1. SimRank : A Measure of Structural-Context Similarity
Advisor : Dr. Hsu
Graduate : Sheng-Hsuan Wang
Author : Glen Jeh
Jennifer Widom

2. Outline Motivation Objective Introduction Basic Graph Model SimRank
Random Surfer-Pairs Model
Future Work
Personal opinion

3. Motivation
The problem of measuring “similarity” of objects arises in many applications.

4. Objective
The approach, applicable in any domain with object-to-object relationships.
Two objects are similar if they are related to similar objects.

5. Introduction

6. Basic Graph Model
We model objects and relationships as a directed graph G=(V,E).
For a node v in a graph, we denote by I(v) and O(v) the set of in-neighbors and out-neighbors.

7. SimRank Basic SimRank Equation
If a=b then s(a,b) is defined to be 1. Otherwise,
Where C is a constant between 0 and 1.
Set s(a,b)=0 when 　　　 or 　　　 .
(1)

8. SimRank Bipartite SimRank Two types of objects.
Example : Shopping graph G.

9. SimRank

10. SimRank Let s(A,B) denote the similarity between persons A and B, for
Let s(c,d) denote the similarity between items c and d, for
(2)
(3)

11. SimRank Computing SimRank－Naive Method is a lower bound on the .
To compute 　　　 from
(if )
(4)
For , and for

12. SimRank The space required is simply to store the results .
The time required is
K:The number of iterations
:The average of |I(a)||I(b)| over all node pairs (a,b).

13. SimRank Computing SimRank－Pruning
set the similarity between two nodes far apart to be 0.
consider node-pairs only for nodes which are near each other.

14. SimRank Radius r, and average such neighbors for a node, then there
will be node-pairs.
The time and space complexities become and respectively.

15. Random Surfer-Pair Model
Expected Distance
Let H be any strongly connected graph.
Let u,v be any two nodes in H.
We define the expected distance d(u,v) from u to v as
(5)

16. Random Surfer-Pair Model
Expected Meeting Distance(EMD).
(6)

17. Random Surfer-Pair Model
Expected-f Meeting Distance
To circumvent the “infinite EMD” problem.
To map all distances to a finite interval.
Exponential function ,where
is a constant.
(7)

18. Random Surfer-Pair Model
Equivalence to SimRank

19. Random Surfer-Pair Model
Theorem.
The SimRank score, with parameter C, between two nodes is their expected-f meeting distance traveling back-edges,
for

20. Future Work Future Work. Divided and conquer and merge.
Divided a corpus into chunks…
Ternary(or more) relationships.

21. Personal Opinion
We believe that the intuition behind SimRank can be used in many domains which based on objects to objects.