Efficient Respondents Selection for Biased Survey using Online Social Networks

Transcription

1 Efficient Respondents Selection for Biased Survey using Online Social Networks Donghyun Kim 1, Jiaofei Zhong 2, Minhyuk Lee 1, Deying Li 3, Alade O. Tokuta 1 1 North Carolina Central University, Durham, NC, USA 2 California State University, East Bay, Hayward, CA, USA 3 Renmin University of China, Beijing, China Presenter: Donghyun (David) Kim Presented at the 2nd Workshop on Computational Social Networks (CSoNet 2014)

2 Agenda 1. Motivation 2. Preliminaries 3. Problem Statement 4. Algorithm 5. Experiment 6. Conclusion

3 1. Motivation

4 Motivation Growing popularity of social networking web sites such as FACEBOOK, Google+, Twitter, etc Online social networks are getting lots of attentions Useful applications of online social network such as online advertising, information propagation, online survey, etc This work investigates the potential of online social network for survey

5 Motivation cont U.S spent more than $1.8 billion for all survey researches in 2012 Online survey is useful to data collection for marketing or political decision making Hard to find right sample group of respondents in online survey The respondent should represent for each community or group

6 Motivation cont The person who belongs to major group in community, activist and has many friend (e.g. B) The person who belongs to minor group in community, has less friend like (e.g. A)

7 Motivation cont

8 Motivation cont Sometimes the minor opinion is more important than major one

9 Motivation cont Representative group in a social network graph frequently, modeled as a dominating set problem Minimum dominating set good choice of a representative group mostly a subset of majority not suitable for our purpose Needs a new dominating set

10 2. Preliminaries

11 Preliminaries Notations G ( V, E) : represents an online social network graph V V(G) : node set E E(G) : edge set V : number of nodes in V G[D] : subgraph of G induced by D, for any subset Nv, V( G) : set of nodes in V neighboring to v in G, for each node v V D V

12 Preliminaries cont Definition 1 (DS) Given a graph G, a subset D V if for eachnode u V \ D, v is adominating set (DS) of D such that(v,u) E G

13 Preliminaries cont Definition 2 (MDSP) Given a graph G, the goal of the minimum dominating set problem (MDSP) is to find a minimum size DS of G

14 Preliminaries cont Definition 3 (Inverse k core) Given a graph G, a subset such that 0 inverse k k - core in Δ, G if D V is, and a where Δ is the degree of for each v D, N v, D positive integer G, D (G) k is an k no more than k neighbors in D

15 3. Problem Statement

16 Problem Statement Definition 4 (IkCDS) Given a graph G, a subset D V is, and a positive integer k D is an inverse k - core dominating set (IkCDS) of G if(a) D is a DS of G and (b)for each Definition 5 (MIkCDSP) v D, N v, D (G) Given a graph G and a positive integer k the goal of the minimum inverse k - core dominating set problem ( MIkCDSP)is to find a minimum size IkCDS of G. k

17 Problem Statement cont MIkCDSP is NP-hard A special case of minimum dominating set problem, which is proven to be NP-hard. As a MIkCDSP result, with MIkCDSP k is n is NP-hard. equivalent to the Our Approach: Greedy Approximation

18 4. Algorithm

19 Algorithm

20 Example G = (V,E), 1 v1 v 2 v3 v 4 v5 v6

21 Example cont v v v3 0 0 v 4 0 v5 0 v6 D Node ni { } v1 v 2 v3 v 4 v5 v X0 { v1, v2, v3, v4, v5, v6}

22 Example cont v v v3 0 0 v 4 0 v5 0 v6 v and v The Candidate are 2 5

23 Example cont v 2 Let s select, hence D { v2} 0 v 4 v1 2 1 v v5 v6 v3 1 Node ni v1 v 2 3 v v 4 v5 v X 0 { v12, v2 4, v3 5, } v4, v5, v6} X1 { v1, v3, v6}

24 Example cont Since X0 Select node We can select v1 D {, 2} v1 v 0 v 4 v1 2 1 v v5 v6 v3 1 Node ni v1 v 2 3 X 0 { v2, 4} v4, v5} X 1 { v 1, v 23, v3, 6} v5, v6} v v 4 v5 v

25 Example cont Since X0 Select node We can select D { v1, v2, v4} v1 0 v 4 v v v5 v6 v3 1 Node ni v1 v 2 3 v v 4 v5 v X 0 { v 4} X 1 { v 1, v 2, v 3, v 54, v 6 } X2 { v5} Now X0 And the result is D { v1, v2, v4}

26 Performance Analysis Proof idea: the algorithm produces a DS D such that D is also a feasible solution of MIkCDSP.

27 5. Experiment

28 Experiment Case Study #1 The Jazz Musician Network The Jazz Musician Network is a collaboration network of jazz musicians P.M Geiser and L.Danon, Community Substructure In Jazz, Jazz musicians that performed between 1912 and 1940, with most of famous in the 1920's.

29 Experiment cont Cytospace visualization tools

30 Experiment cont Compare average degree among all nodes, MIkCDSP vs. Minimum Dominating Set

31 Experiment cont Compare average degree between MIkCDSP and Minimum Dominating Set D 29% 21% 65% 50% 13% 20%

32 Experiment cont Compare average degree with various k value

33 Experiment cont Visualized Result

34 Experiment cont The hard problem is to pick a right sample on online survey We focus to pick a sample with minority opinion, which is have less friends To the best of our knowledge, this is the first attempt to use online social network to improve the result of online survey The result is showing that our algorithm can select nodes which representative minority opinion

35 6. Conclusion

36 Thank You Question?