# Delaunay Component Analysis for Evaluation of Data Representations

arXiv: https://arxiv.org/abs/2202.06866 · HTML: https://mlsanity.com/paper/2202.06866/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Whitening for Self-Supervised Representation Learning](https://mlsanity.com/paper/2007.06346/) (2020)
- [Accelerated Hierarchical Density Clustering](https://mlsanity.com/paper/1705.07321/) (2017)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Geometry Score: A Method For Comparing Generative Adversarial Networks](https://mlsanity.com/paper/1802.02664/) (2018)
- [Learning Object-Centric Representations of Multi-Object Scenes from Multiple Views](https://mlsanity.com/paper/2111.07117/) (2021)
- [Latent Space Roadmap for Visual Action Planning of Deformable and Rigid Object Manipulation](https://mlsanity.com/paper/2003.08974/) (2020)
- [GeomCA: Geometric Evaluation of Data Representations](https://mlsanity.com/paper/2105.12486/) (2021)
- [Comparing Reconstruction- and Contrastive-based Models for Visual Task Planning](https://mlsanity.com/paper/2109.06737/) (2021)

## Built on by (most cited first, 6 of 6)

- [Mind the Gap: Understanding the Modality Gap in Multi-modal Contrastive Representation Learning](https://mlsanity.com/paper/2203.02053/) (2022)
- [Evaluating Latent Space Robustness and Uncertainty of EEG-ML Models under Realistic Distribution Shifts](https://mlsanity.com/paper/2209.11233/) (2022)
- [Robult: Leveraging Redundancy and Modality Specific Features for Robust Multimodal Learning](https://mlsanity.com/paper/2509.03477/) (2025)
- [Hyperbolic Delaunay Geometric Alignment](https://mlsanity.com/paper/2404.08608/) (2024)
- [Training and Evaluation of Deep Policies using Reinforcement Learning and Generative Models](https://mlsanity.com/paper/2204.08573/) (2022)
- [Progressive Voronoi Diagram Subdivision: Towards A Holistic Geometric Framework for Exemplar-free Class-Incremental Learning](https://mlsanity.com/paper/2207.14202/) (2022)

## Abstract (arXiv)

Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data representations have been proposed. In this work, we introduce Delaunay Component Analysis (DCA) - an evaluation algorithm which approximates the data manifold using a more suitable neighbourhood graph called Delaunay graph. This provides a reliable manifold estimation even for challenging geometric arrangements of representations such as clusters with varying shape and density as well as outliers, which is where existing methods often fail. Furthermore, we exploit the nature of Delaunay graphs and introduce a framework for assessing the quality of individual novel data representations. We experimentally validate the proposed DCA method on representations obtained from neural networks trained with contrastive objective, supervised and generative models, and demonstrate various use cases of our extended single point evaluation framework.