Privacy-preserving LOF outlier detection

LOF is a well-known approach for density-based outlier detection and has received much attention recently. It is important to design a privacy-preserving LOF outlier detection algorithm as the data on which LOF runs is typically spilt among multiple participants and no one is willing to disclose his sensitive information due to legal or moral considerations. This is, however, a hard problem since participants need to find the maximum one of the distances between an object and its k-Nearest Neighbors (k-NN) without learning the information of these objects. In this paper, we propose an efficient protocol for privacy-preserving LOF outlier detection. We first employ a shuffle protocol to permute the distance vectors owned by different participants. Then, we design a secure selection method to obtain the garbled k-NN indexes and shares of k-distance for given objects. For each object, we make use of the k-distance of all objects to construct a vector, based on which the permute protocol is executed again to obtain new shares of k-distance. Finally, the shares corresponding to the garbled k-NN indexes are selected as the expected result. Our protocol ensures that all the intermediates are shared between multiple participants and thus avoid information leaking. In addition, our protocol is efficient as we prove that the computation and communication complexity of our protocol is bounded by $$O(n^2)$$O(n2).