# Recovery Guarantees for Kernel-based Clustering under Non-parametric Mixture Models

arXiv: https://arxiv.org/abs/2110.09476 · HTML: https://mlsanity.com/paper/2110.09476/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 18 Oct 2021.

## Builds on (most cited first, 7 of 7)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Identifiability of Nonparametric Mixture Models and Bayes Optimal Clustering](https://mlsanity.com/paper/1802.04397/) (2018)
- [The geometry of kernelized spectral clustering](https://mlsanity.com/paper/1404.7552/) (2014)
- [Consistent procedures for cluster tree estimation and pruning](https://mlsanity.com/paper/1406.1546/) (2014)
- [On The Identifiability of Mixture Models from Grouped Samples](https://mlsanity.com/paper/1502.06644/) (2015)
- [On the optimality of kernels for high-dimensional clustering](https://mlsanity.com/paper/1912.00458/) (2019)
- [On Robustness of Kernel Clustering](https://mlsanity.com/paper/1606.01869/) (2016)

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

- [Beyond Smoothness: Incorporating Low-Rank Analysis into Nonparametric Density Estimation](https://mlsanity.com/paper/2204.00930/) (2022)
- [Generalized Identifiability Bounds for Mixture Models with Grouped Samples](https://mlsanity.com/paper/2207.11164/) (2022)
- [PMODE: Theoretically Grounded and Modular Mixture Modeling](https://mlsanity.com/paper/2508.21396/) (2025)
- [Multimodal Multi-User Surface Recognition with the Kernel Two-Sample Test](https://mlsanity.com/paper/2303.04930/) (2023)
- [Explainable Clustering of Mixture Models](https://mlsanity.com/paper/2411.01576/) (2024)
- [Nonparametric Kernel Clustering with Bandit Feedback](https://mlsanity.com/paper/2601.07535/) (2026)

## Abstract (arXiv)

Despite the ubiquity of kernel-based clustering, surprisingly few statistical guarantees exist beyond settings that consider strong structural assumptions on the data generation process. In this work, we take a step towards bridging this gap by studying the statistical performance of kernel-based clustering algorithms under non-parametric mixture models. We provide necessary and sufficient separability conditions under which these algorithms can consistently recover the underlying true clustering. Our analysis provides guarantees for kernel clustering approaches without structural assumptions on the form of the component distributions. Additionally, we establish a key equivalence between kernel-based data-clustering and kernel density-based clustering. This enables us to provide consistency guarantees for kernel-based estimators of non-parametric mixture models. Along with theoretical implications, this connection could have practical implications, including in the systematic choice of the bandwidth of the Gaussian kernel in the context of clustering.