# Gini Coefficient as a Unified Metric for Evaluating Many-versus-Many Similarity in Vector Spaces

arXiv: https://arxiv.org/abs/2411.07983 · HTML: https://mlsanity.com/paper/2411.07983/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 12 Nov 2024.

## Builds on (most cited first, 6 of 6)

- [Efficient and robust approximate nearest neighbor search using Hierarchical Navigable Small World graphs](https://mlsanity.com/paper/1603.09320/) (2016)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [Universal Sentence Encoder](https://mlsanity.com/paper/1803.11175/) (2018)
- [Approximate Nearest Neighbor Search in High Dimensions](https://mlsanity.com/paper/1806.09823/) (2018)
- [Repeated Random Sampling for Minimizing the Time-to-Accuracy of Learning](https://mlsanity.com/paper/2305.18424/) (2023)

## Built on by (most cited first, 2 of 2)

- [Multi-level context Modeling for consistent expert selection in Mixture-of-Experts](https://mlsanity.com/paper/2607.16427/) (2026)
- [LF2L: Loss Fusion Horizontal Federated Learning Across Heterogeneous Feature Spaces Using External Datasets Effectively: A Case Study in Second Primary Cancer Prediction](https://mlsanity.com/paper/2603.07249/) (2026)

## Abstract (arXiv)

We demonstrate that Gini coefficients can be used as unified metrics to evaluate many-versus-many (all-to-all) similarity in vector spaces. Our analysis of various image datasets shows that images with the highest Gini coefficients tend to be the most similar to one another, while images with the lowest Gini coefficients are the least similar. We also show that this relationship holds true for vectorized text embeddings from various corpuses, highlighting the consistency of our method and its broad applicability across different types of data. Additionally, we demonstrate that selecting machine learning training samples that closely match the distribution of the testing dataset is far more important than ensuring data diversity. Selection of exemplary and iconic training samples with higher Gini coefficients leads to significantly better model performance compared to simply having a diverse training set with lower Gini coefficients. Thus, Gini coefficients can serve as effective criteria for selecting machine learning training samples, with our selection method outperforming random sampling methods in very sparse information settings.