Subscribe

Issue No.04 - April (2012 vol.24)

pp: 590-604

Sudipto Das , Microsoft Research, Redmond

Ömer Eğecioğlu , University of California - Santa Barbara, Santa Barbara

Amr El Abbadi , University of California - Santa Barbara, Santa Barbara

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TKDE.2010.267

ABSTRACT

The increasing popularity of social networks has initiated a fertile research area in information extraction and data mining. Anonymization of these social graphs is important to facilitate publishing these data sets for analysis by external entities. Prior work has concentrated mostly on node identity anonymization and structural anonymization. But with the growing interest in analyzing social networks as a weighted network, edge weight anonymization is also gaining importance. We present Anónimos, a Linear Programming-based technique for anonymization of edge weights that preserves linear properties of graphs. Such properties form the foundation of many important graph-theoretic algorithms such as shortest paths problem, k-nearest neighbors, minimum cost spanning tree, and maximizing information spread. As a proof of concept, we apply Anónimos to the shortest paths problem and its extensions, prove the correctness, analyze complexity, and experimentally evaluate it using real social network data sets. Our experiments demonstrate that Anónimos anonymizes the weights, improves k-anonymity of the weights, and also scrambles the relative ordering of the edges sorted by weights, thereby providing robust and effective anonymization of the sensitive edge-weights. We also demonstrate the composability of different models generated using Anónimos, a property that allows a single anonymized graph to preserve multiple linear properties.

INDEX TERMS

Anonymization, social networks, shortest paths, linear programming.

CITATION

Sudipto Das, Ömer Eğecioğlu, Amr El Abbadi, "Anónimos: An LP-Based Approach for Anonymizing Weighted Social Network Graphs",

*IEEE Transactions on Knowledge & Data Engineering*, vol.24, no. 4, pp. 590-604, April 2012, doi:10.1109/TKDE.2010.267REFERENCES

