# A Novel Intrinsic Measure of Data Separability

arXiv: https://arxiv.org/abs/2109.05180 · HTML: https://mlsanity.com/paper/2109.05180/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 42 references that are in the map.
- First posted on arXiv 11 Sep 2021.

## Builds on (most cited first, 8 of 8)

- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Deep Learning for Anomaly Detection: A Review](https://mlsanity.com/paper/2007.02500/) (2020)
- [How Complex is your classification problem? A survey on measuring classification complexity](https://mlsanity.com/paper/1808.03591/) (2018)
- [Model Complexity of Deep Learning: A Survey](https://mlsanity.com/paper/2103.05127/) (2021)
- [How deep is deep enough? -- Quantifying class separability in the hidden layers of deep neural networks](https://mlsanity.com/paper/1811.01753/) (2018)
- [Analysis of Generalizability of Deep Neural Networks Based on the Complexity of Decision Boundary](https://mlsanity.com/paper/2009.07974/) (2020)
- [A Novel Measure to Evaluate Generative Adversarial Networks Based on Direct Analysis of Generated Images](https://mlsanity.com/paper/2002.12345/) (2020)

## Built on by (most cited first, 9 of 9)

- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Enhancing cluster analysis via topological manifold learning](https://mlsanity.com/paper/2207.00510/) (2022)
- [Several fitness functions and entanglement gates in quantum kernel generation](https://mlsanity.com/paper/2309.03307/) (2023)
- [Robust Support Vector Machines for Imbalanced and Noisy Data via Benders Decomposition](https://mlsanity.com/paper/2503.14873/) (2025)
- [A geometric framework for outlier detection in high-dimensional data](https://mlsanity.com/paper/2207.00367/) (2022)
- [A classification performance evaluation measure considering data separability](https://mlsanity.com/paper/2211.05433/) (2022)
- [Estimating class separability of text embeddings with persistent homology](https://mlsanity.com/paper/2305.15016/) (2023)
- [Beyond Labels: Advancing Cluster Analysis with the Entropy of Distance Distribution (EDD)](https://mlsanity.com/paper/2311.16621/) (2023)
- [The Art of Misclassification: Too Many Classes, Not Enough Points](https://mlsanity.com/paper/2502.08041/) (2025)

## Abstract (arXiv)

In machine learning, the performance of a classifier depends on both the classifier model and the separability/complexity of datasets. To quantitatively measure the separability of datasets, we create an intrinsic measure -- the Distance-based Separability Index (DSI), which is independent of the classifier model. We consider the situation in which different classes of data are mixed in the same distribution to be the most difficult for classifiers to separate. We then formally show that the DSI can indicate whether the distributions of datasets are identical for any dimensionality. And we verify the DSI to be an effective separability measure by comparing to several state-of-the-art separability/complexity measures using synthetic and real datasets. Having demonstrated the DSI's ability to compare distributions of samples, we also discuss some of its other promising applications, such as measuring the performance of generative adversarial networks (GANs) and evaluating the results of clustering methods.