Topological Metric for Unsupervised Embedding Quality Evaluation
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908718059225088 |
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| author | Shestov, Aleksei Klenitskiy, Anton Denisova, Daria Dzagkoev, Amurkhan Petrovich, Daniil Savchenko, Andrey Makarenko, Maksim |
| author_facet | Shestov, Aleksei Klenitskiy, Anton Denisova, Daria Dzagkoev, Amurkhan Petrovich, Daniil Savchenko, Andrey Makarenko, Maksim |
| contents | Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Metric for Unsupervised Embedding Quality Evaluation Shestov, Aleksei Klenitskiy, Anton Denisova, Daria Dzagkoev, Amurkhan Petrovich, Daniil Savchenko, Andrey Makarenko, Maksim Machine Learning Information Retrieval Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection. |
| title | Topological Metric for Unsupervised Embedding Quality Evaluation |
| topic | Machine Learning Information Retrieval |
| url | https://arxiv.org/abs/2512.15285 |