Distributed Classification in Peer-to-Peer Networks

1. Distributed Classification in Peer-to-Peer Networks Ping Luo, Hui Xiong, Kevin Lü, Zhongzhi Shi Institute of Computing Technology, Chinese Academy of Sciences Presentation by: Satya Bulusu

2. Overview • Introduction • Building Local Classifiers • Distributed Plurality Voting • Experimental Results • Related Works • Summary

3. Research Motivation • Widespread use of P2P networks and sensor networks • Data to be analyzed are distributed on nodes of these large-scale dynamic networks • Traditional distributed data mining algorithms must be extended to fit this new environment • Motivating Examples • - P2P anti-spam networks • - Automatic organization of web documents in P2P • environments • A distributed classification algorithm is critical in these applications.

4. Research Motivation contd… • New Challenges - highly decentralized peers, do not have the notion of clients and servers - including hundreds or thousands of nodes, impossible global synchronization - frequent topology changes caused by frequent failure and recovery of peers • Algorithm Requirements - scalability, decentralized in-network processing - communication efficient, local synchronism - fault-tolerance

5. Problem Formulation • Given: • A connected topology graph • Each peer owns its local training data for classification • Local neighborhood change is informed to each peer real-timely • Find: • Classification paradigm in this setting • Including how to train and use a global classifier • Objective: • Scalability, communication-efficient, decentralized in-network processing, fault-tolerance • Constraints: • Each peer can only communicate with its immediate neighbors • The network topology changes dynamically

6. Contributions from this paper • An algorithm to build an ensemble classifier for distributed classification in P2P networks by plurality votingon all the local classifiers • Adapt the training paradigm of pasting bites for building local classifiers • An algorithm of (restrictive) Distributed Plurality Voting (DPV)to combine the decisions of local classifiers • Correctness • Optimality • Extensive Experimental Evaluation • Communication overhead and convergence time of DPV • Accuracy comparison with centralized classification

7. Overview • Introduction • Building Local Classifiers • Distributed Plurality Voting • Experimental Results • Related Works • Summary

8. Building Local Classifiers • Pasting Bites by Breiman [JML’99] • Generating small bites of the data by importance sampling based on the out-of-bag error of classifiers built so far • Stopping criteria: difference of errors between two successive iteration is below a threshold • Voting uniformly all the classifiers • The more data on a local node, the more classifiers generated on it, the more votes it owns.

9. Overview • Introduction • Building Local Classifiers • Distributed Plurality Voting • Experimental Results • Related Works • Summary

10. Problem Formulation Of DPV • Given: • A group of peers in a graph would like to agree on one of options. • Each peer conveys its preference by initializing a voting vector , where is the number of votes on the i-th option. • Local neighborhood change is informed to each peer real-timely • Find: • The option with the largest number of votes over all peers: • Objective: • Scalability, communication-efficient, decentralized in-network processing, fault-tolerance • Constraints: • Each peer can only communicate with its immediate neighbors • The network topology changes dynamically

11. An Example Of DPV The third option is the answer.

12. Comparison Between DPV and Distributed Majority Voting (DMV, by Wolff et al. [TSMC’04]) • DMV Given: • A group of peers in a graph • Each peer conveys its preference by kainitializing a 2-tuple , where stands for the number of the votes for certain option and stands for the number of the total vote on this peer. • The majority ratio • DMV Find: • Check whether the voting proportion of the specified option is above : • DMV Converted to DPV: • Replacing the 2-tuple on each peer with the voting vector

13. Comparison Between DPV and DMV contd… • DPV vs. DMV • DPV is a multi-values function while DMV is a binary predicate. • DMV can be solved by converting it to DPV. • However, DMV can only solve 2-option DPV problems. For a d-option DPV problem, pairwise comparisons among all d options must be performed by DMV for times (Multiple Choice Voting [TSMC’04]). • DPV finds the maximally supported option directly, and thus saves a lot of communication overhead and the time for convergence. • DPV is the general form of DMV

14. Challenges for DPV • No central server to add all voting vectors, Only communication between immediate neighbors • Dynamic change of not only the network topology but also the local voting vectors • Supporting not only one-shot query, but also continuous monitor the current voting result according to the latest network status

15. DPV Protocol Overview • Assumption: • it includes a mechanism to maintain an un-directional spanning tree for the dynamic P2P network. The protocol performs on this tree (duplicate insensitive). • A node is informed of changes in the status of adjacent nodes. • Protocol Overview • Each node performs the same algorithm independently • Specify how nodes initialize and react under different situations: a message received, neighboring node detached or joined, the local voting vector changed • When the node status changes under the above situation, the node notifies this change to the other neighbors only if the condition for sending messagessatisfies. • To guarantee that each node in the network converges toward the correct plurality

16. The Condition for Sending Messages contd… Message Sent (5,2,1)+(2,0,0)=(7,2,1) 7-2=5 7-1=6 (8,6,1)+(2,0,0)=(10,6,1) 10-4=4 10-1=9 4<5 9>6 The differences between the votes of maximally voted option and any other option decrease.

