  A common way to evaluate the reliability of dimensionality reduction (DR)
embeddings is to quantify how well labeled classes form compact, mutually
separated clusters in the embeddings. This approach is based on the assumption
that the classes stay as clear clusters in the original high-dimensional space.
However, in reality, this assumption can be violated; a single class can be
fragmented into multiple separated clusters, and multiple classes can be merged
into a single cluster. We thus cannot always assure the credibility of the
evaluation using class labels. In this paper, we introduce two novel quality
measures -- Label-Trustworthiness and Label-Continuity (Label-T&C) -- advancing
the process of DR evaluation based on class labels. Instead of assuming that
classes are well-clustered in the original space, Label-T&C work by (1)
estimating the extent to which classes form clusters in the original and
embedded spaces and (2) evaluating the difference between the two. A
quantitative evaluation showed that Label-T&C outperform widely used DR
evaluation measures (e.g., Trustworthiness and Continuity, Kullback-Leibler
divergence) in terms of the accuracy in assessing how well DR embeddings
preserve the cluster structure, and are also scalable. Moreover, we present
case studies demonstrating that Label-T&C can be successfully used for
revealing the intrinsic characteristics of DR techniques and their
hyperparameters.

Machine Learning