Графы знаний
TRANSCRIPT
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Графы знанийЛекция 7 - Knowledge Graph Embeddings
М. Галкин, Д. Муромцев
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Сегодня
2
1. Introduction 2. Представление знаний в графах - RDF & RDFS & OWL 3. Хранение знаний в графах - SPARQL & Graph Databases4. Однородность знаний - RDF* & Wikidata & SHACL & ShEx5. Интеграция данных в графы знаний - Semantic Data Integration 6. Введение в теорию графов - Graph Theory Intro 7. Векторные представления графов - Knowledge Graph Embeddings8. Машинное обучение на графах - Graph Neural Networks & KGs 9. Некоторые применения - Question Answering & Query Embedding
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Представление знаний - онтологическое
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genre genreplayed played
starredIn starredIn
characterIn
Leonard Nimoy Star Trek Star Wars Alec Guinness
Spock Science Fiction Obi-Wan Kenobi
LeonardNimoy starredIn StarTrek;played Spock.
Spock characterIn StarTrek .
AlecGuinness starredIn StarWars;played Obi-Wan.
StarWars genre SciFi .
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Представление знаний - статистическое
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genre genreplayed played
starredIn starredIn
characterIn
Leonard Nimoy Star Trek Star Wars Alec Guinness
Spock Science Fiction Obi-Wan Kenobi
Spock = [0.1, 0.2, 0.3]Leonard Nimoy = [0.4, 0.8, 0.1]Star Trek = [0.22, 0.34, 0.87]
characterIn = [0.1, 0.1, 0.6]
Obi-Wan = [0.05, 0.25, 0.37]Alec Guinness = [0.33, 0.5, 0.3]Star Wars = [0.18, 0.4, 0.9]
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Embedding - что мы хотим получить
5
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Big Picture in ℝ5
6
Graph Encoder
Node classification Entity MatchingLink prediction Query Embedding
Knowledge Graph
Inductive
Transductive Triples
Hyper-relational
Supervised
Unsupervised
Unimodal
Multimodal
Small
Large (sampling)
TASK
SETTING
Theoretical Understanding
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В этой лекции
7
Graph Encoder
Node classification Entity MatchingLink prediction Query Embedding
Knowledge Graph
Inductive
Transductive Triples
Hyper-relational
Supervised
Unsupervised
Unimodal
Multimodal
Small
Large (sampling)
TASK
SETTING
Theoretical Understanding
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В этой лекции
8
Transductive
Triples
Supervised
Unimodal
Small
Весь граф известен во время тренировки
KG состоит только из триплетов (про RDF* - позднее) без литералов
Обучение с учителем на конкретной задаче. Сигнал - известные связи
Только граф, без текста / видео / изображений / геометрии / другого
Стандартные датасеты - до 100К узлов
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Почему бы не взять методы из прошлой лекции?
Классический граф- Ненаправленный- Нет типов связей
9
1
7
4
6
5
2
3
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Почему бы не взять методы из прошлой лекции?
Классический граф- Ненаправленный- Нет типов связей
10
1
7
4
6
5
2
31
7
4
6
5
2
3
Наш клиент- Направленный- Мультиграф- Много типов связей
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Классический Link Prediction
Вероятность связи как функция от вершин
11
1
7
4
6
5
2
3
1 3p( , ) = f( , ) 1 3
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KG Link Prediction (KG Completion)
12Nickel et al. A review of relational machine learning for knowledge graphs. IEEE. 2015
genre genreplayed played
starredIn starredIn
characterIn
Leonard Nimoy Star Trek Star Wars Alec Guinness
Spock Science Fiction Obi-Wan Kenobi
characterIn
(Obi-Wan, characterIn, ?)
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characterIn
KG Link Prediction (KG Completion)
13Nickel et al. A review of relational machine learning for knowledge graphs. IEEE. 2015
genre genreplayed played
starredIn starredIn
characterIn
Leonard Nimoy Star Trek Star Wars Alec Guinness
Spock Science Fiction Obi-Wan Kenobi
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KG Link Prediction - Input
14
1
3 34 4
2 2
1
2 3 5 7
1 4 6e2id1: Spock2: Leonard Nimoy3: Star Trek4: SciFi5: Star Wars6: Obi-Wan7: Alec Guinness
r2id1: characterIn2: starredIn3: genre4: played
1 1 32 4 12 2 33 3 45 3 47 2 57 4 66 1 ?
