Privacy-preserving collaborative fuzzy clustering

In this paper, we address this challenge with a two-stage scheme called RG+RP: in the first stage, each participant perturbs his/her data by passing the data through a nonlinear function called repeated Gompertz (RG); in the second stage, he/she then projects his/her perturbed data to a lower dimension in an (almost) distance-preserving manner, using a specific random projection (RP) matrix. The nonlinear RG function is designed to mitigate maximum a posteriori (MAP) estimation attacks, while random projection resists independent component analysis (ICA) attacks and ensures clustering accuracy. The proposed two-stage randomisation scheme is assessed in terms of its recovery resistance to MAP estimation attacks. Preliminary theoretical analysis as well as experimental results on synthetic and real-world datasets indicate that RG+RP has better recovery resistance to MAP estimation attacks than most state-of-the-art techniques. For clustering, fuzzy c-means (FCM) is used. Results using seven cluster validity indices, root mean squared error (RMSE) and accuracy ratio show that clustering results based on two-stage-perturbed data are comparable to the clustering results based on raw data - this confirms the utility of our privacy-preserving scheme when used with either FCM or HCM.