- [1] Y.-Y. Ahn, S. Han, H. Kwak, S. Moon, and H. Jeong, "Analysis of Topological Characteristics of Huge Online Social Networking Services,"
Proc. 16th Int'l Conf. World Wide Web (WWW), pp. 835-844, 2007.- [2] L. Backstrom, D. Huttenlocher, J. Kleinberg, and X. Lan, "Group Formation in Large Social Networks: Membership, Growth, and Evolution,"
Proc. 12th ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining (KDD), pp. 44-54, 2006.- [3] A. Mislove, M. Marcon, K.P. Gummadi, P. Druschel, and B. Bhattacharjee, "Measurement and Analysis of Online Social Networks,"
Proc. Seventh ACM SIGCOMM Conf. Internet Measurement (IMC), pp. 29-42, 2007.- [4] M.K. Sparrow, "The Application of Network Analysis to Criminal Intelligence: An Assessment of the Prospects,"
Social Networks, vol. 13, pp. 251-274, 1991.- [5] S. Amer-Yahia, L.V.S. Lakshmanan, and C. Yu, "Socialscope: Enabling Information Discovery on Social Content Sites,"
Proc. Conf. Innovative Data Systems Research (CIDR), 2009.- [6] S. Hill, F. Provost, and C. Volinsky, "Network-Based Marketing: Identifying Likely Adopters via Consumer Networks,"
Statistical Science, vol. 22, no. 2, pp. 256-275, 2006.- [7] L. Getoor and C.P. Diehl, "Link Mining: A Survey,"
SIGKDD Explorations Newsletter, vol. 7, no. 2, pp. 3-12, 2005.- [8] L. Backstrom, C. Dwork, and J. Kleinberg, "Wherefore Art Thou R3579X?: Anonymized Social Networks, Hidden Patterns, and Structural Steganography,"
Proc. Int'l Conf. World Wide Web (WWW), pp. 181-190, 2007.- [9] A. Korolova, R. Motwani, S. Nabar, and Y. Xu, "Link Privacy in Social Networks,"
Proc. IEEE 24th Int'l Conf. Data Eng. (ICDE), pp. 1355-1357, 2008.- [10] A. Campan and T.M. Truta, "A Clustering Approach for Data and Structural Anonymity in Social Networks,"
Proc. Privacy, Security, and Trust in KDD Workshop (PinKDD), pp. 1-10, 2008.- [11] G. Cormode, D. Srivastava, S. Bhagat, and B. Krishnamurthy, "Class-Based Graph Anonymization for Social Network Data,"
Proc. Very Large Databases Endowment, vol. 2, no. 1, pp. 766-777, 2009.- [12] G. Cormode, D. Srivastava, T. Yu, and Q. Zhang, "Anonymizing Bipartite Graph Data Using Safe Groupings,"
Proc. Very Large Databases Endowment, vol. 1, no. 1, pp. 833-844, 2008.- [13] M. Hay, G. Miklau, D. Jensen, D. Towsley, and P. Weis, "Resisting Structural Re-Identification in Anonymized Social Networks,"
Proc. Very Large Databases Endowment, vol. 1, no. 1, pp. 102-114, 2008.- [14] K. Liu and E. Terzi, "Towards Identity Anonymization on Graphs,"
Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 93-106, 2008.- [15] B. Zhou and J. Pei, "Preserving Privacy in Social Networks against Neighborhood Attacks,"
Proc. IEEE 24th Int'l Conf. Data Eng. (ICDE), pp. 506-515, 2008.- [16] L. Zou, L. Chen, and M.T. Özsu, "K-Automorphism: A General Framework for Privacy Preserving Network Publication,"
Proc. Very Large Databases Endowment, vol. 2, no. 1, pp. 946-957, 2009.- [17] J.M. Kumpula, J.P. Onnela, J. Saramaki, K. Kaski, and J. Kertesz, "Emergence of Communities in Weighted Networks,"
Physical Rev. Letters, vol. 99, pp. 228 701-1-228 701-4, 2007.- [18] R. Toivonen, J.M. Kumpula, J. Saramäki, J.-P. Onnela, J. Kertész, and K. Kaski, "The Role of Edge Weights in Social Networks: Modelling Structure and Dynamics,"
Noise and Stochastics in Complex Systems and Finance, vol. 6601, no. 1, pp. B1-B8, 2007.- [19] D. Kempe, J. Kleinberg, and E. Tardos, "Maximizing the Spread of Influence through a Social Network,"
Proc. Ninth ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining (KDD), pp. 137-146, 2003.- [20] E.W. Dijkstra, "A Note on Two Problems in Connexion with Graphs,"
Numerische Mathematik, vol. 1, pp. 269-271, 1959.- [21] J.B. Kruskal, "On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem,"
Proc. the Am. Math. Soc., vol. 7, no. 1,pp. 48-50, Feb. 1956.- [22] J. Tang, J. Zhang, L. Yao, J. Li, L. Zhang, and Z. Su, "Arnetminer: Extraction and Mining of Academic Social Networks,"
Proc. 14th ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining (KDD), pp. 990-998, 2008.- [23] M. Stoer and F. Wagner, "A Simple Min-Cut Algorithm,"
J. ACM, vol. 44, no. 4, pp. 585-591, 1997.- [24] A.M. Gibbons,
Algorithmic Graph Theory. Cambridge Univ. Press, 1985.- [25] E. Horowitz and S. Sahni,
Fundamentals of Computer Algorithms. CS Press, 1978.- [26] S. Das, Ömer Eğecioğlu, and A. El Abbadi, "Anonymizing Weighted Social Network Graphs,"
Proc. IEEE 26th Int'l Conf. Data Eng. (ICDE), pp. 904-907, 2010.- [27] L. Sweeney, "k-Anonymity: A Model for Protecting Privacy,"
Int'l J. Uncertainty Fuzziness and Knowledge-Based Systems, vol. 10, no. 5, pp. 557-570, 2002.- [28] C. Spearman, "The Proof and Measurement of Association between Two Things,"
Am. J. Psychology, vol. 15, pp. 72-101, Feb. 1904.- [29] C.H. Papadimitriou and K. Steiglitz,
Combinatorial Optimization: Algorithms and Complexity, p. 173. Dover, 1998.- [30] R.W. Floyd, "Algorithm 97: Shortest Path,"
Comm. ACM, vol. 5, no. 6, p. 345, 1962.- [31] LPSolve 5.5, http://lpsolve.sourceforge.net5.5/, 2011.
- [32] K. Liu, K. Das, T. Grandison, and H. Kargupta,
Privacy-Preserving Data Analysis on Graphs and Social Networks, Chapter 21, pp. 419-437. CRC Press, Dec. 2008.- [33] X. Wu, X. Ying, K. Liu, and L. Chen,
A Survey of Algorithms for Privacy-Preservation of Graphs and Social Networks, ser. Managing and Mining Graph Data, Chapter 14, pp. 421-454. Kluwer Academic Publishers, Mar. 2010.- [34] X. Ying and X. Wu, "Randomizing Social Networks: A Spectrum Preserving Approach,"
Proc. Eighth SIAM Conf. Data Mining, pp. 739-750, 2008.- [35] E. Zheleva and L. Getoor, "Preserving the Privacy of Sensitive Relationships in Graph Data,"
Proc. First ACM SIGKDD Int'l Conf. Privacy, Security, and Trust in KDD (PinKDD), pp. 153-171, 2007.- [36] L. Liu, J. Wang, J. Liu, and J. Zhang, "Privacy Preservation in Social Networks with Sensitive Edge Weights,"
Proc. SIAM Int'l Conf. Data Mining (SDM), pp. 954-965, 2009. |