重尾核在t-SNE可视化中揭示了更精细的簇结构
Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisations
摘要：
T分布随机邻域嵌入（t-SNE）是一种广泛使用的数据可视化技术。它与其前身SNE的不同之处在于低维相似性核：高斯核被重尾柯西核取代，解决了SNE的“拥挤问题”。在这里，我们开发了一个有效的实现t-SNE的$t$ -分布内核与任意自由度的$ν$，与$ν\to\infty$相应的SNE和$ν=1$相应的标准t-SNE。使用理论分析和玩具的例子，我们表明，$ν<1$可以进一步减少拥挤的问题，并揭示更精细的集群结构，是不可见的标准t-SNE。我们进一步证明了带尾内核对大型现实数据集（如MNIST、单细胞RNA测序数据和HathiTrust库）的显著影响。我们使用领域知识来确认所揭示的聚类是有意义的。总的来说，我们认为，修改t-SNE内核的尾部重量可以产生额外的洞察数据的集群结构。
英文摘要：
T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the "crowding problem" of SNE. Here, we develop an efficient implementation of t-SNE for a $t$-distribution kernel with an arbitrary degree of freedom $ν$, with $ν\to\infty$ corresponding to SNE and $ν=1$ corresponding to the standard t-SNE. Using theoretical analysis and toy examples, we show that $ν<1$ can further reduce the crowding problem and reveal finer cluster structure that is invisible in standard t-SNE. We further demonstrate the striking effect of heavier-tailed kernels on large real-life data sets such as MNIST, single-cell RNA-sequencing data, and the HathiTrust library. We use domain knowledge to confirm that the revealed clusters are meaningful. Overall, we argue that modifying the tail heaviness of the t-SNE kernel can yield additional insight into the cluster structure of the data.
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