Типичный вход KG embedding моделей
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Relational Patterns
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knows(a, b) -> knows(b, a)Симметричность
Антисимметричность
Инверсия
Композиция
Отношения 1-N
friend(a, b) -> ¬friend(b, a)
cast(a, b) -> starredIn(b, a)
mother(a, b) ⋀ husband(b, c) -> father(a, c)
hasCity(country, city1),
hasCity(country, city2), ...
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Knowledge Graph Embeddings
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Goal: encode nodes so that similarity in the embedding space (e.g., dot product) approximates similarity in the original network
Tensor Factorization
Translation
Neural Networks
Graph Neural Nets Source: Stanford CS224w, http://web.stanford.edu/class/cs224w/
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Knowledge Graph Embeddings
17
Tensor Factorization
Translation
Neural Networks
Shallow embedding(каждый узел и тип связи -> уникальный вектор)
Source: Stanford CS224w, http://web.stanford.edu/class/cs224w/
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KGE - Graphs as Tensors
18Nickel et al. A review of relational machine learning for knowledge graphs. IEEE. 2015
genre genreplayed played
starredIn starredIn
characterIn
Leonard Nimoy Star Trek Star Wars Alec Guinness
Spock Science Fiction Obi-Wan Kenobi
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KGE - Graphs as Tensors
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starredIn
Leonard Nimoy Star Trek
0 1
0 0
starredIn
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KGE - Graphs as Tensors
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starredIn
Leonard Nimoy Star Trek
0 1 0
0 0 0
0 0 0
starredIn
played
characterIn
Spock
0 0 1
0 0 0
0 0 0
played
0 0 0
0 0 0
0 1 0
characterIn
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0 0 0
0 0 0
0 1 0
KGE - Graphs as Tensors
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starredIn
Leonard Nimoy Star Trek
0 1 0
0 0 0
0 0 0
starredIn
played
characterIn
Spock
0 0 1
0 0 0
0 0 0
played
0 0 0
0 0 0
0 1 0
characterIn
0 0 1
0 0 0
0 0 0
0 1 0
0 0 0
0 0 0
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KGE - RESCAL
Goal - factorize a sparse 3D tensor to dense E and R
22
Tensor Factorization
Nickel et al. A review of relational machine learning for knowledge graphs. IEEE. 2015
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KGE - RESCAL
Goal - factorize a sparse 3D tensor to dense E and R
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Tensor Factorization
Nickel et al. A review of relational machine learning for knowledge graphs. IEEE. 2015
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KGE - RESCAL
Goal - factorize a sparse 3D tensor to dense E and R
24
Tensor Factorization
Yang et al. Embedding Entities And Relations For Learning And Inference In Knowledge Bases. ICLR 2015
RESCAL
Entity matrix Relations matrix Score function (e1,r,e2)
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KGE - DistMult
Goal - factorize a sparse 3D tensor to dense E and R
25
Tensor Factorization
Yang et al. Embedding Entities And Relations For Learning And Inference In Knowledge Bases. ICLR 2015
RESCAL
diag(Wk)
DistMult
Entity matrix Relations matrix Score function (e1,r,e2)
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KGE - DistMult & Patterns
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Tensor Factorization
Симметричность
Антисимметричность
Инверсия
Композиция
Отношения 1-N
Умножение коммутативно
Невозможно геометрически
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KGE - ComplEx
ComplEx - let’s use complex numbers instead of real
27
Tensor Factorization
Trouillon et al. Complex Embeddings for Simple Link Prediction. ICML 2016
DistMult
Entity matrix Relations matrix Score function (e1,r,e2)
ComplEx
Антисимметричность
Теперь можно
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KGE - ComplEx & Patterns
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Tensor Factorization
Симметричность
Антисимметричность
Инверсия
Композиция
Отношения 1-N
При Im(r) = 0
Возможно при
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KGE - TuckER
Goal - factorize a sparse 3D tensor to dense core W, entities E and relations R
29
Tensor Factorization
Balazevic et al. TuckER: Tensor Factorization for Knowledge Graph Completion. EMNLP 2019
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KGE - TransE
30
Tensor Factorization
Translation
Translate entities and relations into one embedding space
Wang et al. Knowledge Graph Embedding by Translating on Hyperplanes. AAAI 2014Bordes et al. Translating Embeddings for Modeling Multi-relational Data. NIPS 2013
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KGE - TransE
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Tensor Factorization
Translation
Translate entities and relations into one embedding space
Bordes et al. Translating Embeddings for Modeling Multi-relational Data. NIPS 2013
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KGE - TransE & Patterns
32
Tensor Factorization
Translation
Bordes et al. Translating Embeddings for Modeling Multi-relational Data. NIPS 2013
Симметричность
Антисимметричность
Инверсия
КомпозицияОтношения 1-N
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KGE - TransE
33
Tensor Factorization
TranslationLOTS of models
Cai et al. A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications. IEEE TKDE 2017
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KGE - Incorporating OWL Rules
34
Tensor Factorization
Translation
Nayyeri et al. LogicENN: A Neural Based Knowledge Graphs Embedding Model with Logical Rules. https://arxiv.org/abs/1908.07141
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KGE - RotatE
35
Tensor Factorization
Translation
Sun et al. RotatE: Knowledge Graph Embedding By Relational Rotation In Complex Space. ICLR 2019
Score function:
Loss & Optimization:
Idea: Entities are vectors in complex space
Relations: rotations in complex space
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KGE - RotatE & Patterns
36Sun et al. Rotate: Knowledge graph embedding by relational rotation in complex space. ICLR 2019
Translation
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KGE - Hyperbolic
37
Tensor Factorization
Translation
Nickel et al. Poincaré Embeddings for Learning Hierarchical Representations. NIPS 2017
Goal: embed hierarchical structures into a hyperbolic manifold.
