  Cluster visualization is an essential task for nonlinear dimensionality
reduction as a data analysis tool. It is often believed that Student
t-Distributed Stochastic Neighbor Embedding (t-SNE) can show clusters for well
clusterable data, with a smaller Kullback-Leibler divergence corresponding to a
better quality. There was even theoretical proof for the guarantee of this
property. However, we point out that this is not necessarily the case -- t-SNE
may leave clustering patterns hidden despite strong signals present in the
data. Extensive empirical evidence is provided to support our claim. First,
several real-world counter-examples are presented, where t-SNE fails even if
the input neighborhoods are well clusterable. Tuning hyperparameters in t-SNE
or using better optimization algorithms does not help solve this issue because
a better t-SNE learning objective can correspond to a worse cluster embedding.
Second, we check the assumptions in the clustering guarantee of t-SNE and find
they are often violated for real-world data sets.
