知识图谱：表示、获取与应用的全面综述

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本文是一篇深入探讨知识图谱的综合调查报告，"A Survey on Knowledge Graphs: Representation, Acquisition, and Applications"。作者Shaoxiong Ji、Shirui Pan、Erik Cambria（IEEE资深会员）和Pekka Marttinen、Philip S. Yu（IEEE生命院士）共同研究了这一领域在认知和人类级别智能方面的重要性。知识图谱作为一种结构化的实体间关系表示方式，近年来已经成为研究热点。报告首先关注知识图谱的四个核心主题：1）知识图谱表示学习，即如何将复杂的信息结构转化为易于理解和处理的形式，包括嵌入方法、空间组织、评分函数和辅助信息的优化；2）知识获取与完成，涉及如何从大规模数据中提取和补充知识，这包括基于嵌入的方法、路径推断以及逻辑规则的应用；3）时间知识图谱，强调动态变化和时间依赖性知识的建模和管理；4）知识驱动的应用，展示了知识图谱如何在推荐系统、搜索引擎优化、自然语言处理等实际场景中发挥关键作用。文章详细梳理了每个主题下的最新进展和突破，提供了对现有技术的深入剖析，并提出了对未来研究的前瞻性和可能的研究方向。为了更好地组织和理解这些内容，报告构建了一个全面的分类体系和新的分类框架，使得读者能够清晰地追踪各个子领域的研究脉络和发展趋势。这篇论文不仅概述了知识图谱的基础理论和技术，还揭示了其在推动人工智能进步中的关键角色，为研究人员、开发者和实践者提供了一个宝贵的参考资源，以促进知识图谱在不同领域的创新应用。通过阅读这份报告，读者可以深入了解知识图谱的现状、挑战和未来发展，为自己的研究或工作选择合适的技术路线。

r 2 R

2 R

d⇥d

2 R

d⇥d⇥k

(a) Point-wise space.

Im(u)

u = a + bi

b 2 R

a 2 R

u 2 C

Re(u)

(b) Complex vector space.

−2

−1.5

−1

−0.5

0.5

1.5

−2

−1.5

−1

−0.5

0.5

1.5

0.2

0.4

P (x

)

P (x

)

0.1

0.2

0.3

P (x

, x

)

(Face, HasInstance, *)

(Clock, HasPart, *)

Clock Dial

(d) Manifold space.

Fig. 4: An illustration of knowledge representation in different spaces.

al. [29] leverages expressive hyperbolic isometries and learns a

relation-speciﬁc absolute curvature

in the hyperbolic space.

TorusE [30] solves the regularization problem of TransE via

embedding in an n-dimensional torus space which is a compact

Lie group. With the projection from vector space into torus

space deﬁned as

π : R

→ T

, x 7→ [x]

, entities and relations

are denoted as

[h], [r], [t] ∈ T

. Similar to TransE, it also

learns embeddings following the relational translation in torus

space, i.e.,

[h] + [r] ≈ [t]

. Recently, DihEdral [31] proposes a

dihedral symmetry group preserving a 2-dimensional polygon.

B. Scoring Function

The scoring function is used to measure the plausibility of

facts, also referred to as the energy function in the energy-

based learning framework. Energy-based learning aims to learn

the energy function

(x)

(parameterized by

taking

input) and to make sure positive samples have higher scores

than negative samples. In this paper, the term of the scoring

function is adopted for uniﬁcation. There are two typical types

of scoring functions, i.e., distance-based (Fig. 5a) and similarity-

based (Fig. 5b) functions, to measure the plausibility of a

fact. Distance-based scoring function measures the plausibility

of facts by calculating the distance between entities, where

addictive translation with relations as

h + r ≈ t

is widely used.

Semantic similarity based scoring measures the plausibility of

facts by semantic matching. It usually adopts multiplicative

formulation, i.e.,

≈ t

, to transform head entity near

the tail in the representation space.

distance

(a) Translational distance-

based scoring of TransE.

h t

(h, r)

(b) Semantic similarity-based

scoring of DistMult.

Fig. 5: Illustrations of distance-based and similarity matching

based scoring functions taking TransE [15] and DistMult [32]

as examples.

1) Distance-based Scoring Function: An intuitive distance-

based approach is to calculate the Euclidean distance between

the relational projection of entities. Structural Embedding

(SE) [8] uses two projection matrices and

distance to learn

structural embedding as

(h, t) = kM

r,1

h − M

r,2

. (3)

A more intensively used principle is the translation-based

scoring function that aims to learn embeddings by representing

relations as translations from head to tail entities. Bordes et

al. [15] proposed TransE by assuming that the added embedding

h + r

should be close to the embedding of

with the scoring

function is deﬁned under L

or L

constraints as

(h, t) = kh + r − tk

. (4)

Since that, many variants and extensions of TransE have been

proposed. For example, TransH [19] projects entities and

relations into a hyperplane, TransR [16] introduces separate

projection spaces for entities and relations, and TransD [33]

constructs dynamic mapping matrices

= r

+ I

and

= r

+ I

by the projection vectors

, t

, r

∈ R

. By

replacing Euclidean distance, TransA [34] uses Mahalanobis

distance to enable more adaptive metric learning. Previous

methods used additive score functions, TransF [35] relaxes the

strict translation and uses dot product as

(h, t) = (h + r)

To balance the constraints on head and tail, a ﬂexible translation

scoring function is further proposed.