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KGE - Hyperbolic
38
Tensor Factorization
Translation
Chami et al. Low-Dimensional Hyperbolic Knowledge Graph Embeddings. ACL 2020
Goal: embed hierarchical structures into a hyperbolic manifold
✓ Хорошо работает на иерархических графах
✓ Эффективны на малых размерностях (32-64d)
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KGE - ConvE
Goal: CNNs for predicting a probability of the object
39
Tensor Factorization
Translation
Convolution
Minervini et al. Convolutional 2D Knowledge Graph Embeddings. AAAI 2018
Score function:
Loss & Optimization:
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KGE - ConvKB
40
Tensor Factorization
Translation
Convolution
Nguyen et al. A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network. NAACL 2018
Score function:
Loss & Optimization:
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KGE - CoKE
41
Tensor Factorization
Translation
Transformer
Wang et al. CoKE: Contextualized Knowledge Graph Embeddings. arxiv 2019
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Training & Evaluation
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KGE - Training
43
Entity matrix
Relations matrix
starredIn
played
characterIn
Spock
Spock = [0.1, 0.2, 0.3]Leonard Nimoy = [0.4, 0.8, 0.1]Star Trek = [0.22, 0.34, 0.87]
characterIn = [0.1, 0.1, 0.6]played = [0.2, 0.3, 0.4]starredIn = [0.9, -0.2, 0.1]
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KGE - Training
44
Entity matrix
Relations matrix
starredIn
played
characterIn
Spock
Spock = [0.1, 0.2, 0.3]Leonard Nimoy = [0.4, 0.8, 0.1]Star Trek = [0.22, 0.34, 0.87]
characterIn = [0.1, 0.1, 0.6]played = [0.2, 0.3, 0.4]starredIn = [0.9, -0.2, 0.1]
Optimization
Loss Function
Negative Sampling
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KGE - Training - sLCWA vs LCWA
45
Local Closed World Assumption (LCWA)
stochasticLocal Closed World
Assumption (sLCWA)
● Предсказываем распределение по всем сущностям на выходе (1-N scoring)
● Classification losses:- BCE, CE
● Часто добавляют inverse relations
● Negative sampling
● Contrastive losses:- Margin Ranking Loss - Self-Adversarial Loss- Softplus Loss
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KGE - Adding Inverse Relations
46Nickel et al. A review of relational machine learning for knowledge graphs. IEEE. 2015
genre genreplayed played
starredIn starredIn
characterIn
Leonard Nimoy Star Trek Star Wars Alec Guinness
Spock Science Fiction Obi-Wan Kenobi
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KGE - Adding Inverse Relations
47Nickel et al. A review of relational machine learning for knowledge graphs. IEEE. 2015
genre genreplayed played
starredIn starredIn
characterIn
Leonard Nimoy Star Trek Star Wars Alec Guinness
Spock Science Fiction Obi-Wan Kenobi
played_inverse
played_inverse
characterIn_inverse
starredIn_inverse starredIn_inverse
genre_inverse
➢ 2x больше триплетов
➢ 2х больше типов предикатов
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KGE - Training - sLCWA + Margin Loss
48
Negative sampling: incorrect triples should have lower (higher) score than correct triples
starredIn
starredIn
starredIn
starredIn
starredIn
starredIn
corrupt O
corrupt S
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KGE - Training - sLCWA + Margin Loss
49
Negative sampling: incorrect triples should have lower (higher) score than correct triples
starredIn
starredIn
starredIn
starredIn
starredIn
starredIn
corrupt O
corrupt SNegative Sampling Self-Adversarial Loss (NSSAL) (Sun et al)
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KGE - Training - sLCWA + Margin Loss
50
Negative sampling: incorrect triples should have lower (higher) score than correct triples
starredIn
starredIn
starredIn
starredIn
starredIn
starredIn
corrupt O
corrupt SstarredIn starredIn>f f
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KGE - Training - LCWA + (Binary) Cross-Entropy Loss
51
Model’s output is usually sigmoid / log softmax
starredIn starredIn_inverse
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KGE - Training - sLCWA vs LCWA
