HubsAuthorities Hubs Authorities Hubsauthorities Hubs Authorities The HITS
Hubs&Authorities Hubs Authorities
Hubs&authorities Hubs Authorities
The HITS algorithm 2 a weight-propagation step sampling stepで集めたサイトを隣接行列に しhubやAuthorityにweightをつけていく n hubやAuthorityを見つける n
Hubs&Authorities 高い 高い Hubs weight Authorities weight 低い 低い
Updated of hubs and authority Non-negative authority weight : Xp Non-negative hub weight : Yp (each page p∈V) Xp = Σ Yq ←authority weight increased q→p Yp = Σ Xq ← hub weight increased q→p
Update hubs and authority A : adjacency matrix (隣接行列) x = (x 1, x 2, …, x. N) y = (y 1, y 2, …, y. N) T x = A y ←update rule y = Ax ←update rule T T T x ← A y← A Ax = (A A)x T y ← Ax← AA y = (AA )y T
Authority Weightの正規化 Authority Weight が無意味に増大しないように 毎回の正規化(Hub Weightについても同様) → Authority weight a T → Initialize a = (1, … 1) For I = 0, 1, 2, … → T → a i+1 = A A a i → → Normalize a s. t. || a i+1||=1
-Page. Ranki=4 9/16 分配された和を 均等に配分 A=5/4 11/16 9/16 B=11/16 1/2 C=17/16 11/16
-Page. Rank. A 0 B 0 = C 0 A B Ai+1 1/2 0 1/2 Ai Bi+1 = 0 0 1/2 Bi Ci+1 1/2 1 0 Ci C lim i→∞ Ai 6/5 Bi = 3/5 Ci 6/5 … 1 1 1 5/4 11/16 17/16 9/8 1/2 11/8 5/4 3/4 1 1 1/2 3/2 1 1 1
-Page. Rank. Spider Trap A B Ai+1 1/2 Bi+1 = 0 Ci+1 1/2 C lim i→∞ Ai 0 Bi = 3 Ci 0 … 1/2 35/16 5/8 2 3/8 0 1/2 Ai 1 1/2 Bi 0 0 0 Ci 3/4 7/4 1/2 1 3/2 1 1 1
-Page. Rank. Dead End A B Ai+1 1/2 Bi+1 = 0 Ci+1 1/2 C lim i→∞ Ai 0 Bi = 0 Ci 0 … 1/2 3/16 5/8 1/4 3/8 0 1/2 Ai 0 1/2 Bi 0 0 Ci 3/4 1/2 1 1 1
-Page. Rank. Ai+1 1/2 0 1/2 Bi+1 = (1 -tax) 0 1 1/2 Ci+1 1/2 0 0 Spider Trapの回避 重要度の 1部を 税金として徴収 sample Ai 1 Bi +tax 1 Ci 1 Dead End 効果の回避 税金の再配分 tax = 0. 2 lim i→∞ Ai 7/11 Bi = 21/11 Ci 5/11 … 1 1 1
- Slides: 31