Graph neural network (GNN) provides a powerful expressive way to embed graph-structured data, which has been widely applied and spans many fields. This article found an interesting but unreasonable phenomenon in some classical GNNs, namely label confusion. Theoretically, the dependence between prediction label and ground-truth should gradually increase and tend to converge with training epochs. On the contrary, label confusion shows that the dependence between the predicted label and ground-truth is strong first and then weak. This article explains it from the perspective of feature-noise dependence. Specifically, traditional GNN prediction usually assumes that the ground-truth consists of a mutually independent prediction label (dependent on node features) and noise (independent of node features). However, the propagation aggregation mechanism of GNN will integrate irrelevant information from neighboring nodes into the prediction label, resulting in the prediction label no longer being completely dependent on the node feature, or the noise no longer being completely independent of the node feature. Hence, this article proposes a Label-Dependent GNN to alleviate this problem, called LDGNN. LDGNN mainly consists of two limitations, namely feature-noise (the difference between predicted label and ground-truth) independence, and expectation-variance (EV) separation. Specifically, LDGNN introduces the Hilbert-Schmidt independence criterion (HSIC) as a regularization to minimize the dependence between input features and noise. Note that the main reason for adopting HSIC is that it can measure the nonlinear relationship between any two spatial variables. In this way, HSIC can guide GNN to retain more label-dependence information. Then, LDGNN designs an EV separation to centralize nodes within a class and disperse them between classes to further retain label-dependence information. Through these two strategies, the GNN’s expression ability can be enhanced. Next, we theoretically prove the essential reason why LDGNN alleviates label confusion and has been verified in experiments. To verify the performance of LDGNN, we apply it to four classical GNN models on three datasets, and experimental results demonstrate the effectiveness of LDGNN.

Existing clustering ensemble methods often directly integrate multiple weak base results to obtain a consensus one which can improve the clustering performance. However, since the base results are weak and the clustering ensemble can improve the performance, why not refine the weak base results via the clustering ensemble, and then boost the clustering ensemble with the refined base results? To fulfill this idea, in this article, we propose a novel clustering ensemble method with an adaptive multiplex. We first use the multiplex to represent the multiple weak base results. Then, we learn an updated representation by diffusing the representation on the multiplex with a manifold ranking model. Since the multiplex characterizes the structure information of all base results, the learned representation can ensemble such structure information during diffusion. Next, the multiplex is refined by such representation, which is a process of refining base results via ensemble. We iteratively learn the representation (i.e., do ensemble) and update the multiplex (i.e., do refinement), which can make the ensemble and refinement be boosted by each other. At last, the final consensus result is obtained from the refined multiplex. The extensive experiments demonstrate the effectiveness and superiority of the proposed framework.

Graph convolutional networks (GCNs)GCN have been widely used to learn high-quality representations (a.k.a. embeddings) from multiorder neighbors in recommendation tasks. However, many existing graph convolutional network (GCN)-based methods learn user and item embeddings in the user–item interaction bipartite graph indistinguishably, ignoring the inherent heterogeneity of the bipartite graph, i.e., users and items are two distinct types of entities. This article explores in depth the high-order connections for user and his (her) neighbor items. We propose an innovative model, neighbor item embedding-aware graph convolutional network (NIE-GCN). As opposed to previous GCN-based approaches, NIE-GCN employs a novel dual user aggregationdual user aggregation (DUA) scheme and a neighbor-aware attention mechanism to construct user embeddings and distinguish the contribution of different neighbor nodes. In addition, we propagate information in an alternating manner to eliminate the effects of heterogeneity of user–item interaction bipartite graph. According to detailed experiments on three large-scale datasets, the proposed NIE-GCN significantly outperforms state-of-the-art approaches on the Top-$N$recommendation task while reducing model parameters by about half. Further analyses show the effectiveness and rationality of dual user aggregationDUA and neighbor-aware attention mechanism.

