{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T10:39:23Z","timestamp":1770979163890,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T00:00:00Z","timestamp":1762300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62202060"],"award-info":[{"award-number":["62202060"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2022YFF0604502"],"award-info":[{"award-number":["2022YFF0604502"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The symmetry between different representation spaces plays a crucial role in effectively modeling complex multimodal data. To address the challenge of equipment knowledge graphs containing hierarchical relationships that cannot be fully represented in a single space, this study proposes UMEAD, an unsupervised multimodal entity alignment method based on dual-space embeddings. The method simultaneously learns graph embeddings in both Euclidean and hyperbolic spaces, forming a structural symmetry where the Euclidean space captures local regularities and the hyperbolic space models global hierarchies. Their complementarity achieves a balanced and symmetric representation of multimodal knowledge. An adaptive feature fusion strategy is further employed to dynamically weight semantic and visual modalities, enhancing the symmetry and complementarity between different modalities. To reduce reliance on scarce pre-aligned data, pseudo seed instances are generated from multimodal features, and an iterative constraint mechanism progressively enlarges the training set, enabling unsupervised alignment. Experiments on public datasets, including EMMEAD, FB15K-DB15K, and FB15K-YAGO15K, demonstrate that the combination of dual-space embeddings, adaptive fusion, and iterative constraints significantly improves alignment accuracy. In summary, the proposed method reduces dependence on pre-aligned data, strengthens multimodal and structural alignment, and its symmetric embedding and fusion design offers a promising approach for the construction and application of multimodal knowledge graphs in the equipment domain.<\/jats:p>","DOI":"10.3390\/sym17111869","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T07:58:05Z","timestamp":1762329485000},"page":"1869","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["UMEAD: Unsupervised Multimodal Entity Alignment for Equipment Knowledge Graphs via Dual-Space Embedding"],"prefix":"10.3390","volume":"17","author":[{"given":"Siyu","family":"Zhu","sequence":"first","affiliation":[{"name":"College of Computer Science, Beijing Information Science & Technology University (BISTU), Beijing 102206, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-5676-9582","authenticated-orcid":false,"given":"Qitao","family":"Tai","sequence":"additional","affiliation":[{"name":"College of Computer Science, Beijing Information Science & Technology University (BISTU), Beijing 102206, China"}]},{"given":"Jingbo","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Computer Science, Beijing Information Science & Technology University (BISTU), Beijing 102206, China"}]},{"given":"Mingfei","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Computer Science, Beijing Information Science & Technology University (BISTU), Beijing 102206, China"}]},{"given":"Liang","family":"Wang","sequence":"additional","affiliation":[{"name":"Shaanxi Aerospace Technology Application Research Institute Co., Ltd., Xi\u2019an 710100, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4533-1535","authenticated-orcid":false,"given":"Ning","family":"Li","sequence":"additional","affiliation":[{"name":"College of Computer Science, Beijing Information Science & Technology University (BISTU), Beijing 102206, China"}]},{"given":"Shoulu","family":"Hou","sequence":"additional","affiliation":[{"name":"College of Computer Science, Beijing Information Science & Technology University (BISTU), Beijing 102206, China"}]},{"given":"Xiulei","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Computer Science, Beijing Information Science & Technology University (BISTU), Beijing 102206, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Jiang, X., Xu, C., Shen, Y., Wang, Y., Su, F., Shi, Z., Sun, F., Li, Z., Guo, J., and Shen, H. (2024, January 13\u201317). Toward practical entity alignment method design: Insights from new highly heterogeneous knowledge graph datasets. Proceedings of the ACM Web Conference 2024, Virtual.","DOI":"10.1145\/3589334.3645720"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Tang, J., Zhao, K., and Li, J. (2023). A fused gromov-wasserstein framework for unsupervised knowledge graph entity