Searching Privately by Imperceptible Lying: A Novel Private Hashing Method with Differential Privacy

In the big data era, with the increasing amount of multi-media data, approximate nearest neighbor~(ANN) search has been an important but challenging problem. As a widely applied large-scale ANN search method, hashing has made great progress, and achieved sub-linear search time with low memory space. However, the advances in hashing are based on the availability of large and representative datasets, which often contain sensitive information. Typically, the privacy of this individually sensitive information is compromised. In this paper, we tackle this valuable yet challenging problem and formulate a task termed as private hashing, which takes into account both searching performance and privacy protection. Specifically, we propose a novel noise mechanism, i.e., Random Flipping, and two private hashing algorithms, i.e., PHashing and PITQ, with the refined analysis within the framework of differential privacy, since differential privacy is a well-established technique to measure the privacy leakage of an algorithm. Random Flipping targets binary scenarios and leverages the "Imperceptible Lying" idea to guarantee ε-differential privacy by flipping each datum of the binary matrix (noise addition). To preserve ε-differential privacy, PHashing perturbs and adds noise to the hash codes learned by non-private hashing algorithms using Random Flipping. However, the noise addition for privacy in PHashing will cause severe performance drops. To alleviate this problem, PITQ leverages the power of alternative learning to distribute the noise generated by Random Flipping into each iteration while preserving ε-differential privacy. Furthermore, to empirically evaluate our algorithms, we conduct comprehensive experiments on the image search task and demonstrate that proposed algorithms achieve equal performance compared with non-private hashing methods.