1. Type Similarity Measure and Its Application to Entity Recommendation
Zheng Liang

2. Scenario
80个类型
Scientist
English Physicists
English Mathematicians
Christian Mystics
. . .
Type
Jewish American Scientists
Deists
Nobel Laureates In Physics
Scientist
. . .
105个类型
Italian Physicists
Italian Astrologers
Italian Astronomers
Scientist
. . .
51 个类型
Deists：自然神论者
Christian Mystics：基督教神秘主义
Italian Astrologers
Christian Astrologers
Italian Astronomers
意大利占星家
基督教占星家
意大利天文学家
When viewing a entity, our goal is to recommend the most similar entities based on type similarity.

3. Type Similarity Measure
0 s(txi, tyj ) 1
i wxi =1
j wyj =1
1  i  m
1  j  n
tx1
txi
txm .
ty1
tyj
tyn X Y
wx1
wxi
wxm
wy1
wyj
wyn
s(txi, tyj )
S(Albert_Einstein, Isaac_Newton)= SetSim(X , Y)
wxi is the weight of txi 直观解释：即为 txi在类型集合X中的重要度
0  wxi  1

4. Type Similarity Measure Based on Network Flow
vx1
vxi
vxm vs vt .
vy1
vyj
vyn X Y
Cost
(1, b(vx1 , vy1 ) )
Capacity
(wy1, 0)
(wx1, 0)
(wxi, 0)
(1, b(vxi , vyj ) )
(wyi, 0)
Vs:人工源
Vt:人工汇
(wxm, 0)
(1, b (vxm , vyn ) )
(wyn, 0)
b (vxi , vyj ) = [bij]=1-s(txi, tyj )
1  i  m ; 1  j  n ; 0  bij  1

5. Problem is formalized as follows:
We turn to the problem of finding a maximum flow of minimum cost. (Edmonds, 1972)
Given a network N={V, A, C, B} (V= X  Y  {vs , vt })
Let the cost of a flow f be  (vxi , vyj )A bij fij and let its value be f(vs , vt).
We find a flow which is maximum, but has the lowest cost among the maximums. 

6. b( f ) =  (vxi , vyj )A bij fij
=  (1- sij ) fij
=  fij -  sij fij (最大流,  fij 1）
1-  sij fij
对于两个相同的集合， b( f ) =0
对于两个完全不相同的集合， b( f ) =1 （ sij=0）
b( f )越小， sij fij 越大，表示两个集合相似度越高; 反之，…
0  b( f )  1

7. Type Weight Measure 1: Informational content (Resnik 1992, 1995).
IC(ti )= - logP(ti )=- log(freq(ti )/N)
一元模型，实质就是IDF
wxi =IC(txi ) /  IC(txi ) txi  X
0  wxi  1

8. Type Weight Measure 2: Conditional Entropy 多元模型，考虑上下文
H(txi|Txi) = -  P(X) log P(txi |Txi)
X={ tx1, tx2,…, txm}; txi  X; Txi =X – { txi };
wxi =H(txi|Txi) /  H(txi|Txi) ( 0  wxi  1 )