提出tSNE在大数据下的极限行为，改进算法使其收敛。
Large data limits and scaling laws for tSNE
- 发现tSNE在数据量无穷大时无稳定极限
- 新模型通过重缩放使吸引能量不衰减
- 适合研究高维数据降维极限的学者
本文研究t分布随机邻域嵌入（tSNE）在大数据渐近情况下的性质。我们识别出tSNE目标函数的适当连续极限，可视为基于核的排斥项与渐近消失的拉普拉斯型正则项的组合。结果表明，原始tSNE算法的嵌入在样本数n趋于无穷时无法保持一致极限。为此，我们提出一种重缩放模型，缓解吸引力能量的渐近衰减，该模型具有稳定的极限。
原文摘要 · Abstract (English)
This work considers large-data asymptotics for t-distributed stochastic neighbor embedding (tSNE), a widely-used non-linear dimension reduction algorithm. We identify an appropriate continuum limit of the tSNE objective function, which can be viewed as a combination of a kernel-based repulsion and an asymptotically-vanishing Laplacian-type regularizer. As a consequence, we show that embeddings of the original tSNE algorithm cannot have any consistent limit as $n \to \infty$. We propose a rescaled model which mitigates the asymptotic decay of the attractive energy, and which does have a consistent limit.
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