Robust Angular Synchronization via Directed Graph Neural Networks

The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles $\theta_1, \dots, \theta_n\in[0, 2\pi)$ from $m$ noisy measurements of their offsets \theta_i-\theta_j \;\mbox{mod} \; 2\pi. Applications include, for example, sensor network localization, phase retrieval, and distributed clock synchronization. An extension of the problem to the heterogeneous setting (dubbed $k$-synchronization) is to estimate $k$ groups of angles simultaneously, given noisy observations (with unknown group assignment) from each group. Existing methods for angular synchronization usually perform poorly in high-noise regimes, which are common in applications. In this paper, we leverage neural networks for the angular synchronization problem, and its heterogeneous extension, by proposing GNNSync, a theoretically-grounded end-to-end trainable framework using directed graph neural networks. In addition, new loss functions are devised to encode synchronization objectives. Experimental results on extensive data sets demonstrate that GNNSync attains competitive, and often superior, performance against a comprehensive set of baselines for the angular synchronization problem and its extension, validating the robustness of GNNSync even at high noise levels

Learning Embeddings for Academic Papers

Academic papers contain both text and citation links. Representing such data is crucial for many downstream tasks, such as classification, disambiguation, duplicates detection, recommendation and influence prediction. The success of Skip-gram with Negative Sampling model (hereafter SGNS) has inspired many algorithms to learn embeddings for words, documents, and networks. However, there is limited research on learning the representation of linked documents such as academic papers. This dissertation first studies the norm convergence issue in SGNS and propose to use an L2 regularization to fix the problem. Our experiments show that our method improves SGNS and its variants on different types of data. We observe improvements upto 17.47% for word embeddings, 1.85% for document embeddings, and 46.41% for network embeddings. To learn the embeddings for academic papers, we propose several neural network based algorithms that can learn high-quality embeddings from different types of data. The algorithms we proposed are N2V (network2vector) for networks, D2V (document2vector) for documents, and P2V (paper2vector) for academic papers. Experiments show that our models outperform traditional algorithms and the state-of-the-art neural network methods on various datasets under different machine learning tasks. With the high quality embeddings, we design and present four applications on real-world datasets, i.e., academic paper and author search engines, author name disambiguation, and paper influence prediction

Graph neural networks for network analysis

With an increasing number of applications where data can be represented as graphs, graph neural networks (GNNs) are a useful tool to apply deep learning to graph data. Signed and directed networks are important forms of networks that are linked to many real-world problems, such as ranking from pairwise comparisons, and angular synchronization. In this report, we propose two spatial GNN methods for node clustering in signed and directed networks, a spectral GNN method for signed directed networks on both node clustering and link prediction, and two GNN methods for specific applications in ranking as well as angular synchronization. The methods are end-to-end in combining embedding generation and prediction without an intermediate step. Experimental results on various data sets, including several synthetic stochastic block models, random graph outlier models, and real-world data sets at different scales, demonstrate that our proposed methods can achieve satisfactory performance, for a wide range of noise and sparsity levels. The introduced models also complement existing methods through the possibility of including exogenous information, in the form of node-level features or labels. Their contribution not only aid the analysis of data which are represented by networks, but also form a body of work which presents novel architectures and task-driven loss functions for GNNs to be used in network analysis

Directed Graph Minors and Serial-Parallel Width

Graph minors are a primary tool in understanding the structure of undirected graphs, with many conceptual and algorithmic implications. We propose new variants of \emph{directed graph minors} and \emph{directed graph embeddings}, by modifying familiar definitions. For the class of 2-terminal directed acyclic graphs (TDAGs) our two definitions coincide, and the class is closed under both operations. The usefulness of our directed minor operations is demonstrated by characterizing all TDAGs with serial-parallel width at most $k$; a class of networks known to guarantee bounded negative externality in nonatomic routing games. Our characterization implies that a TDAG has serial-parallel width of $1$ if and only if it is a directed series-parallel graph. We also study the computational complexity of finding a directed minor and computing the serial-parallel width