Privacy-Preserving Federated K-Means Clustering: A Comprehensive Analysis

Federated clustering is a technique that allows multiple parties to work together to perform clustering tasks while keeping their data private. In this article, the authors investigate the trade-off between privacy and efficiency in federated k-means clustering. They show that the number of iterations required for convergence can be used to determine the privacy loss, and that there are limitations to the amount of privacy that can be preserved.
The authors start by explaining the basics of federated clustering, including the use of private data and the goal of partitioning it into clusters. They then introduce the concept of hidden weight matrices (HSSP), which are used to quantify the privacy loss in federated clustering. The authors show that these matrices can be rank deficient due to dependencies between the hidden weights, making it difficult to accurately assess the privacy loss.
To address this challenge, the authors propose a new variant of HSSP called the k-means instance of HSSP. This allows them to better understand the impact of clustering on privacy loss. They also introduce a new metric, the Euclidean distance between the hidden weights and their corresponding recovered binary vectors, which can be used to measure the privacy loss.
The authors then demonstrate their approach using several examples, including one where the number of clusters is unknown and another where the data is non-iid. They show that their method can accurately identify the number of clusters in these cases while preserving privacy.
Finally, the authors conclude by discussing the implications of their findings and highlighting several areas for future research. They note that their approach can be used to improve the efficiency of federated clustering methods while preserving privacy, but that there is still much work to be done in this area.
In summary, this article provides a detailed analysis of the trade-off between privacy and efficiency in federated k-means clustering. The authors propose several new techniques for measuring privacy loss and demonstrate their effectiveness through real-world examples. Their findings have important implications for the development of privacy-preserving clustering methods in the future.