Recommendation System and Social Network:

Influence Model and ApplicationComp4332 Presentation

Lee Man Nok (Lester)ID:20036328

Email: mnlee@ust.hk

Agenda

• Introduce two influence models• Opinion Formation Model• Social and Geographical Influences Model

• Summary• Application Difficulty• Discussion: Q&A

Opinion Formation Model

• Influence-Network (IN) • the network where context-relevant information exchange takes place

• Intrinsic-Item-Anticipation (IIA) • the original opinion taken by individuals, before start to discuss the subject

with their peers

• Influence-Dynamics (ID)• how individuals' “IIA” altered by information exchange via the connections of

the corresponding “IN”

IIA shift due to ID

• We model a possible shift in the IIA as:

• Only influences by immediate neighbors

Algorithm to simulate ID• For each individual, property is assigned randomly by

Normal Distribution. (Assume the origin opinion distribution follows Normal Distribution)

• S refers to a susceptible state and corresponds to the initial state for all nodes at t = 0.

• A refers to an attender state and corresponds to an individual with the property higher than Critical-Anticipation-Threshold

• D refers to a denier state with the property smaller than Critical-Anticipation-Threshold after an information exchange with his/her peers in the Influence-Network happened.

Model Validation: Opinion Formation Model• Use popular network types: Erdos-Renyi (ER) and Power Law (PL), and

real world recommender datasets• Estimate Trust coefficient and Critical-Anticipation-Threshold• Measure Statistics • Kullback-Leibler (KL) divergence < 5%• mean, median, maximum, and minimum of the simulated and real

attendance distributions (maximum is not exact because missing degree correlations in the simulated networks in contrast to real networks where positive degree correlations, so-called degree assortativity are common)

Social and Geographical Influences Model • Social Graph (S): the friendship relations between users, adjacency

graph• Frequentation Graph (F): the number of check-ins for users in the

different places, bipartite graph• Geographic Graph (G): the check-in probability in a place according to

its distance to another check-in follows a power law distribution, square matrix

KatzFSG Model

• Katz: find users-places relations with Katz centrality

• Use Katz-Based algorithm with Frequentation, Social and Geographic (FSG) information

• FSG: merged graph of F, S and G to provide network relation information

Model Validation: KatzFSG

• Real-world dataset of a Location-Based Social Network • Compare with benchmark method • Collaborative filtering based on F, S and G

• Composed methods: (F+S, F+G, S+G, F+S+G, KatzFS, FuseFS and KatzFS+G, etc)

• KatzFSG gained the highest recall

Summary

• Opinion Formation Model• Influence-Dynamics depends on population TRUST COEFFICIENT• Intrinsic-Item-Anticipation vs CRITICAL-ANTICIPATION-THRESHOLD

• Social and Geographical Influences Model• Merge SOCIAL, FREQUENTATION and GEOGRAPHIC graph • KATZ CENTRALITY to explain user-place relation

Application Difficulty

• Opinion Formation Model• Consider only immediate neighbors influences but ignore Katz Centrality E.g. items introduced by friends’ friends • Apply only on population level since hard to find individual trust and

threshold

• Social and Geographical Influences Model• High computation cost since extending bipartite graph with frequentation

information E.g. many times of huge matrix multiplication • Hard to update graph information

Q & A

• Reference:• Decisions@RecSys 2012: Dublin, Ireland• Recommendation systems in the scope of opinion formation: a model

(Marcel Blattner, Matus Medo)

• RSWeb@RecSys 2013: Hong Kong, China• Recommendation of shopping places based on social and geographical

influences(Romain Picot-Clémente, Cécile Bothorel)