Secure Multi-party Projection Method For High-dimensional Data Visualization

This paper proposes a secure multi-party projection scheme to reconstruct existing projection algorithms into a privacy-preserving version of multi-party joint projection.In the era of big data,data is often distributed on multiple privacy-sensitive sites.Individual data owners need a secure joint projection method for joint analysis of distributed high-dimensional data.However,existing high-dimensional approaches are designed for singlesite projection only.The centralization of data would lead to data leaking.Some researchers have proposed solutions to the data privacy problem of joint projection,but its security and practicability are insufficient.The main work of this paper is as follows:First,this paper arranges the projection process to the secure multiparty computation(SMPC)framework based on the Paillier encryption algorithm and ”Blinding” technology to propose a general secure multi-party projection computing process,which defines the computation tasks and privacy requirements.Second,in order to solve the data privacy problem in multi-party joint projection,this paper improves the noise-adding method of ”Blinding” technology.For the conditional probability operation based on Euclidean distance of high-dimensional data,this paper proposes the“Row-wise Blinding” technology;For the the eigen-decomposition and inversion operation of the covariance matrix of high-dimensional data,this paper proposes the“Eigen-Blinding” technology and ”Matrix Blinding” technology,respectively.Based on Paillier encryption algorithm,”Blinding” technology,and three improved technologies,this paper proposes a feasible secure multiparty projection scheme,which effectively allows multi-party to securely and jointly analyze high-dimensional data.Finally,we apply the secure multi-party projection scheme to the typical t-SNE,UMAP,PCA,and LLE to propose four secure multi-party projection algorithms: smp-t-SNE,smp-UMAP,smp-PCA,and smp-LLE.Where smp-t-SNE and smp-UMAP use “Row-wise Blinding” technology;smpPCA uses“Eigen-Blinding” technology;smp-LLE uses“Row-wise Blinding” technology and ”Matrix Blinding” technology.In addition,this paper designs experiments to analyze the effect of the secure multi-party projection algorithm.The experimental results show that: for the non-randomized projection algorithm,the result of the secure multi-party projection algorithm is the same as the original algorithm;for the projection algorithm with randomness,the difference in projection quality between the two is insignificant and can be considered equivalent.