How can we augment a dynamic graph for improving the performance of dynamic graph neural networks? Graph augmentation has been widely utilized to boost the learning performance of GNN-based models. However, most existing approaches only enhance spatial structure within an input static graph by transforming the graph, and do not consider dynamics caused by time such as temporal locality, i.e., recent edges are more influential than earlier ones, which remains challenging for dynamic graph augmentation. In this work, we propose TiaRa (Time-aware Random Walk Diffusion), a novel diffusion-based method for augmenting a dynamic graph represented as a discrete-time sequence of graph snapshots. For this purpose, we first design a time-aware random walk proximity so that a surfer can walk along the time dimension as well as edges, resulting in spatially and temporally localized scores. We then derive our diffusion matrices based on the time-aware random walk, and show they become enhanced adjacency matrices that both spatial and temporal localities are augmented. Throughout extensive experiments, we demonstrate that TiaRa effectively augments a given dynamic graph, and leads to significant improvements in dynamic GNN models for various graph datasets and tasks.
Heterogeneous trajectory forecasting is critical for intelligent transportation systems, but it is challenging because of the difficulty of modeling the complex interaction relations among the heterogeneous road agents as well as their agent-environment constraints. In this work, we propose a risk and scene graph learning method for trajectory forecasting of heterogeneous road agents, which consists of a Heterogeneous Risk Graph (HRG) and a Hierarchical Scene Graph (HSG) from the aspects of agent category and their movable semantic regions. HRG groups each kind of road agent and calculates their interaction adjacency matrix based on an effective collision risk metric. HSG of the driving scene is modeled by inferring the relationship between road agents and road semantic layout aligned by the road scene grammar. Based on this formulation, we can obtain effective trajectory forecasting in driving situations, and superior performance to other state-of-the-art approaches is demonstrated by exhaustive experiments on the nuScenes, ApolloScape, and Argoverse datasets.
In graph learning, there have been two predominant inductive biases regarding graph-inspired architectures: On the one hand, higher-order interactions and message passing work well on homophilous graphs and are leveraged by GCNs and GATs. Such architectures, however, cannot easily scale to large real-world graphs. On the other hand, shallow (or node-level) models using ego features and adjacency embeddings work well in heterophilous graphs. In this work, we propose a novel scalable shallow method -- GLINKX -- that can work both on homophilous and heterophilous graphs. GLINKX leverages (i) novel monophilous label propagations, (ii) ego/node features, (iii) knowledge graph embeddings as positional embeddings, (iv) node-level training, and (v) low-dimensional message passing. Formally, we prove novel error bounds and justify the components of GLINKX. Experimentally, we show its effectiveness on several homophilous and heterophilous datasets.
Multi-agent learning has gained increasing attention to tackle distributed machine learning scenarios under constrictions of data exchanging. However, existing multi-agent learning models usually consider data fusion under fixed and compulsory collaborative relations among agents, which is not as flexible and autonomous as human collaboration. To fill this gap, we propose a distributed multi-agent learning model inspired by human collaboration, in which the agents can autonomously detect suitable collaborators and refer to collaborators' model for better performance. To implement such adaptive collaboration, we use a collaboration graph to indicate the pairwise collaborative relation. The collaboration graph can be obtained by graph learning techniques based on model similarity between different agents. Since model similarity can not be formulated by a fixed graphical optimization, we design a graph learning network by unrolling, which can learn underlying similar features among potential collaborators. By testing on both regression and classification tasks, we validate that our proposed collaboration model can figure out accurate collaborative relationship and greatly improve agents' learning performance.
Heterogeneous graph neural network has unleashed great potential on graph representation learning and shown superior performance on downstream tasks such as node classification and clustering. Existing heterogeneous graph learning networks are primarily designed to either rely on pre-defined meta-paths or use attention mechanisms for type-specific attentive message propagation on different nodes/edges, incurring many customization efforts and computational costs. To this end, we design a relation-centered Pooling and Convolution for Heterogeneous Graph learning Network, namely PC-HGN, to enable relation-specific sampling and cross-relation convolutions, from which the structural heterogeneity of the graph can be better encoded into the embedding space through the adaptive training process. We evaluate the performance of the proposed model by comparing with state-of-the-art graph learning models on three different real-world datasets, and the results show that PC-HGN consistently outperforms all the baseline and improves the performance maximumly up by 17.8%.
