Class Angular Distortion Index for Dimensionality Reduction
For practitioners using t-SNE or UMAP, CADI provides a new way to assess whether cluster arrangements in 2D projections are trustworthy, addressing a known failure mode of existing cluster quality metrics.
The paper introduces the Class Angular Distortion Index (CADI), a metric that uses angles among point triples to evaluate how faithfully dimensionality reduction preserves cluster organization. It demonstrates that CADI detects misleading cluster arrangements where existing metrics fail, and shows its differentiability enables a new DR optimization technique.
Dimensionality reduction (DR) techniques are often characterized by whether they preserve global, high-level structures in the data or local, neighborhood structures. This distinction matters in visualization: global methods can obscure clusters while local methods can over-emphasize them. Yet, even when clusters appear distinct, their relative arrangement in the projection may be arbitrary or misleading, a common issue in techniques such as t-SNE and UMAP. Existing cluster quality metrics either only measure cluster separability or assume spherical, globular clusters in the original space. We introduce the Class Angular Distortion Index (CADI), a metric that uses internal angles among point triples to determine the faithfulness of cluster organization in a projection. We show cases on both real and synthetic data where existing cluster metrics fail, but CADI provides an interpretable result. Since it relies on computing angles, CADI is also differentiable, enabling optimization. We demonstrate this with a CADI-based DR technique.