1. Maximizing Product Adoption in Social Networks
Smriti Bhagat, Amit Goyal, Laks Lakshmanan
(Paper appeared in WSDM 2012)

2. Viral Marketing
Objective: Given a social network, find a small number of individuals (seed set), who when convinced about a product will influence others by word-of-mouth, leading to a large number of adoptions of the product
Studied as the Influence Maximization Problem§
0.9
0.2
Linear Threshold and Independent Cascades are two popular diffusion models
Node: User in a social network
(green – seed set)
Edge: Friendship among users
Edge Weight: Influence probability
§D. Kempe, J. Kleinberg, and E ́. Tardos. Maximizing the spread of influence through a social network. In KDD’03.

3. Previous Work Two classical influence propagation models§:
Independent cascades
Linear threshold
Each user is initially inactive, the seed set is activated (influenced)
When the influence from the set of active friends exceeds a threshold for a user v, the user activates
Influence is used as a proxy for adoption
§D. Kempe, J. Kleinberg, and E ́. Tardos. Maximizing the spread of influence through a social network. In KDD’03.

4. Influence ⇏ Adoption
Observation: Only a subset of influenced users actually adopt the marketed product
Influenced
Adopt
Awareness/information spreads in an epidemic-like manner while adoption depends on factors such as product quality and price§
§S. Kalish. A new product adoption model with price, advertising, and uncertainty. Management Science, 31(12), 1985.

5. Influence ⇏ Adoption
Moreover we found that there exist users who help in information propagation without actually adoption the product – tattlers.

6. Our Model (LT-C) Model Parameters A is the set of active friends
User v
Model Parameters
A is the set of active friends
fv(A) is the activation function
ru,i is the (predicted) rating for product i given by user u
αv is the probability of user v adopting the product
βv is the probability of user v promoting the product

7. Maximizing Product Adoption
Problem: Given a social network and product ratings, find k users such that by targeting them the expected spread (expected number of adopters) under the LT-C model is maximized
Problem is NP-hard
The spread function is monotone and submodular yielding a 1-1/e approximation to the optimal using a greedy approach

8. Evaluation
Data and Parameters
Key Findings

9. Data
Number of nodes
13K
6040
1892
Number of edges
192.4K
209K*
25.4K
Number of edges with non-zero weight
75.7K
154K
15.7K
Average degree
14.8
34.6
13.4
Number of movies / artists
25K
3706
17.6K
Number of ratings
1.84M 1M
259K
Flixster dataset has 2.3M special ratings, of which 730K ratings are “want to see it” and 1.6M are “not interested”
last.fm has “loved” and “banned” songs
*Movielens does not have an explicit social graph and we infer it from the ratings log, based on Jaccard similarity – in a recommender system, information/influence flows indirectly via recommendations.

10. Evaluation
Data and Parameters
Key Findings

11. Spread Estimates
Flixster
MovieLens
Our model (LT-C) better predicts spread for all datasets
Last.fm

12. Spread depends on product quality
Better quality products
have better coverage
Classical LT model on the
other hand predicts equal
coverage for all products

13. Different seeds for different products
Flixster
MovieLens

14. Key Takeaways
Only a fraction of users who are influenced do adopt the product
The influence of an adopter on her friends is a function of the adopter’s experience with the product, in addition to propagation probability
Non-adopters can play a role of “information bridges” helping in spreading the influence/information, and thus adoption by other users

15. Thanks !!!