Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold

Seonghyeon Jeong; Hau-Tieng Wu

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arXiv · 2401.17675

Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold

Seonghyeon Jeong·Hau-Tieng Wu

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Abstract

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.

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stat.ML cs.DS cs.LG

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BibTeX RIS

Seonghyeon Jeong, Hau-Tieng Wu. 2024-01-31. Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold. https://arxiv.org/abs/2401.17675

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