Recently, many data mining models based on heterogeneous graph (HG) have emerged. Among these, HG embedding is an important and indispensable process. However, the existing HG embedding models usually use graph neural network to learn embeddings separately on different meta-paths, ignoring the fact that different meta-paths contain not only their unique semantics but also related semantics. This may result in semantic overlap or irrelevance, which needs to be a feasible and effective tradeoff for high-quality HG embedding, yet studies thereof have rarely been reported. In this article, we propose semantic tradeoff HG embedding (STHGE) by first introducing the Hilbert–Schmidt independence criterion (HSIC) as restriction. The main idea of STHGE is to regard semantic tradeoff as independence tradeoff (or correlation) between different meta-path spaces. Specifically, we first transform the original features of nodes into different meta-path feature spaces with HSIC restriction between them. Then, we use graph attention network to learn the embeddings of nodes on different meta-paths with HSIC restrictions. Finally, we concatenate the embeddings on different meta-paths to perform prediction. Experimental results on three heterogeneous datasets not only demonstrate the effectiveness of STHGE but also demonstrate that STHGE can achieve a new semantic tradeoff between different meta-paths. Furthermore, we demonstrate the robustness of STHGE.

The graph neural network (GNN) has demonstrated its superior power in various data mining tasks and has been widely applied in diversified fields. The core of GNN is the aggregation and combination functions, and mainstream GNN studies focus on the enhancement of these functions. However, GNNs face a common challenge, i.e., useless features contained in neighbor nodes may be integrated into the target node during the aggregation process. This leads to poor node embedding and undermines downstream tasks. To tackle this problem, this article proposes a novel GNN optimization framework GNN-MHSIC by introducing the nonparametric dependence method Hilbert-Schmidt independence criterion (HSIC) under the guidance of information bottleneck. HSIC is utilized to guide the information propagation among layers of a GNN from multiaspect views. GNN-MHSIC aims to achieve three main objectives: 1) minimizing the HSIC between the input features and the propagation layers; 2) maximizing the HSIC between the propagation layers and the ground truth; and 3) minimizing the HSIC between the propagation layers. With a multiaspect design, GNN-MHSIC can minimize the propagation of redundant information while preserving relevant information about the target node. We prove GNN-MHSIC's finite upper and lower bounds theoretically and evaluate it experimentally with four classic GNN models, including the graph convolutional network, the graph attention network (GAT), the heterogeneous GAT, and the heterogeneous graph (HG) propagation network on three widely used HGs. The results illustrate the usefulness and performance of GNN-MHSIC.

Graph-based recommender system has attracted widespread attention and produced a series of research results. Because of the powerful high-order connection modeling capabilities of the Graph Neural Network, the performance of these graph-based recommender systems are far superior to those of traditional neural network-based collaborative filtering models. However, from both analytical and empirical perspectives, the apparent performance improvement is accompanied with a significant time overhead, which is noticeable in large-scale graph topologies. More importantly, the intrinsic data-sparsity problem substantially limits the performance of graph-based recommender systems, which compelled us to revisit graph-based recommendation from a novel perspective. In this article, we focus on analyzing the time complexity of graph-based recommender systems to make it more suitable for real large-scale application scenarios. We propose a novel end-to-end graph recommendation model called the Collaborative Variational Graph Auto-Encoder (CVGA), which uses the information propagation and aggregation paradigms to encode user–item collaborative relationships on the user–item interaction bipartite graph. These relationships are utilized to infer the probability distribution of user behavior for parameter estimation rather than learning user or item embeddings. By doing so, we reconstruct the whole user–item interaction graph according to the known probability distribution in a feasible and elegant manner. From the perspective of the graph auto-encoder, we convert the graph recommendation task into a graph generation problem and are able to do it with approximately linear time complexity. Extensive experiments on four real-world benchmark datasets demonstrate that CVGA can be trained at a faster speed while maintaining comparable performance over state-of-the-art baselines for graph-based recommendation tasks. Further analysis shows that CVGA can effectively mitigate the data sparsity problem and performs equally well on large-scale datasets.