Secure Tensor Decomposition for Heterogeneous Multimedia Data in Cloud Computing

With the rapid development and proliferation of multimedia systems and applications, there is a growing need to handle multimedia heterogeneous data safely and efficiently on the cloud. Tensor models are effective in representing multimedia multidimensional data, and the tensor decomposition is one of the basic building blocks of data analysis and learning models. In this article, we propose a secure tensor singular value decomposition (<inline-formula> <tex-math notation="LaTeX">${S}$ </tex-math></inline-formula>-tSVD), in which the time-domain operation is converted into a scheme featuring frequency-domain multilinear circular unfolding–folding. First, we represent various multimedia data as cipher subtensors, using fully homomorphic encryption. We then take the fast Fourier transform (FFT) approach to launch a new multiplication operation along the tubal fibers of a unified high-order tensor. Second, relying on the homomorphism of addition and multiplication theory, we prove the fully homomorphic consistency of the proposed <inline-formula> <tex-math notation="LaTeX">${S}$ </tex-math></inline-formula>-tSVD algorithm. Third, we provide an elegant solution to tackle the typical dimensionality inconsistency problem while working with multiple subtensors. Finally, we carry out theoretical analyses with respect to dimensionality reduction, reconstruction error of <inline-formula> <tex-math notation="LaTeX">${S}$ </tex-math></inline-formula>-tSVD, running time, and data security. We use real unstructured video data and semistructured XML documents, integrating them within a unified tensor model for decomposition. We demonstrate that the error ratio of the <inline-formula> <tex-math notation="LaTeX">${S}$ </tex-math></inline-formula>-tSVD is lower than the same compression ratio compared to the SVD decomposition and tSVD-slice approaches. Moreover, the specific <inline-formula> <tex-math notation="LaTeX">${S}$ </tex-math></inline-formula>-tSVD decomposition not only enables effective data mining and dimensionality reduction but also ensures the accuracy of the decomposition result and data privacy protection.

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