http://www.icml-2011.org/papers/434_icmlpaper.pdf

1. Preserving Personalized
Pagerank in Subgraphs
(Andrea Vattani, Deepayan Chakrabarti, Maxim
Gurevich)
1

8. a a
b
c c

13. “Due to space
constraints, complete
proofs of our claims
will appear in the full
version of the paper.”

16. p = αr + (1 − α)A D
t −1
p
p
α
r
A
D

17. r
r[i]

18. ∞
[t]
pi (j) = α(1 − α)pi (j)
t=0 t
[t] 1
pi (j) =
d+ (kl )
k1 =i,k2 ,··· ,kt+1 =j l=1

20. G = (V, E)
S⊂V
p
G
pG[S]
˜
p G

21. ˜
min d(p , p
G G[S]
)

22. |S| = o(n/ log n)
1/2 − o(1) Ω(|S|)
S ⊂S
∗
u
S
∗
S u
∗
u

26. wG (i, j) = 1
j∈V

27. G = (V, wG )
S⊂V
H = (S ∪ SIN K, wH )

28. pi (j)
G
= pi (j)
H
∀i, j ∈ S

31. a
a
sampling a,c
b SINK
Remove b
c
c

32. ∞
wH (x, y)+ = (1 − α)wG (x, z)wG (z, y) [(1 − α)wG (z, z)]
t
t=0

33. wH (x, SIN K)+ = wG (x, z) − wH (x, y)
y=z;wG (z,y)>0

36. P H pi
H
= pi
G
WH
1
t
WH = (I − α(P ) )
H −1
1−α
O(E + |S| ) 2

38. wH (u, v) < τ
wH (u, SIN K)+ = wH (u, v), wH (u, v) = 0

42. ||P (j) − P (j)||1
H R
1−α
≤ 2τ
|S| + 1 α
P (j)
H
P (j)
R

45. v= pj (i),
G
i∈S
j∈V S
r(j) = r(j ), j, j ∈ V S
pr (i), ∀i ∈ S
G

49. SINK
Page
Rank

51. 1 1
wH (SOU RCE, l) = pj
G
(k)wG (k.l), l ∈ S
|V S| α
j,k∈V S
wH (SOU RCE, SIN K) = 1 − wH (SOU RCE, i)
i∈S

53. pr (i) = pr
G H
(i), ∀i ∈ S

 r(k), k∈S
r (k) = ρ|V S|, k = SOU RCE

0, k = SIN K