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Privacy-Preserving K-means Clustering over Vertically Partitioned Data Reporter ： Ximeng Liu Supervisor: Rongxing Lu School of EEE, NTU

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Presentation on theme: "Privacy-Preserving K-means Clustering over Vertically Partitioned Data Reporter ： Ximeng Liu Supervisor: Rongxing Lu School of EEE, NTU"— Presentation transcript:

1 Privacy-Preserving K-means Clustering over Vertically Partitioned Data Reporter ： Ximeng Liu Supervisor: Rongxing Lu School of EEE, NTU http://www.ntu.edu.sg/home/rxlu/seminars.htm

2 References 1.Vaidya J, Clifton C. Privacy-preserving k-means clustering over vertically partitioned data[C]//Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining. ACM, 2003: 206-215.

3 http://www.ntu.edu.sg/home/rxlu/seminars.htm Introduction K-means clustering is a simple technique to group items into k clusters.

4 http://www.ntu.edu.sg/home/rxlu/seminars.htm Introduction The k-means algorithm also requires an initial assignment (approximation) for the values/positions of the k means. This is an important issue, as the choice of initial points determines the final solution.

5 http://www.ntu.edu.sg/home/rxlu/seminars.htm Introduction Vertically partitioned data: The data for a single entity are split across multiple sites, and each site has information for all the entities for a specific subset of the attributes.

6 http://www.ntu.edu.sg/home/rxlu/seminars.htm K-means algorithm ： Introduction- K-means

7 http://www.ntu.edu.sg/home/rxlu/seminars.htm Introduction Each item is placed in its closest cluster, and the cluster centers are then adjusted based on the data placement. This repeats until the positions stabilize.

8 http://www.ntu.edu.sg/home/rxlu/seminars.htm Problems So what’s the problem when we use vertically partitioned data to store data? How can we keep the data privacy?

9 http://www.ntu.edu.sg/home/rxlu/seminars.htm Problems At first glance, this might appear simple – each site can simply run the k-means algorithm on its own data. This would preserve complete privacy. But it will not work. How can we compute it privately?

10 http://www.ntu.edu.sg/home/rxlu/seminars.htm Problems

11 http://www.ntu.edu.sg/home/rxlu/seminars.htm Problems The second problem is knowing when to quit, i.e., when the difference between μ and μ0 is small enough; How to privately compute this?

12 http://www.ntu.edu.sg/home/rxlu/seminars.htm Formally define the problem Let r be the number of parties, each having different attributes for the same set of entities. n is the number of the common entities. The parties wish to cluster their joint data using the k- means algorithm. Let k be the number of clusters required.

13 http://www.ntu.edu.sg/home/rxlu/seminars.htm Formally define the problem The final result of the k-means clustering algorithm is the value/position of the means of the k clusters, with each side only knowing the means corresponding to their own attributes, and the final assignment of entities to clusters

14 http://www.ntu.edu.sg/home/rxlu/seminars.htm Formally define the problem

15 http://www.ntu.edu.sg/home/rxlu/seminars.htm Privacy Preserving k-means clustering

16 http://www.ntu.edu.sg/home/rxlu/seminars.htm Privacy Preserving k-means clustering

17 http://www.ntu.edu.sg/home/rxlu/seminars.htm Algorithm: checkThreshold

18 http://www.ntu.edu.sg/home/rxlu/seminars.htm Subroutine: Securely Finding the Closest Cluster Next algorithm is used as a subroutine in the k-means clustering algorithm to privately find the cluster which is closest to the given point, i.e., which cluster should a point be assigned to.

19 http://www.ntu.edu.sg/home/rxlu/seminars.htm Subroutine: Securely Finding the Closest Cluster The problem is formally defined as follows: Consider parties, each with their own k-element vector

20 http://www.ntu.edu.sg/home/rxlu/seminars.htm Subroutine: Securely Finding the Closest Cluster

21 http://www.ntu.edu.sg/home/rxlu/seminars.htm Permutation

22 http://www.ntu.edu.sg/home/rxlu/seminars.htm Permutation

23 http://www.ntu.edu.sg/home/rxlu/seminars.htm Permutation 6. 7.

24 http://www.ntu.edu.sg/home/rxlu/seminars.htm Closest cluster: Find minimum distance cluster

25 http://www.ntu.edu.sg/home/rxlu/seminars.htm Closest cluster: Find minimum distance cluster

26 http://www.ntu.edu.sg/home/rxlu/seminars.htm Closest cluster: Find minimum distance cluster

27 http://www.ntu.edu.sg/home/rxlu/seminars.htm Closest cluster: Find minimum distance cluster

28 http://www.ntu.edu.sg/home/rxlu/seminars.htm Secure Multiparty Computation / Secure Comparison Secure two party computation was first investigated by Yao and was later generalized to multiparty computation. The seminal paper by Goldreich proves that there exists a secure solution for any functionality.

29 http://www.ntu.edu.sg/home/rxlu/seminars.htm Secure Multiparty Computation / Secure Comparison Combinatorial circuit is needed in this paper. But the author does not introduce how to implement the secure add and compare function.

30 http://www.ntu.edu.sg/home/rxlu/seminars.htm Discussion Any Question?

31 http://www.ntu.edu.sg/home/rxlu/seminars.htm Thank you Rongxing’s Homepage: http://www.ntu.edu.sg/home/rxlu/index.htm PPT available @: http://www.ntu.edu.sg/home/rxlu/seminars.htm http://www.ntu.edu.sg/home/rxlu/seminars.htm Ximeng’s Homepage: http://www.liuximeng.cn/

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