Classes are not Clusters: Improving Label-based Evaluation of Dimensionality Reduction

Hyeon Jeon, Yun-Hsin Kuo, Michael Aupetit, Kwan-Liu Ma, Jinwook Seo

Room: 104

2023-10-25T22:48:00ZGMT-0600Change your timezone on the schedule page
Exemplar figure, described by caption below
Guidelines to infer the Cluster-Label Matching (CLM) of the high-dimensional data based on the CLM of the embedded data (left column) and the scores given by Label-T (Trustworthiness) and Label-C (Continuity) (first row)
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Dimensionality Reduction, Reliability, Clustering, Clustering Validation Measures, Dimensionality Reduction Evaluation


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.