Fault diagnostics are extremely important to decide proper actions toward fault isolation and system restoration. The growing integration of inverter-based distributed energy resources imposes strong influences on fault detection using traditional overcurrent relays. This paper utilizes emerging graph learning techniques to build a new temporal recurrent graph neural network models for fault diagnostics. The temporal recurrent graph neural network structures can extract the spatial-temporal features from data of voltage measurement units installed at the critical buses. From these features, fault event detection, fault type/phase classification, and fault location are performed. Compared with previous works, the proposed temporal recurrent graph neural networks provide a better generalization for fault diagnostics. Moreover, the proposed scheme retrieves the voltage signals instead of current signals so that there is no need to install relays at all lines of the distribution system. Therefore, the proposed scheme is generalizable and not limited by the number of relays installed. The effectiveness of the proposed method is comprehensively evaluated on the Potsdam microgrid and IEEE 123-node system in comparison with other neural network structures.
Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to estimate the entries of such transition matrices based on the relative weights of edges. However, we are often confronted with incomplete data, which turns the construction of the transition matrix based on a weighted graph into an inference problem. Moreover, we often have access to additional information, which capture topological constraints of the system, i.e. which edges in a weighted graph are (theoretically) possible and which are not, e.g. transportation networks, where we have access to passenger trajectories as well as the physical topology of connections, or a set of social interactions with the underlying social structure. Combining these two different sources of information to infer transition matrices is an open challenge, with implications on the downstream network analysis tasks. Addressing this issue, we show that including knowledge on such topological constraints can improve the inference of transition matrices, especially for small datasets. We derive an analytically tractable Bayesian method that uses repeated interactions and a topological prior to infer transition matrices data-efficiently. We compare it against commonly used frequentist and Bayesian approaches both in synthetic and real-world datasets, and we find that it recovers the transition probabilities with higher accuracy and that it is robust even in cases when the knowledge of the topological constraint is partial. Lastly, we show that this higher accuracy improves the results for downstream network analysis tasks like cluster detection and node ranking, which highlights the practical relevance of our method for analyses of various networked systems.
This paper introduces a novel Framelet Graph approach based on p-Laplacian GNN. The proposed two models, named p-Laplacian undecimated framelet graph convolution (pL-UFG) and generalized p-Laplacian undecimated framelet graph convolution (pL-fUFG) inherit the nature of p-Laplacian with the expressive power of multi-resolution decomposition of graph signals. The empirical study highlights the excellent performance of the pL-UFG and pL-fUFG in different graph learning tasks including node classification and signal denoising.
Existing message passing neural networks for heterogeneous graphs rely on the concepts of meta-paths or meta-graphs due to the intrinsic nature of heterogeneous graphs. However, the meta-paths and meta-graphs need to be pre-configured before learning and are highly dependent on expert knowledge to construct them. To tackle this challenge, we propose a novel concept of meta-node for message passing that can learn enriched relational knowledge from complex heterogeneous graphs without any meta-paths and meta-graphs by explicitly modeling the relations among the same type of nodes. Unlike meta-paths and meta-graphs, meta-nodes do not require any pre-processing steps that require expert knowledge. Going one step further, we propose a meta-node message passing scheme and apply our method to a contrastive learning model. In the experiments on node clustering and classification tasks, the proposed meta-node message passing method outperforms state-of-the-arts that depend on meta-paths. Our results demonstrate that effective heterogeneous graph learning is possible without the need for meta-paths that are frequently used in this field.
Graph few-shot learning is of great importance among various graph learning tasks. Under the few-shot scenario, models are often required to conduct classification given limited labeled samples. Existing graph few-shot learning methods typically leverage Graph Neural Networks (GNNs) and perform classification across a series of meta-tasks. Nevertheless, these methods generally rely on the original graph (i.e., the graph that the meta-task is sampled from) to learn node representations. Consequently, the graph structure used in each meta-task is identical. Since the class sets are different across meta-tasks, node representations should be learned in a task-specific manner to promote classification performance. Therefore, to adaptively learn node representations across meta-tasks, we propose a novel framework that learns a task-specific structure for each meta-task. To handle the variety of nodes across meta-tasks, we extract relevant nodes and learn task-specific structures based on node influence and mutual information. In this way, we can learn node representations with the task-specific structure tailored for each meta-task. We further conduct extensive experiments on five node classification datasets under both single- and multiple-graph settings to validate the superiority of our framework over the state-of-the-art baselines. Our code is provided at https://github.com/SongW-SW/GLITTER.
Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within graph learning processes. This paper therefore addresses this issue by proposing a flexible algorithmic framework for graph learning under low-rank structural constraints on the covariance matrix. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution (a generalization of Gaussian graphical models to possibly heavy-tailed distributions), where the covariance matrix is optionally constrained to be structured as low-rank plus diagonal (low-rank factor model). The resolution of this class of problems is then tackled with Riemannian optimization, where we leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models. Numerical experiments on real-world data sets illustrate the effectiveness of the proposed approach.
