1. Privacy-Preserving Self- Organizing Map Shuguo Han and Wee Keong Ng Center for Advanced Information Systems, School of Computer Engineering,Nanyang Technological University, Singapore (DaWak 2007) 12009/11/02

2. Outline Introduction SOM Privacy-preserving SOM protocol Conclusion 22009/11/02

3. Introduction various data mining algorithms have been enhanced with a privacy preserving version for horizontally and/or vertically partitioned data propose a protocol for privacy-preserving self- organizing map for vertically partitioned data involving two parties. 2009/11/023

4. SOM Self-organizing map (SOM) is awidely used algorithmfor transforming data sets to a lower dimensional space to facilitate visualization To projection of the data set while preserving the topological properties of the data set. SOM is a feed-forward neural network without any hidden layer adjusting input. 2009/11/024

5. SOM Competition phase, 不斷學習使輸出與目標值能達到相同值後結束 input data X(t) = [Xi(t),X2(t),..., Xd(t)] each neuron’s weight vector (randomly initial weight ) Wj(t) = [Wj,1(t),Wj,2(t),...,Wj,d(t) ] 2009/11/025

6. SOM Euclidean distance: Winner neuron: Update weight vector 2009/11/026 Z 為學習函式, 越大表學習越快, 一般介於 0~1 之間

7. Privacy-preserving SOM protocol Protocol 1. Privacy-Preserving Self- Organizing Map , the weight vector holds two private component vector. At step t=0 where and are securely and randomly generated respectively 2009/11/027

8. Privacy-preserving SOM protocol input data X = (X1,X2,..., Xd) from feature space  The different between SOM and stand SOM is that the subprotocol are required to perform some computations securely 2009/11/028

9. Privacy-preserving SOM protocol Protocol 2. Secure Computation of Closest Cluster Protocol => to find winner neuron by applying the secure scalar product protocol [2,4]. 2009/11/029

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11. Privacy-preserving SOM protocol Correctness 2009/11/0211

12. Privacy-preserving SOM protocol Protocol 3. Secure Weight Vector Update Protocol 2009/11/0212 // adjust all neuron’s weight vector // j is how many neurons in this grid // i is how many attributes of input

13. Privacy-preserving SOM protocol Correctness 2009/11/0213

14. Privacy-preserving SOM protocol Protocol 4. Secure Detection of Termination Protocol 2009/11/0214

15. Privacy-preserving SOM protocol Correctness stop 2009/11/0215

16. Conclusion (1) to securely discover the winner neuron from data privately held by two parties (2) to securely update weight vectors of neurons (3) to securely determine the termination status of SOM. 2009/11/0216