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Harnessing the Cloud for Secure and Efficient Outsourcing of Non-negative Matrix Factorization

Non-negative matrix factorization (NMF) is the task of factoring a non-negative matrix into the product of two (smaller) non-negative matrices. As an important data analysis technique, NMF finds applications in many areas of science and engineering. Real-world NMF tasks often involve large-scale matrices and incur expensive computation costs. Consequently, we consider the cloud computing paradigm, where a resource-constrained client outsources the NMF task to a powerful but untrustworthy cloud. In many applications, the input of and the solution to the NMF task usually contain the client’s private information, which necessitates privacy-preserving outsourcing. In this paper, we first reveal the privacy breaches of a recent NMF outsourcing scheme. Then, for enhanced privacy protection, we employ certain matrix transformations and present a new construction, which can solve the NMF task in a masked yet verifiable manner. Theoretical analysis shows that our proposal is cheating-resistant, recoverable, and privacy-preserving. Experiments on synthetic and real-world data demonstrate that our proposal not only brings significant cost savings to a client but also accelerates the task solving.