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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2401.17675 |
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| _version_ | 1866929230182350848 |
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| author | Jeong, Seonghyeon Wu, Hau-Tieng |
| author_facet | Jeong, Seonghyeon Wu, Hau-Tieng |
| contents | We present a theoretical foundation regarding the boundedness of the t-SNE algorithm. t-SNE employs gradient descent iteration with Kullback-Leibler (KL) divergence as the objective function, aiming to identify a set of points that closely resemble the original data points in a high-dimensional space, minimizing KL divergence. Investigating t-SNE properties such as perplexity and affinity under a weak convergence assumption on the sampled dataset, we examine the behavior of points generated by t-SNE under continuous gradient flow. Demonstrating that points generated by t-SNE remain bounded, we leverage this insight to establish the existence of a minimizer for KL divergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold Jeong, Seonghyeon Wu, Hau-Tieng Machine Learning Data Structures and Algorithms 90C26, 90C30 F.2.2; F.2.0; G.4 We present a theoretical foundation regarding the boundedness of the t-SNE algorithm. t-SNE employs gradient descent iteration with Kullback-Leibler (KL) divergence as the objective function, aiming to identify a set of points that closely resemble the original data points in a high-dimensional space, minimizing KL divergence. Investigating t-SNE properties such as perplexity and affinity under a weak convergence assumption on the sampled dataset, we examine the behavior of points generated by t-SNE under continuous gradient flow. Demonstrating that points generated by t-SNE remain bounded, we leverage this insight to establish the existence of a minimizer for KL divergence. |
| title | Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold |
| topic | Machine Learning Data Structures and Algorithms 90C26, 90C30 F.2.2; F.2.0; G.4 |
| url | https://arxiv.org/abs/2401.17675 |