# Differentially-Private Hierarchical Clustering with Provable Approximation Guarantees

arXiv: https://arxiv.org/abs/2302.00037 · HTML: https://mlsanity.com/paper/2302.00037/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 64 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 22 of 22)

- [RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Response](https://mlsanity.com/paper/1407.6981/) (2014)
- [A cost function for similarity-based hierarchical clustering](https://mlsanity.com/paper/1510.05043/) (2015)
- [Differentially Private Clustering: Tight Approximation Ratios](https://mlsanity.com/paper/2008.08007/) (2020)
- [Approximate Hierarchical Clustering via Sparsest Cut and Spreading Metrics](https://mlsanity.com/paper/1609.09548/) (2016)
- [Community detection in sparse networks via Grothendieck's inequality](https://mlsanity.com/paper/1411.4686/) (2014)
- [Private estimation algorithms for stochastic block models and mixture models](https://mlsanity.com/paper/2301.04822/) (2023)
- [How Robust are Reconstruction Thresholds for Community Detection?](https://mlsanity.com/paper/1511.01473/) (2015)
- [Robust recovery for stochastic block models](https://mlsanity.com/paper/2111.08568/) (2021)
- [A simple SVD algorithm for finding hidden partitions](https://mlsanity.com/paper/1404.3918/) (2014)
- [Differentially Private Community Detection for Stochastic Block Models](https://mlsanity.com/paper/2202.00636/) (2022)
- [Differentially Private Correlation Clustering](https://mlsanity.com/paper/2102.08885/) (2021)
- [Differentially Private Graph Learning via Sensitivity-Bounded Personalized PageRank](https://mlsanity.com/paper/2207.06944/) (2022)
- [Minimax Rates for Robust Community Detection](https://mlsanity.com/paper/2207.11903/) (2022)
- [Achieving the Bayes Error Rate in Synchronization and Block Models by SDP, Robustly](https://mlsanity.com/paper/1904.09635/) (2019)
- [Scalable Differentially Private Clustering via Hierarchically Separated Trees](https://mlsanity.com/paper/2206.08646/) (2022)
- [Bisect and Conquer: Hierarchical Clustering via Max-Uncut Bisection](https://mlsanity.com/paper/1912.06983/) (2019)
- [Private Hierarchical Clustering in Federated Networks](https://mlsanity.com/paper/2105.09057/) (2021)
- [Near-Optimal Correlation Clustering with Privacy](https://mlsanity.com/paper/2203.01440/) (2022)
- [Hierarchical Agglomerative Graph Clustering in Poly-Logarithmic Depth](https://mlsanity.com/paper/2206.11654/) (2022)
- [Minimum spanning tree release under differential privacy constraints](https://mlsanity.com/paper/1801.06423/) (2018)
- [A novel brain partition highlights the modular skeleton shared by structure and function](https://mlsanity.com/paper/1410.7959/) (2014)
- [Sublinear Algorithms for Hierarchical Clustering](https://mlsanity.com/paper/2206.07633/) (2022)

## Built on by (most cited first, 5 of 5)

- [Hyperbolic Continuous Structural Entropy for Hierarchical Clustering](https://mlsanity.com/paper/2512.00524/) (2025)
- [Perturb-and-Project: Differentially Private Similarities and Marginals](https://mlsanity.com/paper/2406.04868/) (2024)
- [Differentially Private Synthetic Graphs Preserving Triangle-Motif Cuts](https://mlsanity.com/paper/2507.14835/) (2025)
- [On the Price of Differential Privacy for Hierarchical Clustering](https://mlsanity.com/paper/2504.15580/) (2025)
- [On the Optimal Number of Grids for Differentially Private Non-Interactive K-Means Clustering](https://mlsanity.com/paper/2603.26963/) (2026)

## Abstract (arXiv)

Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially private approximation algorithms for hierarchical clustering under the rigorous framework introduced by (Dasgupta, 2016). We show strong lower bounds for the problem: that any ε-DP algorithm must exhibit O(|V|2/ ε)-additive error for an input dataset V. Then, we exhibit a polynomial-time approximation algorithm with O(|V|2.5/ ε)-additive error, and an exponential-time algorithm that meets the lower bound. To overcome the lower bound, we focus on the stochastic block model, a popular model of graphs, and, with a separation assumption on the blocks, propose a private 1+o(1) approximation algorithm which also recovers the blocks exactly. Finally, we perform an empirical study of our algorithms and validate their performance.