# Differentially Private Vertical Federated Clustering

arXiv: https://arxiv.org/abs/2208.01700 · HTML: https://mlsanity.com/paper/2208.01700/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 81 references that are in the map.
- First posted on arXiv 2 Aug 2022.

## Builds on (most cited first, 27 of 27)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [The Secret Sharer: Evaluating and Testing Unintended Memorization in Neural Networks](https://mlsanity.com/paper/1802.08232/) (2018)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Distributed learning of deep neural network over multiple agents](https://mlsanity.com/paper/1810.06060/) (2018)
- [The Secret Revealer: Generative Model-Inversion Attacks Against Deep Neural Networks](https://mlsanity.com/paper/1911.07135/) (2019)
- [Privacy Preserving Vertical Federated Learning for Tree-based Models](https://mlsanity.com/paper/2008.06170/) (2020)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (2020)
- [Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms](https://mlsanity.com/paper/1612.07925/) (2016)
- [Federated Forest](https://mlsanity.com/paper/1905.10053/) (2019)
- [Federated Doubly Stochastic Kernel Learning for Vertically Partitioned Data](https://mlsanity.com/paper/2008.06197/) (2020)
- [Differentially Private Clustering: Tight Approximation Ratios](https://mlsanity.com/paper/2008.08007/) (2020)
- [Differentially Private k-Means Clustering](https://mlsanity.com/paper/1504.05998/) (2015)
- [The Value of Collaboration in Convex Machine Learning with Differential Privacy](https://mlsanity.com/paper/1906.09679/) (2019)
- [Differentially Private k-Means with Constant Multiplicative Error](https://mlsanity.com/paper/1804.08001/) (2018)
- [Hybrid Differentially Private Federated Learning on Vertically Partitioned Data](https://mlsanity.com/paper/2009.02763/) (2020)
- [Locating a Small Cluster Privately](https://mlsanity.com/paper/1604.05590/) (2016)
- [Locally Private k-Means in One Round](https://mlsanity.com/paper/2104.09734/) (2021)
- [Clustering Algorithms for the Centralized and Local Models](https://mlsanity.com/paper/1707.04766/) (2017)
- [Learning Privately over Distributed Features: An ADMM Sharing Approach](https://mlsanity.com/paper/1907.07735/) (2019)
- [Improving Privacy-Preserving Vertical Federated Learning by Efficient Communication with ADMM](https://mlsanity.com/paper/2207.10226/) (2022)
- [Back to the Future: an Even More Nearly Optimal Cardinality Estimation Algorithm](https://mlsanity.com/paper/1708.06839/) (2017)
- [Cardinality Estimators do not Preserve Privacy](https://mlsanity.com/paper/1808.05879/) (2018)
- [Efficient Differentially Private F0 Linear Sketching](https://mlsanity.com/paper/2001.11932/) (2020)

## Built on by (most cited first, 10 of 10)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [A Survey for Federated Learning Evaluations: Goals and Measures](https://mlsanity.com/paper/2308.11841/) (2023)
- [Cross-silo Federated Learning with Record-level Personalized Differential Privacy](https://mlsanity.com/paper/2401.16251/) (2024)
- [A Survey of Privacy Threats and Defense in Vertical Federated Learning: From Model Life Cycle Perspective](https://mlsanity.com/paper/2402.03688/) (2024)
- [Private Learning with Public Features](https://mlsanity.com/paper/2310.15454/) (2023)
- [Dynamically Weighted Federated k-Means](https://mlsanity.com/paper/2310.14858/) (2023)
- [FastLloyd: Federated, Accurate, Secure, and Tunable k-Means Clustering with Differential Privacy](https://mlsanity.com/paper/2405.02437/) (2024)
- [Just a Simple Transformation is Enough for Data Protection in Vertical Federated Learning](https://mlsanity.com/paper/2412.11689/) (2024)
- [PBM-VFL: Vertical Federated Learning with Feature and Sample Privacy](https://mlsanity.com/paper/2501.13916/) (2025)
- [VertCoHiRF: Decentralized Vertical Clustering Beyond k-means](https://mlsanity.com/paper/2602.07279/) (2026)

## Abstract (arXiv)

In many applications, multiple parties have private data regarding the same set of users but on disjoint sets of attributes, and a server wants to leverage the data to train a model. To enable model learning while protecting the privacy of the data subjects, we need vertical federated learning (VFL) techniques, where the data parties share only information for training the model, instead of the private data. However, it is challenging to ensure that the shared information maintains privacy while learning accurate models. To the best of our knowledge, the algorithm proposed in this paper is the first practical solution for differentially private vertical federated k-means clustering, where the server can obtain a set of global centers with a provable differential privacy guarantee. Our algorithm assumes an untrusted central server that aggregates differentially private local centers and membership encodings from local data parties. It builds a weighted grid as the synopsis of the global dataset based on the received information. Final centers are generated by running any k-means algorithm on the weighted grid. Our approach for grid weight estimation uses a novel, light-weight, and differentially private set intersection cardinality estimation algorithm based on the Flajolet-Martin sketch. To improve the estimation accuracy in the setting with more than two data parties, we further propose a refined version of the weights estimation algorithm and a parameter tuning strategy to reduce the final k-means utility to be close to that in the central private setting. We provide theoretical utility analysis and experimental evaluation results for the cluster centers computed by our algorithm and show that our approach performs better both theoretically and empirically than the two baselines based on existing techniques.