Arrival and Departure Dynamics in Social Networks

Arrival and Departure Dynamics in Social Networks
Shaomei Wu, Atish Das Sarma, Alex Fabrikant, Silvio Lattanzi, Andrew Tomkins

In this paper, we consider the natural arrival and departure of users in a social network, and ask whether the dynamics of arrival, which have been studied in some depth, also explain the dynamics of departure, which are not as well studied.

Through study of the DBLP co-authorship network and a large online social network, we show that the dynamics of departure behave differently from the dynamics of formation.

In particular, the probability of departure of a user with few friends may be understood most accurately as a function of the raw number of friends who are active. For users with more friends, however, the probability of departure is best predicted by the overall fraction of the user's neighborhood that is active, independent of size.

We then study global properties of the sub-graphs induced by active and inactive users, and show that active users tend to belong to a core that is densifying and is significantly denser than the inactive users. Further, the inactive set of users exhibit a higher density and lower conductance than the degree distribution alone can explain. These two aspects suggest that nodes at the fringe are more likely to depart and subsequent departure are correlated among neighboring nodes in tightly-knit communities.

Another publication from the same category: Machine Learning and Data Science

IEEE Computing Conference 2018, London, UK

Regularization of the Kernel Matrix via Covariance Matrix Shrinkage Estimation

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix of the data requires outer products. Therefore, their spectral properties are tightly connected. This allows us to examine the kernel matrix through the sample covariance matrix in the feature space and vice versa. The use of kernels often involves a large number of features, compared to the number of observations. In this scenario, the sample covariance matrix is not well-conditioned nor is it necessarily invertible, mandating a solution to the problem of estimating high-dimensional covariance matrices under small sample size conditions. We tackle this problem through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix (also known as the "target") with the aim of minimizing the mean-squared error (MSE). We propose a distribution-free kernel matrix regularization approach that is tuned directly from the kernel matrix, avoiding the need to address the feature space explicitly. Numerical simulations demonstrate that the proposed regularization is effective in classification tasks.