Published in ACM 2014 International Conference on Knowledge Discovery and Data Mining (SIGKDD 2014) Abstract: People's interests are dynamically evolving, often affected by external factors such as trends promoted by the media or adopted by their friends. In this work, we model interest evolution through dynamic interest cascades: we consider a scenario where a user's interests may be affected by (a) the interests of other users in her social circle, as well as (b) suggestions she receives from a recommender system. In the latter case, we model user reactions through either attraction or aversion towards past suggestions. We study this interest evolution process, and the utility accrued by recommendations, as a function of the system's recommendation strategy. We show that, in steady state, the optimal strategy can be computed as the solution of a semi-definite program (SDP). Using datasets of user ratings, we provide evidence for the existence of aversion and attraction in real-life data, and show that our optimal strategy can lead to significantly improved recommendations over systems that ignore aversion and attraction.

1. Optimal Recommendationsunder Attraction, Aversion andSocial Influence
Wei Lu (UBC)
StratisIoannidis (Technicolor)
SmritiBhagat(Technicolor)
LaksV.S. Lakshmanan(UBC)

2. Users Engaging with Recommender Systems
Attraction
Aversion 
Influence…
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3. Challenges
•Making recommendations & modeling user interest are intertwined
•Since recommendations play a role in changing user interest
•Recommendations should be made in a global manner
•Since social influence effect may trigger interest cascade
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4. Main Contributions
•An interest evolution model with attraction, aversion, and social influence
•Use Semi-Definite Programming (SDP)to provide near-optimal recommendations
•Outperform matrix factorization recommendations significantly
•Show from real data that attraction and aversion phenomena do exist
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5. Interest Evolution Model
Inherent interests
Social Influence
Attracted to
recommendations
Aversive to
recommendations
At any time t, user
selects social behavior
with probability and
personal behavior with
probability
Personal Social
1 − 훽 훽
훼푖
훾푖
훿푖
훼푖 + 훾푖 + 훿푖 = 1
푢푠푒푟 푖
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6. Dynamic system of interest evolution
푣푖(푡)
푢푖(푡)
Utility = <푢푖푡,푣푖푡>
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7. Recommendation Problem
What should the recommender’s strategy be, taking into account the joint effect of these factors so as to maximize users’ utility
Recommendations to different users can’t be made in isolation
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8. The evolution process is a Markov Chain
It converges to a steady state
Interest Evolution: Steady State
social
influence
matrix
expected
inherent
profile
matrix
expected
item profile
matrix
prob. of
attraction,
aversion
matrices
prob. of
inherent
interest
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Expected user
profile matrix
(1 row per user)

9. Recommendation Objective
Multiply with
Social welfare: Expected total utility over all users
Global Recommendation Problem
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10. • Variables to solve:
• Quadratically-Constrained Quadratic Optimization
Problem (QCQP)
• Not convex, in general 
• Our solution strategy: Relaxation
Global Recommendation
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11. •Global Recommendation: Semi-Definite Program (SDP) with a rank-1 constraint
•Relaxation: Drop rank-1 constraint SDP only
•Solve the SDP relaxation
•IF (rank-1): done!
•ELSE: there exists a randomized algorithm giving a 4/7 approximation
•Observation: In our experiments, all solution matrices are rank-1, hence optimal 
SDP Relaxation
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12. Datasets
Objectives
•Find evidence of attraction and aversion from data
•Evaluate SDP solutions
•Baseline (MF-Local): Recommend based on inherent profiles only
Experiments
Flixster
FilmTipSet
MovieLens
#users
4.6K
0.4K
8.9K
#items
25K
4.3K
3.8K
#ratings
1.8M
118K
1.3M
#edges
44K
N/A
N/A
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13. Heavy tail: existence of strongly attracted and aversive users
Finding evidence of attraction & aversion
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MovieLens

14. Incorporating evolution probabilities into Matrix Factorization leads to better predictions
Finding evidence of attraction & aversion
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15. •Synthetic SN: Forest-Fire, Kronecker, Power-law
•Y-axis: 푆퐷푃푠표푙푢푡푖표푛−푏푎푠푒푙푖푛푒 푏푎푠푒푙푖푛푒 ∗100%
Varying Social Effect $beta$ (Synthetic)
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16. Social Welfare on Real Data
SDP outperforms baseline on three real-world datasets, in terms of Social Welfare
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17. •Study the optimality of SDP relaxation in theory
•Improve scalability of SDP-based algorithms by exploiting special structural features
•Study other factors for interest evolution
Future Work
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18. Thank you!