Why Can't I See My Clusters? A Precision-Recall Approach to Dimensionality Reduction Validation
This addresses the challenge for data analysts and researchers in efficiently validating DR projections when expected clusters are not visible, though it is incremental as it builds on an existing framework.
The paper tackles the problem of missing expected cluster structures in dimensionality reduction (DR) visualizations by introducing precision and recall metrics to evaluate the relationship phase of DR, enabling faster and more reliable hyperparameter tuning and artifact detection.
Dimensionality Reduction (DR) is widely used for visualizing high-dimensional data, often with the goal of revealing expected cluster structure. However, such a structure may not always appear in the projections. Existing DR quality metrics assess projection reliability (to some extent) or cluster structure quality, but do not explain why expected structures are missing. Visual Analytics solutions can help, but are often time-consuming due to the large hyperparameter space. This paper addresses this problem by leveraging a recent framework that divides the DR process into two phases: a relationship phase, where similarity relationships are modeled, and a mapping phase, where the data is projected accordingly. We introduce two supervised metrics, precision and recall, to evaluate the relationship phase. These metrics quantify how well the modeled relationships align with an expected cluster structure based on some set of labels representing this structure. We illustrate their application using t-SNE and UMAP, and validate the approach through various usage scenarios. Our approach can guide hyperparameter tuning, uncover projection artifacts, and determine if the expected structure is captured in the relationships, making the DR process faster and more reliable.