# Class Angular Distortion Index for Dimensionality Reduction

arXiv: https://arxiv.org/abs/2605.00637 · HTML: https://mlsanity.com/paper/2605.00637/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 56 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Deep Metric Learning with Angular Loss](https://mlsanity.com/paper/1708.01682/) (2017)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projections](https://mlsanity.com/paper/2107.07859/) (2021)
- [Unveiling High-dimensional Backstage: A Survey for Reliable Visual Analytics with Dimensionality Reduction](https://mlsanity.com/paper/2501.10168/) (2025)
- [ZADU: A Python Library for Evaluating the Reliability of Dimensionality Reduction Embeddings](https://mlsanity.com/paper/2308.00282/) (2023)
- [Classes are not Clusters: Improving Label-based Evaluation of Dimensionality Reduction](https://mlsanity.com/paper/2308.00278/) (2023)
- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [Multi-Perspective, Simultaneous Embedding](https://mlsanity.com/paper/1909.06485/) (2019)
- [Balancing between the Local and Global Structures (LGS) in Graph Embedding](https://mlsanity.com/paper/2308.16403/) (2023)
- [When Dimensionality Reduction Meets Graph (Drawing) Theory: Introducing a Common Framework, Challenges and Opportunities](https://mlsanity.com/paper/2412.06555/) (2024)
- [Sailing in high-dimensional spaces: Low-dimensional embeddings through angle preservation](https://mlsanity.com/paper/2406.09876/) (2024)
- [Metric Design != Metric Behavior: Improving Metric Selection for the Unbiased Evaluation of Dimensionality Reduction](https://mlsanity.com/paper/2507.02225/) (2025)
- [Dataset-Adaptive Dimensionality Reduction](https://mlsanity.com/paper/2507.11984/) (2025)
- [UMATO: Bridging Local and Global Structures for Reliable Visual Analytics with Dimensionality Reduction](https://mlsanity.com/paper/2508.16227/) (2025)
- [How Scale Breaks "Normalized Stress" and KL Divergence: Rethinking Quality Metrics](https://mlsanity.com/paper/2510.08660/) (2025)

## Abstract (arXiv)

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.