マルチエージェン卜型拡張SIRモデルを用いた情報拡散シミュレーションの評価

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(1)Vol.2014-ICS-173 No.7 2014/1/23. IPSJ SIG Technical Report. SIR. 1,a). 3. 2. 2 1. 2011. 3. 11. 4. 5. 6. 1,b). Twitter. SIR. SIR. Twitter. 1.. [2] Twitter Twitter [1]. Twitter Twitter [3] Twitter. 2011. 3. 11 Twitter. 1. The University of Electro-Communications. Twitter. 2. The University of Tokyo 3. Osaka University 4. Keio University 5. Wakayama University 6. a) b). National Institute of Advanced Industrial Science and Technology [email protected] [email protected]. ⓒ 2014 Information Processing Society of Japan. Twitter. 1.

(2) Vol.2014-ICS-173 No.7 2014/1/23. IPSJ SIG Technical Report. SIR Twitter 2. 3. 3.1 3.1.1 SIR SIR SIR. 2. Twitter. Kermack. [8][9] SIR. SIR S Suseptible. I Infectious R Recovered. Twitte. S. 3. I. ρ(S→I) I. I. ρ(I→R) R. [3]. S 1. I. R. t. I. I(t) R. S. S(t). R(t). ⎧ dS(t) ⎪ = −ρ(S→I) I(t)S(t) ⎪ ⎪ ⎨ dt. [4]. dI(t). =ρ. (1). I(t)S(t) − ρ(I→R) I(t). (S→I) ⎪ dt ⎪ ⎪ ⎩ dR(t) = ρ (I→R) I(t). dt. Twitter. N. N = S(t) +. I(t) + R(t) 3.1.2. [3] SIR. [5] Sakaki. Twitte. R R S [6]. R. I. 3. Twitter Twitter. Stefan. Twitter. 3. • S [7] Twitter. ⓒ 2014 Information Processing Society of Japan. • Iget • I. 2.

(3) Vol.2014-ICS-173 No.7 2014/1/23. IPSJ SIG Technical Report. • Rget. I. • R. ρ(Iget →I). ρ(S→R) ρ(Iget →R) ρ(I→R) ρ(Rget →R) Rget. ⎧ F dS(t) ⎪ ⎪ = − I(t)S(t) ⎪ ⎪ dt N ⎪ ⎪ dIget (t) F ⎪ ⎪ = (1 − ρ(S→I) ) I(t)S(t) ⎪ ⎪ dt N ⎪ ⎪ F ⎨ −ρ(Iget →I) Iget (t)I(t) N ⎪ ⎪ ⎪ ⎪ ⎪ dI(t) F ⎪ ⎪ = ρ(S→I) I(t)S(t) ⎪ ⎪ ⎪ dt N ⎪ ⎪ F ⎩ +ρ Iget (t)I(t) (Iget →I). S. Iget. I. (3) (2) 3.2 [3] S. I. I. R. N. ⎧ F F dS(t) ⎪ ⎪ = − I(t)S(t) − R(t)S(t) ⎪ ⎪ dt N N ⎪ ⎪ dIget (t) F ⎪ ⎪ = (1 − ρ(S→I) ) I(t)S(t) ⎪ ⎪ dt N ⎪ ⎪ F ⎪ ⎪ −ρ(Iget →I) Iget (t)I(t) ⎪ ⎪ N ⎪ ⎪ F ⎪ ⎪ − Iget (t)R(t) ⎪ ⎪ N ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ dI(t) F ⎪ ⎪ = ρ(S→I) I(t)S(t) ⎪ ⎪ dt N ⎪ ⎪ F ⎪ ⎪ +ρ(Iget →I) Iget (t)I(t) ⎪ ⎪ N ⎪ ⎪ F ⎪ ⎪ − I(t)R(t) ⎪ ⎪ N ⎪ ⎪ ⎨. dRget (t) F ⎪ = (1 − ρ(S→R) ) R(t)S(t) ⎪ ⎪ dt N ⎪ ⎪ F ⎪ ⎪ +(1 − ρ(Iget →R) ) Iget (t)R(t) ⎪ ⎪ N ⎪ ⎪ ⎪ F ⎪ ⎪ +(1 − ρ(I→R) ) I(t)R(t) ⎪ ⎪ N ⎪ ⎪ F ⎪ ⎪ −ρ(Rget →R) Rget (t)R(t) ⎪ ⎪ N ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ dR(t) F ⎪ ⎪ = ρ(S→R) R(t)S(t) ⎪ ⎪ dt N ⎪ ⎪ F ⎪ ⎪ +ρ(Iget →R) Iget (t)R(t) ⎪ ⎪ N ⎪ ⎪ F ⎪ ⎪ +ρ(I→R) I(t)R(t) ⎪ ⎪ ⎪ N ⎪ ⎪ F ⎩ +ρ(R →R) Rget (t)R(t) get. R. (3). N. N. 4.. F. SIR. SNS SIR. S SIR. Twitter 4.1 I. t 1 F S(t) N F Iget (t) N. [10]. S Iget (2) ρ(S→I) S. ⓒ 2014 Information Processing Society of Japan. 3.