Recently, ITransF [36] enables hidden concepts discovery

and statistical strength transferring by learning associations

between relations and concepts via sparse attention vectors,

with scoring function deﬁned as

(h, t) =



· D · h + r − α

· D · t



, (5)

where

D ∈ R

n×d×d

is stacked concept projection matrices

of entities and relations and

, α

∈ [0, 1]

are attention

vectors calculated by sparse softmax, TransAt [37] integrates

relation attention mechanism with translational embedding,

and TransMS [38] transmits multi-directional semantics with

nonlinear functions and linear bias vectors, with the scoring

function as

(h, t) = k−tanh(t◦r)◦h+r−tanh(h◦r)◦t+α·(h◦t)k

1/2

. (6)

KG2E [25] in Gaussian space and ManifoldE [27] with

manifold also use the translational distance-based scoring

function. KG2E uses two scoring methods, i.e, asymmetric

KL-divergence and symmetric expected likelihood. While the

scoring function of ManifoldE is deﬁned as

(h, t) =



M(h, r, t) − D



, (7)

where

is the manifold function, and

is a relation-speciﬁc

manifold parameter.

2) Semantic Matching: Another direction is to calculate

the semantic similarity. SME [39] proposes to semantically

match separate combinations of entity-relation pairs of

(h, r)

and

(r, t)

. Its scoring function is deﬁned with two versions of

matching blocks - linear and bilinear block, i.e.,

(h, t) = g

left

(h, r)

right

(r, t). (8)

The linear matching block is deﬁned as

left

(h, t) = M

l,1

l,2

+ b

, and the bilinear form is

left

(h, r) = (M

l,1

h) ◦

l,2

r)+b

. By restricting relation matrix

to be diagonal

for multi-relational representation learning, DistMult [32]

proposes a simpliﬁed bilinear formulation deﬁned as

(h, t) = h

diag(M

)t. (9)

To capture productive interactions in relational data and

compute efﬁciently, HolE [20] introduces a circular correlation

of embedding, which can be interpreted as a compressed

tensor product, to learn compositional representations. By

deﬁning a perturbed holographic compositional operator as

p(a, b; c) = (c ◦a)? b

, where

is a ﬁxed vector, the expanded

holographic embedding model HolEx [40] interpolates the

HolE and full tensor product method. It can be viewed as linear

concatenation of perturbed HolE. Focusing on multi-relational

inference, ANALOGY [21] models analogical structures of

relational data. It’s scoring function is deﬁned as

(h, t) = h

t, (10)

with relation matrix constrained to be normal matrices in linear

mapping, i.e.,

= M

for analogical inference.

Crossover interactions are introduced by CrossE [41] with an

interaction matrix

C ∈ R

×d

to simulate the bi-directional

interaction between entity and relation. The relation speciﬁc

interaction is obtained by looking up interaction matrix as

= x

. By combining the interactive representations and

matching with tail embedding, the scoring function is deﬁned

f(h, r, t) = σ



tanh (c

◦ h + c

◦ h ◦ r + b) t



. (11)

The semantic matching principle can be encoded by neural

networks further discussed in Sec. III-C.

The two methods mentioned above in Sec.

III-A

4 with group

representation also follow the semantic matching principle. The

scoring function of TorusE [30] is deﬁned as:

min

(x,y)∈([h]+[r])×[t]

kx − yk

. (12)

By modeling

relations as group elements, the scoring

function of DihEdral [31] is deﬁned as the summation of

components:

(h, t) = h

Rt =

l=1

(l)>

(l)

, (13)

where the relation matrix

is deﬁned in block diagonal form

for

(l)

∈ D

, and entities are embedded in real-valued space

for h

(l)

and t

(l)

∈ R

C. Encoding Models

This section introduces models that encode the interactions

of entities and relations through speciﬁc model architectures,

including linear/bilinear models, factorization models, and

neural networks. Linear models formulate relations as a

linear/bilinear mapping by projecting head entities into a

representation space close to tail entities. Factorization aims

to decompose relational data into low-rank matrices for

representation learning. Neural networks encode relational data

with non-linear neural activation and more complex network

structures. Several neural models are illustrated in Fig. 6.

1) Linear/Bilinear Models: Linear/bilinear models encode

interactions of entities and relations by applying linear operation

as:

(h, t) = M





, (14)

or bilinear transformation operations as Eq. 10. Canonical

methods with linear/bilinear encoding include SE [8], SME [39],

DistMult [32], ComplEx [22], and ANALOGY [21]. For

TransE [15] with L2 regularization, the scoring function can

be expanded to the form with only linear transformation with

one-dimensional vectors, i.e.,

kh + r − tk

= 2r

(h − t) − 2h

t + krk

+ khk

+ ktk

. (15)

Wang et al. [46] studied various bilinear models and eval-

uated their expressiveness and connections by introducing

the concepts of universality and consistency. The authors

further showed that the ensembles of multiple linear models

can improve the prediction performance through experiments.

Recently, to solve the independence embedding issue of entity

vectors in canonical Polyadia decomposition, SimplE [47]

introduces the inverse of relations and calculates the average

canonical Polyadia score of (h, r, t) and (t, r

−1

, h) as

(h, t) =



h ◦ rt + t ◦ r



, (16)

where

is the embedding of inversion relation. More bilinear

models are proposed from a factorization perspective discussed

in the next section.

2) Factorization Models: Factorization methods formulated

KRL models as three-way tensor

decomposition. A general

principle of tensor factorization can be denoted as

hrt

≈

, with the composition function following the semantic

matching pattern. Nickel et al. [48] proposed the three-way

rank-

factorization RESCAL over each relational slice of

knowledge graph tensor. For

-th relation of

relations, the

k-th slice of X is factorized as

≈ AR

. (17)

The authors further extended it to handle attributes of entities

efﬁciently [49]. Jenatton et al. [50] then proposed a bilinear

structured latent factor model (LFM), which extends RESCAL

by decomposing

i=1

. By introducing three-

way Tucker tensor decomposition, TuckER [51] learns to

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