Multiplicative Attribute Graph Model of Real-World Networks

Large scale real-world network data such as social and information networks are ubiquitous. The study of such social and information networks seeks to find patterns and explain their emergence through tractable models. In most networks, and especially in social networks, nodes have a rich set of attributes (e.g., age, gender) associated with them. Here we present a model that we refer to as the Multiplicative Attribute Graphs (MAG), which naturally captures the interactions between the network structure and the node attributes. We consider a model where each node has a vector of categorical latent attributes associated with it. The probability of an edge between a pair of nodes then depends on the product of individual attribute-attribute affinities. The model yields itself to mathematical analysis and we derive thresholds for the connectivity and the emergence of the giant connected component, and show that the model gives rise to networks with a constant diameter. We analyze the degree distribution to show that MAG model can produce networks with either log-normal or power-law degree distributions depending on certain conditions.Comment: 33 pages, 6 figure

Modeling Social Networks with Node Attributes using the Multiplicative Attribute Graph Model

Networks arising from social, technological and natural domains exhibit rich connectivity patterns and nodes in such networks are often labeled with attributes or features. We address the question of modeling the structure of networks where nodes have attribute information. We present a Multiplicative Attribute Graph (MAG) model that considers nodes with categorical attributes and models the probability of an edge as the product of individual attribute link formation affinities. We develop a scalable variational expectation maximization parameter estimation method. Experiments show that MAG model reliably captures network connectivity as well as provides insights into how different attributes shape the network structure.Comment: 15 pages, 7 figures, 7 table

Donor Retention in Online Crowdfunding Communities: A Case Study of DonorsChoose.org

Online crowdfunding platforms like DonorsChoose.org and Kickstarter allow specific projects to get funded by targeted contributions from a large number of people. Critical for the success of crowdfunding communities is recruitment and continued engagement of donors. With donor attrition rates above 70%, a significant challenge for online crowdfunding platforms as well as traditional offline non-profit organizations is the problem of donor retention. We present a large-scale study of millions of donors and donations on DonorsChoose.org, a crowdfunding platform for education projects. Studying an online crowdfunding platform allows for an unprecedented detailed view of how people direct their donations. We explore various factors impacting donor retention which allows us to identify different groups of donors and quantify their propensity to return for subsequent donations. We find that donors are more likely to return if they had a positive interaction with the receiver of the donation. We also show that this includes appropriate and timely recognition of their support as well as detailed communication of their impact. Finally, we discuss how our findings could inform steps to improve donor retention in crowdfunding communities and non-profit organizations.Comment: preprint version of WWW 2015 pape

From Amateurs to Connoisseurs: Modeling the Evolution of User Expertise through Online Reviews

Recommending products to consumers means not only understanding their tastes, but also understanding their level of experience. For example, it would be a mistake to recommend the iconic film Seven Samurai simply because a user enjoys other action movies; rather, we might conclude that they will eventually enjoy it -- once they are ready. The same is true for beers, wines, gourmet foods -- or any products where users have acquired tastes: the `best' products may not be the most `accessible'. Thus our goal in this paper is to recommend products that a user will enjoy now, while acknowledging that their tastes may have changed over time, and may change again in the future. We model how tastes change due to the very act of consuming more products -- in other words, as users become more experienced. We develop a latent factor recommendation system that explicitly accounts for each user's level of experience. We find that such a model not only leads to better recommendations, but also allows us to study the role of user experience and expertise on a novel dataset of fifteen million beer, wine, food, and movie reviews.Comment: 11 pages, 7 figure