Random-walk-based network embedding algorithms like DeepWalk and node2vec are widely used to obtain euclidean representation of the nodes in a network prior to performing downstream inference tasks. However, despite their impressive empirical performance, there is a lack of theoretical results explaining their large-sample behavior. In this paper, we study node2vec and DeepWalk through the perspective of matrix factorization. In particular, we analyze these algorithms in the setting of community detection for stochastic blockmodel graphs (and their degree-corrected variants). By exploiting the row-wise uniform perturbation bound for leading singular vectors, we derive high-probability error bounds between the matrix factorization-based node2vec/DeepWalk embeddings and their true counterparts, uniformly over all node embeddings. Based on strong concentration results, we further show the perfect membership recovery by node2vec/DeepWalk, followed by K-means/medians algorithms. Specifically, as the network becomes sparser, our results guarantee that with large enough window size and vertex number, applying K-means/medians on the matrix factorization-based node2vec embeddings can, with high probability, correctly recover the memberships of all vertices in a network generated from the stochastic blockmodel (or its degree-corrected variants). The theoretical justifications are mirrored in the numerical experiments and real data applications, for both the original node2vec and its matrix factorization variant.

State-backed platform manipulation (SBPM) on Twitter has been a prominent public issue since the 2016 US election cycle. Identifying and characterizing users on Twitter as belonging to a state-backed campaign is an important part of mitigating their influence. In this paper, we propose a novel time series feature grounded in social science to characterize dynamic user networks on Twitter. We introduce a classification approach, motif functional data analysis (MFDA), that captures the evolution of motifs in temporal networks, which is a useful feature for analyzing malign influence. We evaluate MFDA on data from known SBPM campaigns on Twitter and representative authentic data and compare performance to other classification methods. To further leverage our dynamic feature, we use the changes in network structure captured by motifs to help uncover real-world events using anomaly detection.

Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality reduction methods allow out-of-sample extensions, by which an embedding can be applied to observations not present in the training set. Applied to graphs, the out-of-sample extension problem concerns how to compute the embedding of a vertex that is added to the graph after an embedding has already been computed. In this paper, we consider the out-of-sample extension problem for two graph embedding procedures: the adjacency spectral embedding and the Laplacian spectral embedding. In both cases, we prove that when the underlying graph is generated according to a latent space model called the random dot product graph, which includes the popular stochastic block model as a special case, an out-of-sample extension based on a least-squares objective obeys a central limit theorem. In addition, we prove a concentration inequality for the out-of-sample extension of the adjacency spectral embedding based on a maximum-likelihood objective. Our results also yield a convenient framework in which to analyze trade-offs between estimation accuracy and computational expenses, which we explore briefly. Finally, we explore the performance of these out-of-sample extensions as applied to both simulated and real-world data. We observe significant computational savings with minimal losses to the quality of the learned embeddings, in keeping with our theoretical results.

In this work, we show that using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the remaining vertices can be classified with error converging to Bayes optimal using the $(k)$-nearest-neighbors classification rule. We evaluate the proposed methods on simulated data and a graph derived from Wikipedia.

Given an attributed graph representation of data, vertex nomination works to find the group of vertices which are of interest, e.g., those vertices whose attributes are different from others', or the connection among those vertices are more frequent. In this paper we present an algorithm to estimate the power of nominating these interesting vertices. This algorithm is based on Wilcoxon rank sum test. It requires to embed graph vertices into a low dimensional space. Two graph embedding methods, adjacency spectral embedding and multidimensional scaling composed with canonical correlation analysis are employed. We investigate a case where two graphs are available for modeling the same objects in different spaces, and show the effects of data fusion on vertex nomination power.

Significant advances have been made in heuristic search for classical planning in the last six years. Most of these planners use A* style search. We report on two sound and complete domain-independent classical planners AWA* (adjusted weighted A*) and MAWA* (modified AWA*) in this paper. AWA* is the first planner to use node-dependent weighting in A*. MAWA* uses a two-phase heuristic evaluation. MAWA* applies node-dependent weighting to a subset of the nodes in the fringe, after the two-phase evaluation. We report on an empirical comparison of AWA*, MAWA* with classical planners AltAlt, FF and STAN 4. Both AWA* and MAWA* outperform AltAlt and STAN 4. Both AWA* and MAWA* solve many problems that FF does not. The ideas in AWA* and MAWA* are general enough to be applicable in solving other planning problems like temporal planning and planning with resources and numerical variables.