拓展t-SNE收敛性理论，揭示其在广义核下的稳定分布特性。
Equilibrium Distribution for t-Distributed Stochastic Neighbor Embedding with Generalized Kernels
- 提出广义输入输出核的明确形式，统一建模框架。
- 证明当数据量趋近无穷时，t-SNE收敛至稳定分布。
- 为高维数据可视化提供更强理论支撑，适合理论研究者。
t-分布随机邻域嵌入（t-SNE）是一种经典的高维数据可视化算法，通过寻找低维表示来呈现复杂数据结构。本文研究了具有广义核的t-SNE的收敛性，并扩展了Auffinger与Fletcher在2023年的成果。工作首先给出了广义输入核和输出核的明确形式，随后证明：在特定条件下，随着数据点数量趋于无穷，t-SNE算法对广泛的输入与输出核均收敛至一个平衡分布。
原文摘要 · Abstract (English)
T-distributed stochastic neighbor embedding (t-SNE) is a well-known algorithm for visualizing high-dimensional data by finding low-dimensional representations. In this paper, we study the convergence of t-SNE with generalized kernels and extend the results of Auffinger and Fletcher in 2023. Our work starts by giving a concrete formulation of generalized input and output kernels. Then we prove that under certain conditions, the t-SNE algorithm converges to an equilibrium distribution for a wide range of input and output kernels as the number of data points diverges.
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