Research On Differentially Private Tensor Decomposition

With the rapid development and popularization of information technology and Internet,the world has entered the era of big data.In the cyber s,physics,and social space,massive multi-source heterogeneous data is generated every day,which brings great challenges to traditional data analysis and processing methods,so new theories and methods are needed to solve these problems.Tensors,as a high-order extended form of vectors and matrices,have strong data modeling,characterization and analysis capabilities,and tensor decomposition methods as an important tensor analysis method play an important role in big data analysis and processing.At the same time,with the increasing amount of data,the requirements for big data computation and storage are also increasing,so it is an inevitable trend to outsource the computation and storage services to the cloud.However,because the security and privacy problems of the cloud itself will affect the trust and use of users,the method of implementing secure tensor decomposition in the cloud is worthy of in-depth study.Aiming at two different scenarios of trusted cloud and untrusted cloud,the Tucker decomposition and tensor chain decomposition methods of differential privacy are proposed respectively.In a trusted cloud scenario,a differential privacy tensor decomposition model is proposed,describing the data transmission,analysis,processing and application processes in Cyber-Physical-Social systems and the cloud.Based on the gradient descent Tucker decomposition and tensor train decomposition algorithm,the differential privacy method is integrated into the calculation process of tensor decomposition,and design the gradient perturbed differentially private Tucker decomposition and tensor train decomposition algorithm,and the theoretical derivation proves that the algorithm can meet the definition of differential privacy.In the untrusted cloud scenario,a differential privacy tensor decomposition model with roles of cloud,edge,and third party is proposed,and the process of data transmission,analysis,and processing between various roles is further analyzed.The previously proposed algorithm is improved to adapt it to the needs of untrusted cloud scenarios,and solve the problem that the original data must be stored locally,which can not only complete the calculation through the edge node and the cloud,but also meet the security and privacy requirements.And give a theoretical proof that the algorithm satisfies the definition of differential privacy.Finally,all the proposed algorithms are simulated on the real data set.The experimental results show that compared with the tensor decomposition algorithm without privacy protection,the differential privacy technology has little effect on the accuracy of tensor decomposition.It also will not bring much computational overhead and communication overhead.