Dynamics of the accelerated t-SNE
Abstract: This paper investigates the dynamics of t-Stochastic Neighbor Embedding (t-SNE), a popular tool for visualizing complex datasets in exploratory data analysis, optimized by the Nesterov’s accelerated gradient method. Building on the foundational work that connects t-SNE with spectral clustering and dynamical systems, we extend the analysis to include accelerated dynamics which is not addressed in the previous work, revealing the emergence of Bessel and modified Bessel functions as a novel aspect of the algorithm’s behavior characterizing the temporal evolution of the accelerated t-SNE. Because the ordinary differential equation corresponding to the optimization process under consideration has a closed-form solution, by performing eigenvalue decomposition of the data’s adjacency matrix as a pre-processing step, we can obtain low-dimensional embeddings at any point in time without performing sequential optimization. This advancement not only enhances the practical utility of t-SNE but also contributes to a deeper understanding of its underlying dynamics.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Yoshinobu_Kawahara1
Submission Number: 4205
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