DIGRAC: Digraph Clustering Based on Flow Imbalance

Node clustering is a powerful tool in the analysis of networks. We introduce a graph neural network framework to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss, which can be used for network clustering. Here, we propose directed flow imbalance measures, which are tightly related to directionality, to reveal clusters in the network even when there is no density difference between clusters. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. DIGRAC optimizes directed flow imbalance for clustering without requiring label supervision, unlike existing GNN methods, and can naturally incorporate node features, unlike existing spectral methods. Experimental results on synthetic data, in the form of directed stochastic block models, and real-world data at different scales, demonstrate that our method, based on flow imbalance, attains state-of-the-art results on directed graph clustering, for a wide range of noise and sparsity levels and graph structures and topologies.Comment: 36 pages (10 pages for main text, 3 pages for references

Study on Mental Pension and Its Influence Factors of Rural Empty-nest Old Men

With the continuous development of urbanization and aging, the rate of empty-nest old man in rural areas in China continues to rise. Due to the “Healthy China” strategy proposed by the 19th CPC National Congress and the changing family structure in rural areas, the vulnerable elders in rural vulnerable population have been placed in a prominent place. It is urgent to solve mental pension for the elderly in the countryside. On the basis of comprehensively understanding the connotation of mental support, we analyzed the data from the 2012 Renmin University of China. The factors influencing the mental pension of rural empty-nest old men were divided into three categories and 19 types. We deeply summarized the impact of different factors on the mental pension of rural empty-nest old men

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