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

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arxiv 2401.17675 v1 pith:2BL5XNLH submitted 2024-01-31 stat.ML cs.DScs.LG

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

classification stat.ML cs.DScs.LG
keywords t-snepointsdivergencegradientconvergenceflowgeneratedunder
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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  1. On the continuum limit of t-SNE for data visualization

    stat.ML 2026-04 unverdicted novelty 8.0

    t-SNE converges in the large-data limit to a non-convex variational energy with attraction and repulsion terms that admits a unique smooth minimizer but infinitely many discontinuous ones in one dimension.