# Improving the Utility of Differentially Private Clustering through Dynamical Processing

arXiv: https://arxiv.org/abs/2304.13886 · HTML: https://mlsanity.com/paper/2304.13886/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 68 references that are in the map.
- First posted on arXiv 27 Apr 2023.

## Builds on (most cited first, 11 of 11)

- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Differentially Private Mixture of Generative Neural Networks](https://mlsanity.com/paper/1709.04514/) (2017)
- [New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemma](https://mlsanity.com/paper/2205.08532/) (2022)
- [Differentially Private k-Means Clustering](https://mlsanity.com/paper/1504.05998/) (2015)
- [Differentially Private Algorithms for Learning Mixtures of Separated Gaussians](https://mlsanity.com/paper/1909.03951/) (2019)
- [Locally Private k-Means in One Round](https://mlsanity.com/paper/2104.09734/) (2021)
- [An Information-Theoretic Analysis of Hard and Soft Assignment Methods for Clustering](https://mlsanity.com/paper/1302.1552/) (2013)
- [Differentially-Private Clustering of Easy Instances](https://mlsanity.com/paper/2112.14445/) (2021)
- [Federating Recommendations Using Differentially Private Prototypes](https://mlsanity.com/paper/2003.00602/) (2020)
- [Possibility results for graph clustering: A novel consistency axiom](https://mlsanity.com/paper/1806.06142/) (2018)
- [Privacy-Preserving Distributed Expectation Maximization for Gaussian Mixture Model using Subspace Perturbation](https://mlsanity.com/paper/2209.07833/) (2022)

## Abstract (arXiv)

This study aims to alleviate the trade-off between utility and privacy of differentially private clustering. Existing works focus on simple methods, which show poor performance for non-convex clusters. To fit complex cluster distributions, we propose sophisticated dynamical processing inspired by Morse theory, with which we hierarchically connect the Gaussian sub-clusters obtained through existing methods. Our theoretical results imply that the proposed dynamical processing introduces little to no additional privacy loss. Experiments show that our framework can improve the clustering performance of existing methods at the same privacy level.