Knowledgebra: An Algebraic Learning Framework for Knowledge Graph
Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion a...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Machine Learning and Knowledge Extraction |
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| Online Access: | https://www.mdpi.com/2504-4990/4/2/19 |
| _version_ | 1827659014796738560 |
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| author | Tong Yang Yifei Wang Long Sha Jan Engelbrecht Pengyu Hong |
| author_facet | Tong Yang Yifei Wang Long Sha Jan Engelbrecht Pengyu Hong |
| author_sort | Tong Yang |
| collection | DOAJ |
| description | Knowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion and link prediction. However, existing KG embedding methods fell short to provide a systematic solution for the global consistency of knowledge representation. We developed a mathematical language for KG based on an observation of their inherent algebraic structure, which we termed as <i>Knowledgebra</i>. By analyzing five distinct algebraic properties, we proved that the semigroup is the most reasonable algebraic structure for the relation embedding of a general knowledge graph. We implemented an instantiation model, <i>SemE</i>, using simple matrix semigroups, which exhibits state-of-the-art performance on standard datasets. Moreover, we proposed a regularization-based method to integrate chain-like logic rules derived from human knowledge into embedding training, which further demonstrates the power of the developed language. As far as we know, by applying abstract algebra in statistical learning, this work develops the first formal language for general knowledge graphs, and also sheds light on the problem of neural-symbolic integration from an algebraic perspective. |
| first_indexed | 2024-03-09T23:13:37Z |
| format | Article |
| id | doaj.art-609f07df5733412798160f0332b5c05b |
| institution | Directory Open Access Journal |
| issn | 2504-4990 |
| language | English |
| last_indexed | 2024-03-09T23:13:37Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machine Learning and Knowledge Extraction |
| spelling | doaj.art-609f07df5733412798160f0332b5c05b2023-11-23T17:40:24ZengMDPI AGMachine Learning and Knowledge Extraction2504-49902022-05-014243244510.3390/make4020019Knowledgebra: An Algebraic Learning Framework for Knowledge GraphTong Yang0Yifei Wang1Long Sha2Jan Engelbrecht3Pengyu Hong4Department of Physics, Boston College, Chestnut Hill, MA 02135, USADepartment of Computer Science, Brandeis University, Waltham, MA 02453, USADepartment of Computer Science, Brandeis University, Waltham, MA 02453, USADepartment of Physics, Boston College, Chestnut Hill, MA 02135, USADepartment of Computer Science, Brandeis University, Waltham, MA 02453, USAKnowledge graph (KG) representation learning aims to encode entities and relations into dense continuous vector spaces such that knowledge contained in a dataset could be consistently represented. Dense embeddings trained from KG datasets benefit a variety of downstream tasks such as KG completion and link prediction. However, existing KG embedding methods fell short to provide a systematic solution for the global consistency of knowledge representation. We developed a mathematical language for KG based on an observation of their inherent algebraic structure, which we termed as <i>Knowledgebra</i>. By analyzing five distinct algebraic properties, we proved that the semigroup is the most reasonable algebraic structure for the relation embedding of a general knowledge graph. We implemented an instantiation model, <i>SemE</i>, using simple matrix semigroups, which exhibits state-of-the-art performance on standard datasets. Moreover, we proposed a regularization-based method to integrate chain-like logic rules derived from human knowledge into embedding training, which further demonstrates the power of the developed language. As far as we know, by applying abstract algebra in statistical learning, this work develops the first formal language for general knowledge graphs, and also sheds light on the problem of neural-symbolic integration from an algebraic perspective.https://www.mdpi.com/2504-4990/4/2/19algebraic learningknowledge graphcategorysemigrouplogic reasoningneural-symbolic integration |
| spellingShingle | Tong Yang Yifei Wang Long Sha Jan Engelbrecht Pengyu Hong Knowledgebra: An Algebraic Learning Framework for Knowledge Graph Machine Learning and Knowledge Extraction algebraic learning knowledge graph category semigroup logic reasoning neural-symbolic integration |
| title | Knowledgebra: An Algebraic Learning Framework for Knowledge Graph |
| title_full | Knowledgebra: An Algebraic Learning Framework for Knowledge Graph |
| title_fullStr | Knowledgebra: An Algebraic Learning Framework for Knowledge Graph |
| title_full_unstemmed | Knowledgebra: An Algebraic Learning Framework for Knowledge Graph |
| title_short | Knowledgebra: An Algebraic Learning Framework for Knowledge Graph |
| title_sort | knowledgebra an algebraic learning framework for knowledge graph |
| topic | algebraic learning knowledge graph category semigroup logic reasoning neural-symbolic integration |
| url | https://www.mdpi.com/2504-4990/4/2/19 |
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