Maximizing Product Adoption in Social Networks

Smriti Bhagat, Amit Goyal, Laks Lakshmanan(Paper appeared in WSDM 2012)

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§

Node: User in a social network (green – seed set)Edge: Friendship among usersEdge Weight: Influence probability

0.2

0.9

§D. Kempe, J. Kleinberg, and E . Tardos. Maximizing the spread of influence through a social network. In KDD’03. ́�

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. ́�

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.

Influence ⇏ Adoption Moreover we found that there exist users who help

in information propagation without actually adoption the product – tattlers.

Our Model (LT-C)

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

User vActive Friends

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

Evaluation• Data and Parameters• Key Findings

Data

Number of nodes 13K 6040 1892Number of edges 192.4K 209K* 25.4KNumber of edges with non-zero weight 75.7K 154K 15.7KAverage degree 14.8 34.6 13.4Number of movies / artists 25K 3706 17.6KNumber of ratings 1.84M 1M 259K

*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.

• 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

Evaluation• Data and Parameters• Key Findings

Spread Estimates

Our model (LT-C) better predicts spread for all datasets

Flixster

MovieLens

Last.fm

Spread depends on product quality

Better quality products have better coverage

Classical LT model on theother hand predicts equalcoverage for all products

Different seeds for different products

FlixsterMovieLens

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

Thanks !!!