Towards A Practical Cluster Analysis Over Encrypted Data

Cluster analysis is one of the most significant unsupervised machine learning methods, and it is being utilized in various fields associated with privacy issues including bioinformatics, finance and image processing. In this paper, we propose a practical solution for privacy-preserving cluster analysis based on homomorphic encryption (HE). Our work is the first HE solution for the mean-shift clustering algorithm. To reduce the super-linear complexity of the original mean-shift algorithm, we adopt a novel random sampling method called dust sampling approach, which perfectly suits with HE and achieves the linear complexity. We also substitute non-polynomial kernels by a new polynomial kernel so that it can be efficiently computed in HE.The HE implementation of our modified mean-shift clustering algorithm based on the approximate HE scheme HEAAN shows prominent performance in terms of speed and accuracy. It takes approx. 30min with 99% accuracy over several public datasets with hundreds of data, and even for the dataset with 262, 144 data, it takes 82 min only when SIMD operations in HEAAN is applied. Our results outperform the previously best known result (SAC 2018) by over 400 times.