52
Local Closed World Assumption (LCWA)
stochasticLocal Closed World
Assumption (sLCWA)
+ Быстрее сходится+ Быстрый evaluation
- Output shape: [bs, num_entities]- Батчи съедают много GPU памяти- Софт-лимит: 100К сущностей
+ Output shape: [bs*num_negs, 1]+ Работает на больших графах + Меньше GPU consumption
- Медленно сходится- Нужно дополнительно
подбирать margin , temperature- Долгий evaluation
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KGE - Training - Metrics
53
starredIn
starredIn
starredIn
starredIn
starredIn
starredIn
0.89
0.34
0.66
0.89
0.93
0.98
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KGE - Training - Metrics
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starredIn
starredIn
starredIn
starredIn
starredIn
starredIn
0.89
0.34
0.66
0.89
0.93
0.98
Corrupt O
Corrupt S MR MRR Avg H@k
Rank 1 3
2 0.66Reciprocal rank
1 ⅓
Hits@1 1 0 0.5
Hits@3 1 1 1.0
Hits@10 1 1 1.0
Как правило, все метрики подсчитываются в
отфильтрованном режиме
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KGE - Training - Filtered Metrics
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exampleMovie exampleMovie
Star Trek Star Wars
Science Fiction● Часто, у пары (head, relation) может быть
несколько корректных объектов (tails).
● Необходима поправка в ранжирование - отфильтровать прочие корректные ответы
● Допустим, оцениваем предсказания триплета(Science Fiction, exampleMovie, Star Wars)
rank = 2 Unfiltered 0.03 0.87 0.18 0.85 0.10 0.23 0.13
rank = 1 Filtered 0.03 -inf 0.18 0.85 0.10 0.23 0.13
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Datasets & Benchmarks
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Datasets
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WN18 FB15k FB15k-237(Freebase)
WN18RR(WordNet)
CoDEx (Wikidata)
YAGO 3-10
OGB Wiki KG
KDD Cup Wikidata
# entities
Don’t use(please)
15K 40K 2-70K 125K 2.5M 87M
# edges 272k 80k 33-550K 1M 13M 504M
# relations 237 11 42-69 34 ~1000 1,315
… и много других
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KGE - Benchmarking / SOTA
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Tensor Factorization
Balazevic et al. TuckER: Tensor Factorization for Knowledge Graph Completion. EMNLP 2019
Принято демонстрировать SOTA по сравнению с baselines
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KGE - Benchmarking / SOTA
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Tensor Factorization
Translation
Sun et al. RotatE: Knowledge Graph Embedding By Relational Rotation In Complex Space. ICLR 2019
Принято демонстрировать SOTA по сравнению с baselines
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KGE - Benchmarking / SOTA
60Ali et al. Bringing Light Into the Dark: A Large-scale Evaluation of Knowledge Graph Embedding Models Under a Unified Framework. arxiv:2006.13365
Baselines strike back - правильный подбор гиперпараметров делает старые модели сильными
Dataset: FB15k-237
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KG Embeddings Library: PyKEEN
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https://github.com/pykeen/pykeen
Ali et al. Bringing Light Into the Dark: A Large-scale Evaluation of Knowledge Graph Embedding Models Under a Unified Framework. arxiv:2006.13365
→ PyTorch 😍→ 26 datasets + your own graphs→ 28 KG embedding models and counting
→ 7 losses→ 6 optimizers→ 16 metrics→ 5 regularizers→ 2 training loops→ 3 negative samplers→ Tracking in MLFlow, WANDB, TensorBoard,
and more
📈 Benchmarked!
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В следующей серии
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1. Introduction 2. Представление знаний в графах - RDF & RDFS & OWL 3. Хранение знаний в графах - SPARQL & Graph Databases4. Однородность знаний - RDF* & Wikidata & SHACL & ShEx5. Интеграция данных в графы знаний - Semantic Data Integration 6. Введение в теорию графов - Graph Theory Intro 7. Векторные представления графов - Knowledge Graph Embeddings8. Машинное обучение на графах - Graph Neural Networks & KGs 9. Некоторые применения - Question Answering & Query Embedding