Graph Clustering with Graph Neural Networks

Graph Neural Networks (GNNs) have achieved state-of-the-art results on many graph analysis tasks such as node classification and link prediction. However, important unsupervised problems on graphs, such as graph clustering, have proved more resistant to advances in GNNs. In this paper, we study unsupervised training of GNN pooling in terms of their clustering capabilities. We start by drawing a connection between graph clustering and graph pooling: intuitively, a good graph clustering is what one would expect from a GNN pooling layer. Counterintuitively, we show that this is not true for state-of-the-art pooling methods, such as MinCut pooling. To address these deficiencies, we introduce Deep Modularity Networks (DMoN), an unsupervised pooling method inspired by the modularity measure of clustering quality, and show how it tackles recovery of the challenging clustering structure of real-world graphs. In order to clarify the regimes where existing methods fail, we carefully design a set of experiments on synthetic data which show that DMoN is able to jointly leverage the signal from the graph structure and node attributes. Similarly, on real-world data, we show that DMoN produces high quality clusters which correlate strongly with ground truth labels, achieving state-of-the-art results

A Force-Directed Approach for Offline GPS Trajectory Map Matching

We present a novel algorithm to match GPS trajectories onto maps offline (in batch mode) using techniques borrowed from the field of force-directed graph drawing. We consider a simulated physical system where each GPS trajectory is attracted or repelled by the underlying road network via electrical-like forces. We let the system evolve under the action of these physical forces such that individual trajectories are attracted towards candidate roads to obtain a map matching path. Our approach has several advantages compared to traditional, routing-based, algorithms for map matching, including the ability to account for noise and to avoid large detours due to outliers in the data whilst taking into account the underlying topological restrictions (such as one-way roads). Our empirical evaluation using real GPS traces shows that our method produces better map matching results compared to alternative offline map matching algorithms on average, especially for routes in dense, urban areas.Comment: 10 pages, 12 figures, accepted version of article submitted to ACM SIGSPATIAL 2018, Seattle, US

Advances on Testing C-Planarity of Embedded Flat Clustered Graphs

We show a polynomial-time algorithm for testing c-planarity of embedded flat clustered graphs with at most two vertices per cluster on each face.Comment: Accepted at GD '1

Applications of Structural Balance in Signed Social Networks

We present measures, models and link prediction algorithms based on the structural balance in signed social networks. Certain social networks contain, in addition to the usual 'friend' links, 'enemy' links. These networks are called signed social networks. A classical and major concept for signed social networks is that of structural balance, i.e., the tendency of triangles to be 'balanced' towards including an even number of negative edges, such as friend-friend-friend and friend-enemy-enemy triangles. In this article, we introduce several new signed network analysis methods that exploit structural balance for measuring partial balance, for finding communities of people based on balance, for drawing signed social networks, and for solving the problem of link prediction. Notably, the introduced methods are based on the signed graph Laplacian and on the concept of signed resistance distances. We evaluate our methods on a collection of four signed social network datasets.Comment: 37 page