This paper investigates differentially private analysis of distance-based outliers. The problem of outlier detection is to find a small number of instances that are apparently distant from the remaining instances. On the other hand, the objective of differential privacy is to conceal presence (or absence) of any particular instance. Outlier detection and privacy protection are thus intrinsically conflicting tasks. In this paper, instead of reporting outliers detected, we present two types of differentially private queries that help to understand behavior of outliers. One is the query to count outliers, which reports the number of outliers that appear in a given subspace. Our formal analysis on the exact global sensitivity of outlier counts reveals that regular global sensitivity based method can make the outputs too noisy, particularly when the dimensionality of the given subspace is high. Noting that the counts of outliers are typically expected to be relatively small compared to the number of data, we introduce a mechanism based on the smooth upper bound of the local sensitivity. The other is the query to discovery top-h subspaces containing a large number of outliers. This task can be naively achieved by issuing count queries to each subspace in turn. However, the variation of subspaces can grow exponentially in the data dimensionality. This can cause serious consumption of the privacy budget. For this task, we propose an exponential mechanism with a customized score function for subspace discovery. To the best of our knowledge, this study is the first trial to ensure differential privacy for distance-based outlier analysis. We demonstrated our methods with synthesized datasets and real datasets. The experimental results show that out method achieve better utility compared to the global sensitivity based methods.
To provide social network data (SN) data to researchers for data analysis, protecting user privacy via anonymization is necessary. One anonymization metric for SN data called k-neighbor [1] [2] focuses on the neighborhood subgraphs, which, for each node, consists of the node's neighbor nodes. This metric ensures that the neighborhood subgraph of every node in the anonymized graph is isomorphic to at least k other neighborhood subgraphs; however, the existing algorithm to realize k-neighbor does not consider case that adding noise edges for anonymization may drastically change the distances of some pairs of nodes, which in turn may alter the structure of the original graph. To solve this problem, we propose an algorithm that focuses on a method to add noise edges such that the change of the distances of the pairs of nodes is suppressed. Through our experiments, we have confirmed that our algorithm maintains the given distances between nodes in the anonymized graph.
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