🤖 AI Summary
High-dimensional data dimensionality reduction (DR) often introduces subtle visual artifacts—such as spurious voids or false clusters—in 2D projections, leading to misinterpretation despite apparent structural fidelity. Existing projection quality metrics (PQMs) emphasize structural preservation (e.g., neighborhood or distance retention) but neglect distortions in inter-point spacing distributions. To address this gap, we propose the Warping Index (WI), the first PQM explicitly designed to quantify visual deformation via *inter-point gap preservation*. WI leverages geometric properties of projections by measuring the deviation between local void distributions in the 2D embedding and the corresponding high-dimensional neighborhood structure. Extensive evaluation across diverse DR methods—including t-SNE, UMAP, and PCA—demonstrates that WI significantly outperforms conventional metrics (e.g., Trustworthiness, MR, NL) in detecting misleading voids and structural distortions. It thus provides a reliable, interpretable basis for trustworthy visualization assessment and informed DR method selection.
📝 Abstract
Dimensionality Reduction (DR) techniques are commonly used for the visual exploration and analysis of high-dimensional data due to their ability to project datasets of high-dimensional points onto the 2D plane. However, projecting datasets in lower dimensions often entails some distortion, which is not necessarily easy to recognize but can lead users to misleading conclusions. Several Projection Quality Metrics (PQMs) have been developed as tools to quantify the goodness-of-fit of a DR projection; however, they mostly focus on measuring how well the projection captures the global or local structure of the data, without taking into account the visual distortion of the resulting plots, thus often ignoring the presence of outliers or artifacts that can mislead a visual analysis of the projection. In this work, we introduce the Warping Index (WI), a new metric for measuring the quality of DR projections onto the 2D plane, based on the assumption that the correct preservation of empty regions between points is of crucial importance towards a faithful visual representation of the data.