Redundancy-Free Self-Supervised Relational Learning for Graph Clustering.

Graph clustering, which learns the node representations for effective cluster assignments, is a fundamental yet challenging task in data analysis and has received considerable attention accompanied by graph neural networks (GNNs) in recent years. However, most existing methods overlook the inherent relational information among the nonindependent and nonidentically distributed nodes in a graph. Due to the lack of exploration of relational attributes, the semantic information of the graph-structured data fails to be fully exploited which leads to poor clustering performance. In this article, we propose a novel self-supervised deep graph clustering method named relational redundancy-free graph clustering (R 2 FGC) to tackle the problem. It extracts the attribute-and structure-level relational information from both global and local views based on an autoencoder (AE) and a graph AE (GAE). To obtain effective representations of the semantic information, we preserve the consistent relationship among augmented nodes, whereas the redundant relationship is further reduced for learning discriminative embeddings. In addition, a simple yet valid strategy is used to alleviate the oversmoothing issue. Extensive experiments are performed on widely used benchmark datasets to validate the superiority of our R 2 FGC over state-of-the-art baselines. Our codes are available at https://github.com/yisiyu95/R2FGC.

D-optimal designs of mean-covariance models for longitudinal data.

Longitudinal data analysis has been very common in various fields. It is important in longitudinal studies to choose appropriate numbers of subjects and repeated measurements and allocation of time points as well. Therefore, existing studies proposed many criteria to select the optimal designs. However, most of them focused on the precision of the mean estimation based on some specific models and certain structures of the covariance matrix. In this paper, we focus on both the mean and the marginal covariance matrix. Based on the mean-covariance models, it is shown that the trick of symmetrization can generate better designs under a Bayesian D-optimality criterion over a given prior parameter space. Then, we propose a novel criterion to select the optimal designs. The goal of the proposed criterion is to make the estimates of both the mean vector and the covariance matrix more accurate, and the total cost is as low as possible. Further, we develop an algorithm to solve the corresponding optimization problem. Based on the algorithm, the criterion is illustrated by an application to a real dataset and some simulation studies. We show the superiority of the symmetric optimal design and the symmetrized optimal design in terms of the relative efficiency and parameter estimation. Moreover, we also demonstrate that the proposed criterion is more effective than the previous criteria, and it is suitable for both maximum likelihood estimation and restricted maximum likelihood estimation procedures.