Personalized page rank Page Rank [page et al., 98 p+1=(E+(1-aw)p With a probability to randomly /lazily jump Personalized page Rank/semi-supervised learning [Haveliwala et al. TKDE 03, Jeh and Widom, WWw03 [ Zhu et al. ICML03, Zhou et al., NIPS 03 1=aq+(1-Wp With a probability to restart with a label prior Walk length: 0 Alpha:0 Distance: Inf Walk length: 0 Alpha: 0. 1 Distance: Inf Walk length:0 Alpha: 0.5 Distance: Inf Lazy random Walk PPR alph ha=0.1) PR(alpha =0.5)Personalized PageRank • PageRank [Page et al., ‘98] – 𝐩 t+𝟏 = (α𝐄 + 1 − α 𝐖)𝐩 t – With a probability to randomly/lazily jump • Personalized PageRank/semi-supervised learning – [Haveliwala et al., TKDE’03, Jeh and Widom, WWW’03] – [Zhu et al., ICML’03, Zhou et al., NIPS’03] – 𝐩 𝑡+𝟏 = α𝐪 + (1 − α)𝐖𝐩 𝑡 – With a probability to restart with a label: prior Lazy Random Walk PPR (alpha = 0.1) PPR(alpha = 0.5) 18