Generalizable Spectral Embedding with an Application to UMAP
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913998366048256 |
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| author | Ben-Ari, Nir Yacobi, Amitai Shaham, Uri |
| author_facet | Ben-Ari, Nir Yacobi, Amitai Shaham, Uri |
| contents | Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability (i.e., out-of-sample extension), scalability, and eigenvectors separation. Existing SE implementations often address two of these drawbacks; however, they fall short in addressing the remaining one. In this paper, we introduce Sep-SpectralNet (eigenvector-separated SpectralNet), a SE implementation designed to address all three limitations. Sep-SpectralNet extends SpectralNet with an efficient post-processing step to achieve eigenvectors separation, while ensuring both generalizability and scalability. This method expands the applicability of SE to a wider range of tasks and can enhance its performance in existing applications. We empirically demonstrate Sep-SpectralNet's ability to consistently approximate and generalize SE, while maintaining SpectralNet's scalability. Additionally, we show how Sep-SpectralNet can be leveraged to enable generalizable UMAP visualization. Our codes are publicly available. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_11305 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizable Spectral Embedding with an Application to UMAP Ben-Ari, Nir Yacobi, Amitai Shaham, Uri Machine Learning Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability (i.e., out-of-sample extension), scalability, and eigenvectors separation. Existing SE implementations often address two of these drawbacks; however, they fall short in addressing the remaining one. In this paper, we introduce Sep-SpectralNet (eigenvector-separated SpectralNet), a SE implementation designed to address all three limitations. Sep-SpectralNet extends SpectralNet with an efficient post-processing step to achieve eigenvectors separation, while ensuring both generalizability and scalability. This method expands the applicability of SE to a wider range of tasks and can enhance its performance in existing applications. We empirically demonstrate Sep-SpectralNet's ability to consistently approximate and generalize SE, while maintaining SpectralNet's scalability. Additionally, we show how Sep-SpectralNet can be leveraged to enable generalizable UMAP visualization. Our codes are publicly available. |
| title | Generalizable Spectral Embedding with an Application to UMAP |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2501.11305 |