On efficient use of entropy centrality for social network analysis and community detection

Transcription

1 On efficient use of entropy centrality for social network analysis and community detection ALEXANDER G. NIKOLAEV, RAIHAN RAZIB, ASHWIN KUCHERIYA PRESENTER: PRIYA BALACHANDRAN MARY ICSI 445/660 12/1/2015 1

2 Outline About the authors Introduction Terms Centrality entropy connection Model Community structure detection Discussion and conclusion 12/1/2015 2

3 About the authors Alexander Nikolaev Assistant Professor in the Department of Industrial and Systems Engineering at University of Buffalo Ph.D., Industrial Engineering from University of Illinois at Urbana M.S., Industrial Engineering from Ohio State University M.S., Applied Physics and Mathematics from Moscow Institute of Physics and Technology Raihan Razib Ph.D., Industrial Engineering from University of Buffalo M.S., Industrial Engineering from University of Buffalo Ashwin Kucheriya M.S., Industrial Engineering from University of Buffalo 12/1/2015 3

4 Introduction Difficulty in existing centrality measures: Function of entire network, fails to identify locally central nodes Computational efficiency Motivation: Borgatti (2005): The way traffic flows in a network (route and method of propagation) Tutzauer (2007): A path based transfer flow, defines centrality as entropy of the transfer s final destination Presented approach: Identifies locally central and globally central nodes in a network Explores a specific type of flow based centrality measures Absorbing Markovian process evolving over finite time 12/1/2015 4

5 Terms Flow : transfer an object along a random route Route/ sequence: Path : Trail : Walk : Mode of propagation: Transfer: only at one place at one time Duplication: multiple copies exist 12/1/2015 5

6 Centrality entropy connection Example 1: 1-3, Level of uncertainty as a function of its origin is destination entropy. Entropy avoids assessing a node s position in the network It focuses on a node s potential to diversify flow propagation 12/1/2015 6

7 Model (Markov model) Markovian Process: A random process that changes state according to a transition rule based on the current state of the system Random walk based flow process follows the Markov property 12/1/2015 7

8 Model (The absorption probability) The proposed model assumes that each node has an absorption probability a. Example: Absorption probability, a = 0.2 for each node Transfer probability for node 1 = (1-0.2)/3 = 0.27 Auxilary nodes represent absorbing states 12/1/2015 8

9 Model (entropy centrality) Transition probability matrix Entropy centrality is given by: where t is the transfer locality 12/1/2015 9

10 Model (The effect of transfer locality adjustment) If the value of t is small the entropy centrality of a node is limited to the local neighborhood it explores in t transitions. Smaller t values reduce impact of far away nodes on the entropy centrality measure Larger t values describes the nodes network positions on a global scale 12/1/

11 Model (The effect of transfer locality adjustment) Zackary s Karate club social network A network consisting of 34 members Network was constructed using a variety of measures to estimate strength of ties 12/1/

12 Model (The effect of transfer locality adjustment) 12/1/

13 Community structure detection The community structure detection algorithm is inspired by Newman and Girvin s (2002) algorithm (computed betweeness centrality) For the proposed approach, it was observed that choosing locality values close to the diameter of the network and absorption probabilities in the range of [0.1,0.2] is convenient for global community detection 12/1/

14 Community structure detection (contd.) Zackary s karate club network 2 factions similar to the two main club communities For 2 community division, 25 iterations were run with t=5 A few outlier nodes 5, 10, 11, 12, 29 were detected 12/1/

15 Community structure detection (contd.) The proposed approach computes entropy centrality The number of centrality evaluations in each iteration is O(N) times greater than the Girvan Newman algorithm Runtime differs by an order of magnitude due to high efficiency of entropy centrality computation 12/1/

16 Community structure detection (contd.) US Division I football network Nodes represent teams, edges represent regular season games between the connected nodes Teams are divided into conferences containing 8 12 teams Inter conference games are not uniformly distributed; teams that do not belong to the same conference and that are geographically closer to each other are likely to play inter conference games 250 iterations and t=5 12/1/

17 Community structure detection (contd.) The Dolphin Network A network of 62 bottlenose dolphins in Doubtful Sound, New Zealand Iterations = 45, t = 5 Nodes 23, 49, 61 were not separated into an isolated cluster The current algorithm design cannot distinguish overlapping communities 12/1/

18 Discussion and Conclusion The proposed approach measures node centrality as the entropy of flow destination in a walk based transfer process with Markovian property. Readjusting the transfer locality can help in discovering locally central nodes, globally central nodes and granular communities in a network Entropy centrality also helps quantify a serial duplication network flow processes which can be helpful for viral marketing studies. It was observed that the current design of the community detection algorithm may not be useful for analyzing directed graphs Runtime-wise the algorithm has similar limitations as the Girvan Newman algorithm, while computational efficiency of one time entropy calculation remains very high 12/1/

19 Discussion and Conclusion (contd.) Future research can focus on entropy centrality can for finding strategic positions for a group of nodes in a network, improving computational efficiency and devise methods for detecting overlapping communities. 12/1/