alignment. arXiv.","DOI":"10.18653\/v1\/2023.findings-acl.205"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Chen, M., Tian, Y., Yang, M., and Zaniolo, C. (2017, January 19\u201325). Multilingual knowledge graph embeddings for cross-lingual knowledge alignment. Proceedings of the IJCAI, Melbourne, Australia.","DOI":"10.24963\/ijcai.2017\/209"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sun, Z., Hu, W., and Zhang, Q. (2018, January 13\u201319). Bootstrapping entity alignment with knowledge graph embedding. Proceedings of the IJCAI, Stockholm, Sweden.","DOI":"10.24963\/ijcai.2018\/611"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhu, H., Xie, R., Liu, Z., and Sun, M. (2017, January 19\u201325). Iterative entity alignment via joint knowledge embeddings. Proceedings of the IJCAI, Melbourne, Australia.","DOI":"10.24963\/ijcai.2017\/595"},{"key":"ref_6","unstructured":"Cao, Y., Liu, Z., Li, C., Liu, Z., Li, J., and Chua, T.S. (August, January 28). Multi-channel graph neural network for entity alignment. Proceedings of the ACL, Florence, Italy."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s10462-024-10866-4","article-title":"A survey: Knowledge graph entity alignment research based on graph embedding","volume":"57","author":"Zhu","year":"2024","journal-title":"Artif. Intell. Rev."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Liu, Y., Li, H., Garcia-Duran, A., Niepert, M., Onoro-Rubio, D., and Rosenblum, D.S. (2019, January 2\u20136). MMKG: Multi-modal knowledge graphs. Proceedings of the Semantic Web: 16th International Conference, ESWC 2019, Portoro\u017e, Slovenia.","DOI":"10.1007\/978-3-030-21348-0_30"},{"key":"ref_9","unstructured":"Lin, Z., Zhang, Z., Wang, M., Shi, Y., Wu, X., and Zheng, Y. (2022, January 12\u201317). Multi-modal contrastive representation learning for entity alignment. Proceedings of the 29th International Conference on Computational Linguistics (COLING 2022), Gyeongju, Republic of Korea."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Li, Q., Ji, C., Guo, S., Liang, Z., Wang, L., and Li, J. (2023). Multi-Modal Knowledge Graph Transformer Framework for Multi-Modal Entity Alignment. arXiv.","DOI":"10.18653\/v1\/2023.findings-emnlp.70"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Trisedya, B.D., Qi, J., and Zhang, R. (2019, January 3\u20135). Neural relation extraction for knowledge graph completion. Proceedings of the NAACL, Florence, Italy.","DOI":"10.18653\/v1\/P19-1023"},{"key":"ref_12","unstructured":"Mao, X., Wang, H., Li, M., Zhang, Y., and Li, Z. (2020, January 7\u201312). MRAEA: An efficient and robust entity alignment method for multimodal knowledge graphs. Proceedings of the AAAI, New York, NY, USA."},{"key":"ref_13","unstructured":"Nickel, M., and Kiela, D. (2017, January 4\u20139). Poincar\u00e9 embeddings for learning hierarchical representations. Proceedings of the NeurIPS, Long Beach, CA, USA."},{"key":"ref_14","unstructured":"Chami, I., Ying, R., R\u00e9, C., and Leskovec, J. (2019, January 8\u201314). Hyperbolic graph neural networks. Proceedings of the NeurIPS, Vancouver, BC, Canada."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sun, Z., Chen, M., Hu, W., Wang, C., Dai, J., and Zhang, W. (2020, January 16\u201320). Knowledge Association with Hyperbolic Knowledge Graph Embeddings. Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing (EMNLP), Online.","DOI":"10.18653\/v1\/2020.emnlp-main.460"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1016\/j.neucom.2021.03.132","article-title":"Multi-modal Entity Alignment in Hyperbolic Space","volume":"461","author":"Guo","year":"2021","journal-title":"Neurocomputing"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yang, H.W., Zou, Y., Shi, P., Lu, W., Lin, J., and Sun, X. (2019, January 3\u20137). Aligning cross-lingual entities with multi-aspect information. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), Hong Kong, China.","DOI":"10.18653\/v1\/D19-1451"},{"key":"ref_18","unstructured":"Simonyan, K., and Zisserman, A. (2015, January 7\u20139). Very deep convolutional networks for large-scale image recognition. Proceedings of the 3rd International Conference on Learning Representations (ICLR 2015), San Diego, CA, USA."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wu, Y., Liu, X., Feng, Y., Wang, Z., and Zhao, D. (2019, January 3\u20137). Jointly learning entity and relation representations for entity alignment. Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP), Hong Kong, China.","DOI":"10.18653\/v1\/D19-1023"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Bollacker, K., Evans, C., Paritosh, P., Sturge, T., and Taylor, J. (2008, January 10\u201312). Freebase: A collaboratively created graph database for structuring human knowledge. Proceedings of the 2008 ACM SIGMOD International Conference on Management of Data, Vancouver, BC, Canada.","DOI":"10.1145\/1376616.1376746"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Auer, S., Bizer, C., Kobilarov, G., Lehmann, J., Cyganiak, R., and Ives, Z. (2007, January 11\u201315). Dbpedia: A nucleus for a web of open data. Proceedings of the International Semantic Web Conference, Busan, Republic of Korea.","DOI":"10.1007\/978-3-540-76298-0_52"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Suchanek, F.M., Kasneci, G., and Weikum, G. (2007, January 8\u201312). Yago: A core of semantic knowledge. Proceedings of the 16th International Conference on World Wide Web, Banff, AB, Canada.","DOI":"10.1145\/1242572.1242667"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Chen, Z., Guo, L., Fang, Y., Zhang, Y., Chen, J., Pan, J.Z., Li, Y., Chen, H., and Zhang, W. (2023, January 6\u201310). Rethinking uncertainly missing and ambiguous visual modality in multi-modal entity alignment. Proceedings of the International Semantic Web Conference, Athens, Greece.","DOI":"10.1007\/978-3-031-47240-4_7"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, Z., Lv, Q., Lan, X., and Zhang, Y. (November, January 31). Cross-lingual knowledge graph alignment via graph convolutional networks. Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing, Brussels, Belgium.","DOI":"10.18653\/v1\/D18-1032"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Wu, Y., Liu, X., Feng, Y., Wang, Z., Yan, R., and Zhao, D. (2019, January 10\u201316). Relation-aware entity alignment for heterogeneous knowledge graphs. Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, Macao, China.","DOI":"10.24963\/ijcai.2019\/733"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"120363","DOI":"10.1016\/j.eswa.2023.120363","article-title":"Leveraging multimodal features for knowledge graph entity alignment based on dynamic self-attention networks","volume":"228","author":"Qian","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhu, Q., Zhou, X., Wu, J., Tan, J., and Guo, L. (2019, January 10\u201316). Neighborhood-aware attentional representation for multilingual knowledge graphs. Proceedings of the IJCAI, Macao, China.","DOI":"10.24963\/ijcai.2019\/269"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Pei, S., Yu, L., Hoehndorf, R., and Zhang, X. (2019, January 13\u201317). Semi-supervised entity alignment via knowledge graph embedding with awareness of degree difference. Proceedings of the World Wide Web Conference, San Francisco, CA, USA.","DOI":"10.1145\/3308558.3313646"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhu, Y., Liu, H., Wu, Z., and Du, Y. (2021, January 2\u20139). Relation-aware neighborhood matching model for entity alignment. Proceedings of the AAAI Conference on Artificial Intelligence, Virtually.","DOI":"10.1609\/aaai.v35i5.16606"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"He, F., Li, Z., Qiang, Y., Liu, A., Liu, G., Zhao, P., Zhang, M., and Chen, Z. (2019). Unsupervised entity alignment using attribute triples and relation triples. Database Systems for Advanced Applications, Proceedings of the 24th International Conference, DASFAA 2019, Chiang Mai, Thailand, 22\u201325 April 2019, Springer International Publishing. Proceedings, Part I 24.","DOI":"10.1007\/978-3-030-18576-3_22"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Liu, X., Hong, H., Wang, X., Chen, Z., Kharlamov, E., Dong, Y., and Tang, J. (2022, January 25\u201329). Selfkg: Self-supervised entity alignment in knowledge graphs. Proceedings of the ACM Web Conference 2022, Lyon, France.","DOI":"10.1145\/3485447.3511945"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Chen, L., Wang, Z., Zhang, J., and Chen, H. (2020, January 28\u201330). Entity alignment for multi-modal knowledge graphs. Proceedings of the 13th International Conference on Knowledge Science, Engineering and Management (KSEM), Hangzhou, China. Available online: https:\/\/link.springer.com\/chapter\/10.1007\/978-3-030-55130-8_12.","DOI":"10.1007\/978-3-030-55130-8_12"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1869\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T08:16:00Z","timestamp":1762330560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/11\/1869"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,5]]},"references-count":32,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["sym17111869"],"URL":"https:\/\/doi.org\/10.3390\/sym17111869","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,5]]}}}