Efficient multi-party privacy preserving federated k-means based on homomorphic encryption

Nowadays, the collection and storage of data is increasingly decentralized, and the demand for data mining on distributed data is growing. Traditional k-means risks privacy leaks through direct data sharing. Existing privacy-preserving methods still expose intermediate cluster details during iterations. This paper introduces DTK-means (distributed privacy-preserving k-means) clustering algorithm, a distributed privacy-preserving k-means method addressing these issues. It involves multiple users and two non-colluding servers. The user locally computes centroids, encrypts them, and submits to the server. The two servers then aggregate these encrypted centroids into global cluster centroids with multiplicative perturbation, ensuring that neither the participants nor the servers have knowledge of the specific details. The scheme includes four algorithms for compute local centroids, data aggregation, compute global centroids and output final cluster centroids, implemented using Paillier homomorphic encryption. An extensive performance analysis is carried out to show that DTK-means ensures that intermediate data and private data are concealed from all parties involved. Participants can accurately perform k-means clustering using these hidden global centroids without any information loss. Furthermore, it can resist collusion attacks, even if one server colludes with all participants except one. Complexity analysis and numerical experiments show that our algorithm has good efficiency.