Why Can't I See My Clusters? A Precision-Recall Approach to Dimensionality Reduction Validation

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.

When Dimensionality Reduction Meets Graph (Drawing) Theory: Introducing a Common Framework, Challenges and Opportunities

In the vast landscape of visualization research, Dimensionality Reduction (DR) and graph analysis are two popular subfields, often essential to most visual data analytics setups. DR aims to create representations to support neighborhood and similarity analysis on complex, large datasets. Graph analysis focuses on identifying the salient topological properties and key actors within networked data, with specialized research on investigating how such features could be presented to the user to ease the comprehension of the underlying structure. Although these two disciplines are typically regarded as disjoint subfields, we argue that both fields share strong similarities and synergies that can potentially benefit both. Therefore, this paper discusses and introduces a unifying framework to help bridge the gap between DR and graph (drawing) theory. Our goal is to use the strongly math-grounded graph theory to improve the overall process of creating DR visual representations. We propose how to break the DR process into well-defined stages, discussing how to match some of the DR state-of-the-art techniques to this framework and presenting ideas on how graph drawing, topology features, and some popular algorithms and strategies used in graph analysis can be employed to improve DR topology extraction, embedding generation, and result validation. We also discuss the challenges and identify opportunities for implementing and using our framework, opening directions for future visualization research.