REVIEW 1 cited by
Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold
read the original 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.
Forward citations
Cited by 1 Pith paper
-
On the continuum limit of t-SNE for data visualization
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.