Discovering frequent graph patterns in a graph database offers valuable information in a variety of applications. However, if the graph dataset contains sensitive data of individuals such as mobile phone-call graphs and web-click graphs, releasing discovered frequent patterns may present a threat to the privacy of individuals. Differential privacy has recently emerged as the de facto standard for private data analysis due to its provable privacy guarantee. In this paper we propose the first differentially private algorithm for mining frequent graph patterns. We first show that previous techniques on differentially private discovery of frequent itemsets cannot apply in mining frequent graph patterns due to the inherent complexity of handling structural information in graphs. We then address this challenge by proposing a Markov Chain Monte Carlo (MCMC) sampling based algorithm. Unlike previous work on frequent itemset mining, our techniques do not rely on the output of a non-private mining algorithm. Instead, we observe that both frequent graph pattern mining and the guarantee of differential privacy can be unified into an MCMC sampling framework. In addition, we establish the privacy and utility guarantee of our algorithm and propose an efficient neighboring pattern counting technique as well. Experimental results show that the proposed algorithm is able to output frequent patterns with good precision.
Discovering frequent patterns from data is a popular exploratory technique in datamining. However, if the data are sensitive (e.g., patient health records, user behavior records) releasing information about significant patterns or trends carries significant risk to privacy. This paper shows how one can accurately discover and release the most significant patterns along with their frequencies in a data set containing sensitive information, while providing rigorous guarantees of privacy for the individuals whose information is stored there. We present two efficient algorithms for discovering the k most frequent patterns in a data set of sensitive records. Our algorithms satisfy differential privacy, a recently introduced definition that provides meaningful privacy guarantees in the presence of arbitrary external information. Differentially private algorithms require a degree of uncertainty in their output to preserve privacy. Our algorithms handle this by returning 'noisy' lists of patterns that are close to the actual list of k most frequent patterns in the data. We define a new notion of utility that quantifies the output accuracy of private top-k pattern mining algorithms. In typical data sets, our utility criterion implies low false positive and false negative rates in the reported lists. We prove that our methods meet the new utility criterion; we also demonstrate the performance of our algorithms through extensive experiments on the transaction data sets from the FIMI repository. While the paper focuses on frequent pattern mining, the techniques developed here are relevant whenever the data mining output is a list of elements ordered according to an appropriately 'robust' measure of interest. The problem of privacy-preserving data mining has attracted considerable attention in recent years because of increasing concerns about the privacy of the underlying data. In recent years, an important data domain which has emerged is that of graphs and structured data. Many data sets such as XML data, transportation networks, traffic in IP networks, social networks and hierarchically structured data are naturally represented as graphs. Existing work on graph privacy has focussed on the problem of anonymizing nodes or edges of a single graph, in which the identity is assumed to be associated with individual nodes. In this paper, we examine the more complex case, where we have a collection of graphs, and the identity is associated with individual graphs rather than nodes or edges. In such cases, the problem of identity anonymization is extremely difficult, since we need to not only anonymize the labels on the nodes, but also the underlying global structural information. In such cases, both the global and local structural information can be a challenge to the anonymization process, since any combination of such information can be used in order to de-identify the underlying graphs. In order to achieve this goal, we will create synthesized representations of the underlying graphs based on aggregate structural analytics of the collection of graphs. The synthesized graphs retain the properties of the original data while satisfying the k-anonymity requirement. Our experimental results show that the synthesized graphs maintain a high level of structural information and compatible classification accuracies with the original data. We present efficient algorithms for releasing useful statistics about graph data while providing rigorous privacy guarantees. Our algorithms work on datasets that consist of relationships between individuals, such as social ties or email communication. The algorithms satisfy edge differential privacy, which essentially requires that the presence or absence of any particular relationship be hidden. Our algorithms output approximate answers to subgraph counting queries. Given a query graph H, for example, a triangle, k-star, or k-triangle, the goal is to return the number of edge-induced isomorphic copies of H in the input graph. The special case of triangles was considered by [2007] and a more general investigation of arbitrary query graphs was initiated by [2009]. We extend the approach of to a new class of statistics, namely k-star queries. We also give algorithms for k-triangle queries using a different approach based on the higher-order local sensitivity. For the specific graph statistics we consider (i.e., k-stars and k-triangles), we significantly improve on the work of : our algorithms satisfy a stronger notion of privacy that does not rely on the adversary having a particular prior distribution on the data, and add less noise to the answers before releasing them. We evaluate the accuracy of our algorithms both theoretically and empirically, using a variety of real and synthetic datasets. We give explicit, simple conditions under which these algorithms add a small amount of noise. We also provide the average-case analysis in the Erdős-Renyi-Gilbert G(n,p) random graph model. Finally, we give hardness results indicating that the approach used for triangles cannot easily be extended to k-triangles (hence justifying our development of a new algorithmic approach).