A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916333866713088 |
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| author | Wang, Zhangyu Xu, Lantian Kong, Zhifeng Wang, Weilong Peng, Xuyu Zheng, Enyang |
| author_facet | Wang, Zhangyu Xu, Lantian Kong, Zhifeng Wang, Weilong Peng, Xuyu Zheng, Enyang |
| contents | Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is difficult due to the different geometry between hyperbolic space and the Euclidean space. To address such difficulties, we first categorize three kinds of illness that harm the performance of the embeddings. Then, we develop a geometry-aware algorithm using a dilation operation and a transitive closure regularization to tackle these illnesses. We empirically validate these techniques and present a theoretical analysis of the mechanism behind the dilation operation. Experiments on synthetic and real-world datasets reveal superior performances of our algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16641 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space Wang, Zhangyu Xu, Lantian Kong, Zhifeng Wang, Weilong Peng, Xuyu Zheng, Enyang Machine Learning Artificial Intelligence Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is difficult due to the different geometry between hyperbolic space and the Euclidean space. To address such difficulties, we first categorize three kinds of illness that harm the performance of the embeddings. Then, we develop a geometry-aware algorithm using a dilation operation and a transitive closure regularization to tackle these illnesses. We empirically validate these techniques and present a theoretical analysis of the mechanism behind the dilation operation. Experiments on synthetic and real-world datasets reveal superior performances of our algorithm. |
| title | A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2407.16641 |