Graph pooling refers to the operation that maps a set of node representations into a compact form for graph-level representation learning. However, existing graph pooling methods are limited by the power of the Weisfeiler–Lehman (WL) test in the performance of graph discrimination. In addition, these methods often suffer from hard adaptability to hyper-parameters and training instability. To address these issues, we propose Hi-PART, a simple yet effective graph neural network (GNN) framework with Hi erarchical Par tition T ree (HPT). In HPT, each layer is a partition of the graph with different levels of granularities that are going toward a finer grain from top to bottom. Such an exquisite structure allows us to quantify the graph structure information contained in HPT with the aid of structural information theory. Algorithmically, by employing GNNs to summarize node features into the graph feature based on HPT’s hierarchical structure, Hi-PART is able to adequately leverage the graph structure information and provably goes beyond the power of the WL test. Due to the separation of HPT optimization from graph representation learning, Hi-PART involves the height of HPT as the only extra hyper-parameter and enjoys higher training stability. Empirical results on graph classification benchmarks validate the superior expressive power and generalization ability of Hi-PART compared with state-of-the-art graph pooling approaches.

Graph Contrastive Learning (GCL) with Graph Neural Networks (GNN) has emerged as a promising method for learning latent node representations in a self-supervised manner. Most of existing GCL methods employ random sampling for graph view augmentation and maximize the agreement of the node representations between the views. However, the random augmentation manner, which is likely to produce very similar graph view samplings, may easily result in incomplete nodal contextual information, thus weakening the discrimination of node representations. To this end, this paper proposes a novel trainable scheme from the perspective of node augmentation, which is theoretically proved to be injective and utilizes the subgraphs consisting of each node with its neighbors to enhance the distinguishability of nodal view. Notably, our proposed scheme tries to enrich node representations via a multi-scale contrastive training that integrates three different levels of training granularity, i.e., subgraph level, graph- and node-level contextual information. In particular, the subgraph-level objective between augmented and original node views is constructed to enhance the discrimination of node representations while graph- and node-level objectives with global and local information from the original graph are developed to improve the generalization ability of representations. Experiment results demonstrate that our framework outperforms existing state-of-the-art baselines and even surpasses several supervised counterparts on four real-world datasets for node classification.

User review data is considered as auxiliary information to alleviate the data sparsity problem and improve the quality of learned user/item or interaction representations in review-based recommender systems. However, existing methods usually model user-item interactions in a holistic manner and neglect the entanglement of the latent intents behind them, e.g., price, quality, or appearance, resulting in suboptimal representations and reducing interpretability. In this paper, we propose a Self-supervised Graph Disentangled Networks for review-based recommendation (SGDN), to separately model the user-item interactions based on the latent factors through the textual review data. To this end, we first model the distributions of interactions over latent factors from both semantic information in review data and structural information in user-item graph data, forming several factor graphs. Then a factorized message passing mechanism is designed to learn disentangled user/item and interaction representations on the factor graphs. Finally, we set an intent-aware contrastive learning task to alleviate the sparsity issue and encourage disentanglement through dynamically identifying positive and negative samples based on the learned intent distributions. Empirical results over five benchmark datasets validate the superiority of SGDN over the state-of-the-art methods and the interpretability of learned intent factors.

Bundle recommendation aims to recommend a bundle of items to users as a whole with user-bundle (U-B) interaction information, and auxiliary user-item (U-I) interaction and bundle-item affiliation information. Recent methods usually use two graph neural networks (GNNs) to model user's bundle preferences separately from the U-B graph (bundle view) and U-I graph (item view). However, by conducting statistical analysis, we find that the auxiliary U-I information is far underexplored due to the following reasons: 1) Loosely combining the predicted results cannot well synthesize the knowledge from both views. 2) The local U-B and U-I collaborative relations might not be consistent, leading to GNN's inaccurate modeling of user's bundle preference from the U-I graph. 3) The U-I interactions are usually modeled equally while the significant ones corresponding to user's bundle preference are less emphasized.

Self-supervised graph-level representation learning has recently received considerable attention. Given varied input distributions, jointly learning graphs’ unique and common features is vital to downstream tasks. Inspired by graph contrastive learning (GCL), which targets maximizing the agreement between graph representations from different views, we propose an Ada ptive self-supervised framework, Ada-MIP, considering both M utual I nformation between views (unique features) and inter-graph P roximity (common features). Specifically, Ada-MIP learns graphs’ unique information through a learnable and probably injective augmenter, which can acquire more adaptive views compared to the augmentation strategies applied by existing GCL methods; to learn graphs’ common information, we employ graph kernels to calculate graphs’ proximity and learn graph representations among which the precomputed proximity is preserved. By sharing a global encoder, graphs’ unique and common information can be well integrated into the graph representations learned by Ada-MIP. Ada-MIP is also extendable to semi-supervised scenarios, with our experiments confirming its superior performance in both unsupervised and semi-supervised tasks.

Influence maximization through social networks has aroused tremendous interests nowadays. However, people’s various expressions or feelings about a same idea often cause ambiguity via word of mouth. Consequently, the problem of how to maximize the spread of “effective information” still remains largely open. In this paper, we consider a practical setting where ideas can deviate from their original version to invalid forms during message passing, and make the first attempt to seek a union of users that maximizes the spread of effective influence, which is formulated as an Influence Maximization with Information Variation (IMIV) problem. To this end, we model the information as a vector, and quantify the difference of two arbitrary vectors as a distance by a matching function. We further establish a process where such distance increases with the propagation and ensure the recipient whose vector distance is less than a threshold can be effectively influenced. Due to the NP-hardness of IMIV, we greedily select users that can approximately maximize the estimation of effective propagation. Especially, for networks of small scales, we derive a condition under which all the users can be effectively influenced. Our models and theoretical findings are further consolidated through extensive experiments on real-world datasets.