Efficient And Privacy-Preserving Tensor Decomposition Methods

In the era of big data,due to the inherent high-dimensional characteristics,tensor,an emerging big data representation tool,has attracted more and more attention.The tensor decomposition algorithms have been also rapidly developed,and widely applied to several domains such as classification,clustering and recommendation.However,due to the high complexity of the decomposition,it is necessary to optimize the tensor decomposition algorithms.In addition,with the development of technologies such as cloud computing and fog computing,tensor decomposition can be outsourced to the fogs and clouds to reduce the costs.However,because fogs and clouds are open,how to carry out tensor decomposition without compromising user's privacy is a challenging issue in fog-cloud computing.In order to solve the above challenges,this thesis proposes a privacy-preserving high-order Bi-Lanczos algorithm and an efficient privacy-preserving TT-based Tucker decomposition algorithm.The basic idea of the high-order Bi-Lanczos method is to extend Bi-Lanczos method to tensor space.Meanwhile,in order to employ fogs and clouds to carry out the high-order Bi-Lanczos while fogs and clouds learn nothing about users' data,a privacy-preserving big data processing model using the synergy of fogs and clouds is designed.With this model,we present a privacy-preserving high-order Bi-Lanczos scheme.Combined the tensor train theory,efficient TT-based Tucker decomposition reduces the number of elements that need to be updated during the gradient-descent Tucker decomposition.To utilize the massive resources of fogs and clouds while protecting user's privacy,a privacy-preserving computing model for efficient TT-based Tucker decomposition is presented,based on which we implements an efficient privacy-preserving TT-based Tucker decomposition scheme.Finally,based on the real-world dataset and the synthetic dataset,we theoretically and empirically analyze the security and efficiency of the proposed privacy-preserving high-order Bi-Lanczos scheme and efficient privacy-preserving TT-based Tucker decomposition scheme.The results demonstrate that the proposed schemes are effective and secure in the semi-honest model.