Machine Learning (cs.LG)

Abstract: In recent years, heterogeneous graph few-shot learning has been proposed to address the label sparsity issue in heterogeneous graphs (HGs), which contain various types of nodes and edges. The existing methods have achieved good performance by transferring generalized knowledge extracted from rich-labeled classes in source HG(s) to few-labeled classes in a target HG. However, these methods only consider the single-heterogeneity scenario where the source and target HGs share a fixed set of node/edge types, ignoring the more general scenario of cross-heterogeneity, where each HG can have a different and non-fixed set of node/edge types. To this end, we focus on the unexplored cross-heterogeneity scenario and propose a novel model for Cross-heterogeneity Graph Few-shot Learning, namely CGFL. In CGFL, we first extract meta-patterns to capture heterogeneous information and propose a multi-view heterogeneous graph neural network (MHGN) to learn meta-patterns across HGs. Then, we propose a score module to measure the informativeness of labeled samples and determine the transferability of each source HG. Finally, by integrating MHGN and the score module into a meta-learning mechanism, CGFL can effectively transfer generalized knowledge to predict new classes with few-labeled data. Extensive experiments on four real-world datasets have demonstrated the superior performance of CGFL over the state-of-the-art methods.

Abstract: This paper studies Byzantine-robust stochastic optimization over a decentralized network, where every agent periodically communicates with its neighbors to exchange local models, and then updates its own local model by stochastic gradient descent (SGD). The performance of such a method is affected by an unknown number of Byzantine agents, which conduct adversarially during the optimization process. To the best of our knowledge, there is no existing work that simultaneously achieves a linear convergence speed and a small learning error. We observe that the learning error is largely dependent on the intrinsic stochastic gradient noise. Motivated by this observation, we introduce two variance reduction methods, stochastic average gradient algorithm (SAGA) and loopless stochastic variance-reduced gradient (LSVRG), to Byzantine-robust decentralized stochastic optimization for eliminating the negative effect of the stochastic gradient noise. The two resulting methods, BRAVO-SAGA and BRAVO-LSVRG, enjoy both linear convergence speeds and stochastic gradient noise-independent learning errors. Such learning errors are optimal for a class of methods based on total variation (TV)-norm regularization and stochastic subgradient update. We conduct extensive numerical experiments to demonstrate their effectiveness under various Byzantine attacks.

Abstract: Graph clustering is a fundamental task in graph analysis, and recent advances in utilizing graph neural networks (GNNs) have shown impressive results. Despite the success of existing GNN-based graph clustering methods, they often overlook the quality of graph structure, which is inherent in real-world graphs due to their sparse and multifarious nature, leading to subpar performance. Graph structure learning allows refining the input graph by adding missing links and removing spurious connections. However, previous endeavors in graph structure learning have predominantly centered around supervised settings, and cannot be directly applied to our specific clustering tasks due to the absence of ground-truth labels. To bridge the gap, we propose a novel method called \textbf{ho}mophily-enhanced structure \textbf{le}arning for graph clustering (HoLe). Our motivation stems from the observation that subtly enhancing the degree of homophily within the graph structure can significantly improve GNNs and clustering outcomes. To realize this objective, we develop two clustering-oriented structure learning modules, i.e., hierarchical correlation estimation and cluster-aware sparsification. The former module enables a more accurate estimation of pairwise node relationships by leveraging guidance from latent and clustering spaces, while the latter one generates a sparsified structure based on the similarity matrix and clustering assignments. Additionally, we devise a joint optimization approach alternating between training the homophily-enhanced structure learning and GNN-based clustering, thereby enforcing their reciprocal effects. Extensive experiments on seven benchmark datasets of various types and scales, across a range of clustering metrics, demonstrate the superiority of HoLe against state-of-the-art baselines.