Purnamrita Sarkar, Andrew Moore
This paper explores two aspects of social network modeling. First, we generalize a successful static model of relationships into a dynamic model that accounts for friendships drifting over time. Second, we show how to make it tractable to learn such models from data, even as the number of entities n gets large. The generalized model associates each entity with a point in p-dimensional Euclidian latent space. The points can move as time progresses but large moves in latent space are improb- able. Observed links between entities are more likely if the entities are close in latent space. We show how to make such a model tractable (sub- quadratic in the number of entities) by the use of appropriate kernel func- tions for similarity in latent space; the use of low dimensional kd-trees; a new ef(cid:2)cient dynamic adaptation of multidimensional scaling for a (cid:2)rst pass of approximate projection of entities into latent space; and an ef(cid:2)- cient conjugate gradient update rule for non-linear local optimization in which amortized time per entity during an update is O(log n). We use both synthetic and real-world data on upto 11,000 entities which indicate linear scaling in computation time and improved performance over four alternative approaches. We also illustrate the system operating on twelve years of NIPS co-publication data. We present a detailed version of this work in .