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Introduction of network analysis with Google Colaboratory -- Diffusion in Networks
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Introduction of network analysis with Google Colaboratory -- Diffusion in Networks
1.
第14回AIツール入門講座 「Google Colaboratoryによる ネットワーク分析入門」 6. ネットワーク上の情報伝搬 SIRなどの感染モデルや、そのシミュレーションについて説明し ます。
2.
情報伝搬・病気感染のモデル化 • SNSでの口コミの情報伝搬をモデル化→限られた広告予算で、 なるべく多くの人に情報を拡散する • 病気が感染するプロセスをモデル化→爆発的感染を防ぐ •
伝搬過程のモデルと、ネットワーク構造のモデルの両方を考え る必要がある
3.
SI model • 2つの状態 •
S: susceptible (感染していない) • I : infected (感染している) • 全員が他の全員と接すると仮定 S I t x
4.
SI modelの例 • b(単位時間に接する人数)を変化させ、感染割合を表示
5.
SIR model • 3つの状態 •
S: susceptible (感染していない) • I : infected (感染している) • R: recovered (回復した) S I R 𝛾𝛿𝜏 1-𝛾𝛿𝜏 S R I
6.
NDlibによるシミュレーション • ネットワーク上の感染シミュレーションを行うライブラリ • https://ndlib.readthedocs.io/en/latest/index.html •
シミュレーションにおける入力 • 対象とするネットワーク • 𝑥0 (時刻t = 0 における状態Iの割合) • 𝛽(状態Sから状態Iに変化する確率) • 𝛾(状態Iから状態Rに変化する確率) • シミュレーションにおける出力 • 状態Sの割合(𝑠)、状態Iの割合(𝑥)、状態Rの割合(𝑟)の時間変化 • 状態Sの割合(𝑠)、状態Iの割合(𝑥)、状態Rの割合(𝑟)の各時刻での増減量
7.
NDlibによるシミュレーション例 • https://ndlib.readthedocs.io/en/latest/tutorial.htmlを参照 Jupyterでは!pip Jupyterで必要 Ndlibをimport