$ |

TransE-GCN | ${r}_{k}^{l+1}=\sigma \left({W}_{1}^{\left(l\right)}{r}_{k}^{\left(l\right)}\right)$ | ${v}_{i}^{\left(\mathrm{l}+1\right)}=\sigma \left({\displaystyle {\displaystyle \sum}_{j\in {N}_{i}^{r}}}{\displaystyle {\displaystyle \sum}_{r\in R}}\frac{1}{{c}_{i,r}}{v}_{j}^{\left(l\right)}{W}_{r}^{\left(l\right)}+{W}_{o}^{\left(l\right)}{v}_{i}^{\left(l\right)}\right)$ |

KE-GCN | ${h}_{r}^{l+1}={\sigma}_{rel}()$ | ${m}_{v}^{l+1}={\displaystyle {\displaystyle \sum}_{\left(u,v\right)\in \mathcal{N}\left(r\right)}}{W}_{r}^{l}\frac{\partial {f}_{r}\left({h}_{u}^{l},{h}_{r}^{l},{h}_{v}^{l}\right)}{\partial {h}_{r}^{l}}$ |

CompGCN | ${h}_{r}^{l+1}={h}_{r}^{l}{W}_{rel}^{l}$ | ${h}_{v}^{l+1}={\displaystyle {\displaystyle \sum}_{\left(u,r\right)\in \mathcal{N}\left(v\right)}}{W}_{r}^{l}{\varphi}_{in}\left({h}_{u}^{l},{h}_{r}^{l}\right)$ |

**Table 7.**Link prediction with different embedding settings. Lower values in MR and Higher Hits are better.

Model | WN18RR | FB15k-237 | ||
---|---|---|---|---|

MR | Hits@10 | MR | Hits@10 | |

TransE [13] | 3384 | 50.1 | 357 | 46.5 |

TransH [61] | 2524 | 50.3 | 255 | 48.6 |

TransR [61] | 3166 | 50.7 | 237 | 51.1 |

TransD [61] | 276 | 50.7 | 246 | 48.4 |

DistMult [61] | 3704 | 47.7 | 411 | 41.9 |

ComplEx [61] | 3921 | 48.3 | 508 | 43.4 |

Tucker [31] | - | 52.6 | - | 54.4 |

ConvE [28] | 5277 | 48 | 246 | 49.1 |

InteractE [37] | 5202 | 52.8 | 172 | 53.5 |

ConvKB [39] | 3324 | 52.4 | 311 | 42.1 |

ConEx [38] | - | 55 | - | 55.5 |

LSA-GAT [49] | 1947 | 44 | 273 | 60 |

HARN [60] | 2113 | 54.2 | 156 | 54.1 |

R-GCN [15] | - | - | - | 41.7 |

RotatE-GCN [17] | - | 55.5 | - | 57.8 |

TransE-GCN [17] | - | 47.7 | - | 50.8 |

COMPGCN [16] | 3533 | 54.6 | 197 | 53.5 |

RotatE [13] | 3384 | 50.1 | 177 | 53.3 |

HAKE [23] | - | 58.2 | - | 54.2 |

KG-BERT [61] | 97 | 52.4 | 153 | 42.0 |

QuatE [13] | 2314 | 58.2 | 87 | 55 |

DualE [30] | 2270 | 44.4 | 91 | 55.9 |

DisenKGAT [59] | 1504 | 57.8 | 179 | 55.3 |

RAGAT [56] | 2390 | 56.22 | 199 | 54.7 |

KBGAT [18] | 1921 | 55.4 | 270 | 33.1 |

Inverse Model [28] | 13,219 | 36 | 7148 | 1.2 |

decentRL + TransE [43] | - | - | 159 | 52.1 |

decentRL + DistMult [43] | - | - | 151 | 54.1 |

RGCN + TransE [43] | - | - | 325 | 44.3 |

RGCN + DistMult [43] | - | - | 230 | 49.9 |

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Zamini, M.; Reza, H.; Rabiei, M.
A Review of Knowledge Graph Completion. *Information* **2022**, *13*, 396.
https://doi.org/10.3390/info13080396

**AMA Style**

Zamini M, Reza H, Rabiei M.
A Review of Knowledge Graph Completion. *Information*. 2022; 13(8):396.
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**Chicago/Turabian Style**

Zamini, Mohamad, Hassan Reza, and Minou Rabiei.
2022. "A Review of Knowledge Graph Completion" *Information* 13, no. 8: 396.
https://doi.org/10.3390/info13080396