Heavy-Tailed Kernels Reveal a Finer Cluster Structure in t-SNE Visualisations

• Published in: Machine Learning and Knowledge Discovery in Databases Vol. 11906; pp. 124 - 139
• Main Authors: Kobak, Dmitry, Linderman, George, Steinerberger, Stefan, Kluger, Yuval, Berens, Philipp
• Format: Book Chapter Journal Article
• Language: English
• Published: Cham Springer International Publishing 2020
• Series: Lecture Notes in Computer Science
• Subjects: Data visualisation; Dimensionality reduction; t-SNE; t-SNE; dimensionality reduction; data visualisation
• DOI: 10.1007/978-3-030-46150-8_8
• ISBN: 9783030461492; 3030461491
• ISSN: 0302-9743

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 $$\nu $$ , with $$\nu \rightarrow \infty $$ corresponding to SNE and $$\nu =1$$ corresponding to the standard t-SNE. Using theoretical analysis and toy examples, we show that $$\nu <1$$ 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.