Node embeddings in dynamic graphs

Abstract

In this paper, we present algorithms that learn and update temporal node embeddings on the fly for tracking and measuring node similarity over time in graph streams. Recently, several representation learning methods have been proposed that are capable of embedding nodes in a vector space in a way that captures the network structure. Most of the known techniques extract embeddings from static graph snapshots. By contrast, modeling the dynamics of the nodes in temporal networks requires evolving node representations. In order to update node representations that reflect the temporal changes in the local graph structure, we rely on ideas for data stream algorithms. For example, we assess neighborhood overlap by a MinHash fingerprint-based algorithm. To evaluate our methods, in addition to the standard link prediction task, we provide dynamic ground truth data for the quantitative evaluation of similarity search by using online updated node embeddings. In our experiments, we constructed tennis tournament Twitter mention graphs as edge streams and compiled dynamic ground truth by using tournament schedule as external source. Our new algorithms outperformed snapshot-based batch methods for both link prediction and similarity search.

Predicting partially observed processes on temporal networks by Dynamics-Aware Node Embeddings (DyANE)

“…In addition, we consider four state of the art embedding methods for temporal networks, which do not use the intermediate step of using a supra-adjacency representation, but directly embed the temporal network, namely: (i) DynamicTriad (DTriad) [33], which embeds the temporal network by modeling triadic closure events; (ii) DynGEM [34], which is based on a deep learning model. It outputs an embedding for the network of each timestamp, initializing the model at timestamp t + 1 with the weights found at time t, thus transferring knowledge from t to t + 1 and learning about the changes from G t to G t+1 ; (iii) StreamWalk [35], which uses time-respecting walks and online machine learning to capture temporal changes in the network structure; (iv) Online learning of second order node similarity (Online-neighbor) [35], which optimizes the embedding to match the neighborhood similarity of pairs of nodes, as measured by the Jaccard index of these neighborhoods.…”

weg2vec: Event embedding for temporal networks

“…Although our method seems to provide high absolute scores for the prediction of spreading outcome, there are a few other recently proposed dynamical network embedding methods, which can be used for the same task. Here we consider two of the most promising ones, the STWalk [31,38], and the Online-Node2vec embedding methods [39,40] to compare their predictive performances to weg2vec. Both methods are thought to build node embeddings for dynamic graphs using the Skip-Gram model, which introduces a significant difference to our event embedding method.…”

Tutorial on graph stream analytics

“…A few years ago, the term fast data [39] arose to capture the idea that streams of data are generated at very high rates from network measurements, call records, web page visits, sensor readings, financial applications [12,70], network monitoring [1,7], security, sensor networks [21], Twitter analysis [10,13,60], and more [22].…”

“…As a hands-on exercise, we demonstrate how the Twitter API [10,13,60] can be deployed as a graph stream source that provides a "retweet" and an "@-mention" edge stream. A key issue for temporal network analysis is the difficulty of evaluation.…”