(4) Vol.2014-ICS-173 No.7 2014/1/23. IPSJ SIG Technical Report. αn. β. t. λ FG 1 β. αn. 4. β. ”M oTβ t” β. ”I” β. 1. ”Iget” ”M oTβ t” ”R”. ”Rget”. :a. ”R”. ’Iget”. a. ’I”. 4. PageRank. ”Rget”. 1. :i i. [3] :s. 3. 2. s. 4.2. 5. MoT Motivation of Tweet MoT 4. M oTβt = M oTβt−1 e. −λ(F G−t). + ikβ sβ. %. 5.1 .. an. (4). n. β. ⓒ 2014 Information Processing Society of Japan. 78. 4.

(5) Vol.2014-ICS-173 No.7 2014/1/23. IPSJ SIG Technical Report. 1 2. 26 S. I. R. 1. 3 26. 2. t=1 1. I. 3 t = 11. 1. R 4 t = 25. 0 2 50,000 =340. 78. =10 =0.5. X = {x1 , x2 , . . . , xn }. Y = {y1 , y2 , . . . , yn }. 2. =15.0 =0.05. d. =0.5 3. d = |x′1 − y1′ | + |x′2 − y2′ | + . . . + |x′n − yn′ | n % |x′i − yi′ | =. i. 0 1. s. (5). 0 1. a. PageRank. i=1. 2 [3]. 6.. 1. 2 3. 6.1 6.2 100 6.2.1. Twitter. 2. 2. ”S”. ”R” ”I”. ”Iget”. ”Rget”. 4. 3.47. 36.25. 15.84 5.18. 2 .. [4]. 3. ⓒ 2014 Information Processing Society of Japan. 5.

(6) Vol.2014-ICS-173 No.7 2014/1/23. IPSJ SIG Technical Report. 7.. 2. Twitter. SIR. [3] SIR. [3]. 3. [4]. 6. 4. 2.79 [1]. 6.2.2. 23 , http://www.soumu.go.jp/johotsusintokei/whitepaper/ ja/h23/pdf/index.html, 2011. [2] :. 1 .. 100. [3]. 4. Twitter. 3.47. ⓒ 2014 Information Processing Society of Japan. NHK 61(7), 16-23, 2011. 2012. 6.

(7) Vol.2014-ICS-173 No.7 2014/1/23. IPSJ SIG Technical Report. [4] Twitter , vol. 112, no. 346, DE2012-29, pp. 87-92, 2012 [5]. [6]. [7]. [8]. [9]. Vol.95 No.3 pp.219-223 2012 Takeshi Sakaki Makoto Okazaki Yutaka Matsuo ”Earthquake Shakes Twitter Users:Real-time Event Detection by Social Sensors” WWW’10 Proceedings of the 19th international conference on World wide web Pages 851-860 2010 Stefan Stieglitz Linh Dang-Xuan ”Political Communication and Influence through Microblogging-An Empirical Analysis of Sentiment in Twitter Messages and Retweet Behavior” 45th Hawaii International Conference on System Sciences 2012 W. O. Kermack, A. G. McKendrick A Contribution to the Mathematical Theory of Epidemics, Proceedings of the Royal Society 115A, pp.700-721, 1927. , , , 2005.. [10] .SITE, 103(78), pp.13-18, 2003. ⓒ 2014 Information Processing Society of Japan. 7.

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