17. The Condition for Sending Messages No Message Sent (5,2,1)+(2,0,0)=(7,2,1) 7-2=5 7-1=6 (8,4,1)+(2,0,0)=(10,4,1) 10-4=6 10-1=9 6>5 9>6 The differences between the votes of maximally voted option and all other options do not decrease.

18. The Correctness of DPV Protocol All the nodes converge to the same result. The difference between the actual votes of maximally voted option and any other option is not smaller than what the protocol have sent. Then, all the nodes converge to the right result.

19. The Optimality of DPV Protocol C1is more restrictive than C2, iff, for any input case if C1 is true then C2is true. C1 is strictly more restrictive than C2, iff, C1 is more restrictive than C2 and there at least exists an input case such that C1is false and C2 is true. isthe most restrictive condition for sending messages to keep the correctness of the DPV protocol. It is the condition, which is the most difficult to satisfy. In this sense, it guarantees the optimality in communication overhead.

20. The Extension of DPV Protocol Restrictive Distributed Plurality Voting: output the maximally voted option whose proportion to all the votes is above a user-specified threshold. It can be used in a classification ensemble in a restrictive manner by leaving out some uncertain instances. The new condition for sending messages is based on the spirit of .

21. Overview • Introduction • Building Local Classifiers • Distributed Plurality Voting • Experimental Results • Related Works • Summary

22. Accuracy of P2P Classification Data: covtype (581012*54, 7 classes) from the UCI database, distributed onto 500 nodes

23. The Performance of DPV Protocol • Experimental Parameters • Difference types of network topology: Power-law Graph, Random Graph, Grid • Number of nodes: 500, 1000, 2000, 4000, 8000, 16000 • 7-option DPV problems • Experimental Metrics • The average communication overhead for each node • The convergence time of the protocol for one-shot query

24. The Performance of DPV Protocol contd… • DPV0vs. RANK (Multiple Choice Voting) • 500 nodes • Averaging 2000 instances of 7-option plurality voting problems a and b are the largest and second largest options, respectively.

25. The Performance of DPV Protocol contd… • The Scalability of DPV0 • Different number of nodes vs. communication overhead of each node Ping Luo KDD 07

26. The Performance of DPV Protocol (4) • The Local Optimality of DPV0 • Communication overhead and convergence time under different conditions for sending messages Ping Luo KDD 07

27. Overview • Introduction • Building Local Classifiers • Distributed Plurality Voting • Experimental Results • Related Works • Summary

28. Related Work - Ensemble Classifiers • Model Combination: (weighted) voting, meta-learning • For Centralized Data • applying different learning algorithms with heterogeneous models • applying a single learning algorithm to different versions of the data • Bagging:random sampling with replacement • Boosting: re-weighting of the mis-classified training examples • Pasting Bites: generating small bites of the data by importance sampling based on the quality of classifiers built so far • For Distributed Data • distributed boosting by Lazarevic et al. [sigkdd’01] • distributed approach to pasting small bites by Chawla et al.[JMLR’04], which uniformly votes hundreds or thousands of classifiers built on all distributed data sites

29. Related Work - P2P Data Mining • Primitive Aggregates • Average • Count, Sum • Max, Min • Distributed Majority Voting by Wolff et al. [TSMC’04] • P2P Data Mining Algorithms • P2P Association Rule Mining by Wolff et al. [TSMC’04] • P2P K-means clustering by Datta et al. [SDM’06] • P2P L2 threshold monitor by Wolff et al. [SDM’06] • Outlier detection in wireless sensor networks by Branch et al. [ICDCS’06] • A classification framework in P2P networks by Siersdorfer et al. [ECIR’06] • Limitations: local classifiers’ propagations, experiments on 16 peers, only focusing on the accuracy issue, without involving any dynamism of P2P networks.

30. Overview • Introduction • Building Local Classifiers • Distributed Plurality Voting • Experimental Results • Related Works • Summary

31. Summary • Proposed an ensemble paradigm for distributed classification in P2P networks • Formalized a generalized Distributed Plurality Voting (DPV) protocol for P2P networks • The property of DPV0 • supporting both one-shot query and continuous monitor • theoretical local optimality in terms of communication overhead • outperforms alternative approaches • scale up to large networks

32. Acknowledgement Q. & A.