Convergence analysis of t-SNE as a gradient flow for point cloud on a
  manifold
Seonghyeon Jeong Hau-Tieng Wu
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.