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Correlated network data publication via differential privacy

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Abstract

With the increasing prevalence of information networks, research on privacy-preserving network data publishing has received substantial attention recently. There are two streams of relevant research, targeting different privacy requirements. A large body of existing works focus on preventing node re-identification against adversaries with structural background knowledge, while some other studies aim to thwart edge disclosure. In general, the line of research on preventing edge disclosure is less fruitful, largely due to lack of a formal privacy model. The recent emergence of differential privacy has shown great promise for rigorous prevention of edge disclosure. Yet recent research indicates that differential privacy is vulnerable to data correlation, which hinders its application to network data that may be inherently correlated. In this paper, we show that differential privacy could be tuned to provide provable privacy guarantees even in the correlated setting by introducing an extra parameter, which measures the extent of correlation. We subsequently provide a holistic solution for non-interactive network data publication. First, we generate a private vertex labeling for a given network dataset to make the corresponding adjacency matrix form dense clusters. Next, we adaptively identify dense regions of the adjacency matrix by a data-dependent partitioning process. Finally, we reconstruct a noisy adjacency matrix by a novel use of the exponential mechanism. To our best knowledge, this is the first work providing a practical solution for publishing real-life network data via differential privacy. Extensive experiments demonstrate that our approach performs well on different types of real-life network datasets.

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Notes

  1. The strong attacker mentioned in [24] cannot be prevented as his prior knowledge (without accessing any database) has allowed him to succeed in a privacy attack. Such a privacy attack is not caused by data sharing and therefore beyond the scope of this paper.

  2. A random vertex labeling satisfies 0-differential privacy because it can be viewed as an application of the exponential mechanism with privacy parameter 0.

  3. If \(v_i\) and \(v_j\) are selected to swap with each other, only one query will be affected. This leads to a lower global sensitivity.

  4. For a region \(R\) not containing elements on the diagonal, \(GS(f)=1\) because a single edge difference cannot change two elements in this region.

  5. ca-GrQc, ca-HepTh and wiki-Vote are publicly available in the Stanford large network dataset collection (http://snap.stanford.edu/data/index.html). STM is provided by the Société de transport de Montréal (http://www.stm.info).

  6. Laplace can barely provide any useful information in terms of degree distribution because its KL-divergence is almost the same as an empty graph (i.e., \(|E| = 0\)).

  7. Step 1 means that sampling is not employed.

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Acknowledgments

We sincerely thank the reviewers for their insightful comments. We thank James Cheng, Ada Wai-Chee Fu and Jia Liu for providing the source code of \(k\)-isomorphism. The research is supported in part by NSERC through Discovery Grants (356065-2013), US NSF through grants CNS-1115234, DBI-0960443 and OISE-1129076 and US Department of Army through grant W911NF-12-1-0066.

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Authors and Affiliations

  1. Hong Kong Baptist University, Kowloon, Hong Kong

    Rui Chen

  2. McGill University, Montreal, Canada

    Benjamin C. M. Fung

  3. University of Illinois at Chicago, Chicago, IL, USA

    Philip S. Yu

  4. Concordia University, Montreal, Canada

    Bipin C. Desai

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  1. Rui Chen
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  2. Benjamin C. M. Fung
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Correspondence to Rui Chen.

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Chen, R., Fung, B.C.M., Yu, P.S. et al. Correlated network data publication via differential privacy. The VLDB Journal 23, 653–676 (2014). https://doi.org/10.1007/s00778-013-0344-8

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