Graph Neural Networks (GNNs) perform well in community detection and molecule classification. Counterfactual Explanations (CE) provide counter-examples to overcome the transparency limitations of black-box models. Due to the growing attention in graph learning, we focus on the concepts of CE for GNNs. We analysed the SoA to provide a taxonomy, a uniform notation, and the benchmarking datasets and evaluation metrics. We discuss fourteen methods, their evaluation protocols, twenty-two datasets, and nineteen metrics. We integrated the majority of methods into the GRETEL library to conduct an empirical evaluation to understand their strengths and pitfalls. We highlight open challenges and future work.
Bundle Recommendation (BR) aims at recommending bundled items on online content or e-commerce platform, such as song lists on a music platform or book lists on a reading website. Several graph based models have achieved state-of-the-art performance on BR task. But their performance is still sub-optimal, since the data sparsity problem tends to be more severe in real bundle recommendation scenarios, which limits graph-based models from more sufficient learning. In this paper, we propose a novel graph learning paradigm called Counterfactual Learning for Bundle Recommendation (CLBR) to mitigate the impact of data sparsity problem and improve bundle recommendation. Our paradigm consists of two main parts: counterfactual data augmentation and counterfactual constraint. The main idea of our paradigm lies in answering the counterfactual questions: "What would a user interact with if his/her interaction history changes?" "What would a user interact with if the bundle-item affiliation relations change?" In counterfactual data augmentation, we design a heuristic sampler to generate counterfactual graph views for graph-based models, which has better noise controlling than the stochastic sampler. We further propose counterfactual loss to constrain model learning for mitigating the effects of residual noise in augmented data and achieving more sufficient model optimization. Further theoretical analysis demonstrates the rationality of our design. Extensive experiments of BR models applied with our paradigm on two real-world datasets are conducted to verify the effectiveness of the paradigm.
Message passing neural networks (MPNNs) have become a dominant flavor of graph neural networks (GNNs) in recent years. Yet, MPNNs come with notable limitations; namely, they are at most as powerful as the 1-dimensional Weisfeiler-Leman (1-WL) test in distinguishing graphs in a graph isomorphism testing frame-work. To this end, researchers have drawn inspiration from the k-WL hierarchy to develop more expressive GNNs. However, current k-WL-equivalent GNNs are not practical for even small values of k, as k-WL becomes combinatorially more complex as k grows. At the same time, several works have found great empirical success in graph learning tasks without highly expressive models, implying that chasing expressiveness with a coarse-grained ruler of expressivity like k-WL is often unneeded in practical tasks. To truly understand the expressiveness-complexity tradeoff, one desires a more fine-grained ruler, which can more gradually increase expressiveness. Our work puts forth such a proposal: Namely, we first propose the (k, c)(<=)-SETWL hierarchy with greatly reduced complexity from k-WL, achieved by moving from k-tuples of nodes to sets with <=k nodes defined over <=c connected components in the induced original graph. We show favorable theoretical results for this model in relation to k-WL, and concretize it via (k, c)(<=)-SETGNN, which is as expressive as (k, c)(<=)-SETWL. Our model is practical and progressively-expressive, increasing in power with k and c. We demonstrate effectiveness on several benchmark datasets, achieving several state-of-the-art results with runtime and memory usage applicable to practical graphs. We open source our implementation at https://github.com/LingxiaoShawn/KCSetGNN.
Cognitive diagnosis is a fundamental yet critical research task in the field of intelligent education, which aims to discover the proficiency level of different students on specific knowledge concepts. Despite the effectiveness of existing efforts, previous methods always considered the mastery level on the whole students, so they still suffer from the Long Tail Effect. A large number of students who have sparse data are performed poorly in the model. To relieve the situation, we proposed a Self-supervised Cognitive Diagnosis (SCD) framework which leverages the self-supervised manner to assist the graph-based cognitive diagnosis, then the performance on those students with sparse data can be improved. Specifically, we came up with a graph confusion method that drops edges under some special rules to generate different sparse views of the graph. By maximizing the consistency of the representation on the same node under different views, the model could be more focused on long-tailed students. Additionally, we proposed an importance-based view generation rule to improve the influence of long-tailed students. Extensive experiments on real-world datasets show the effectiveness of our approach, especially on the students with sparse data.
Natural Language Processing and Machine Learning have considerably advanced Computational Literary Studies. Similarly, the construction of co-occurrence networks of literary characters, and their analysis using methods from social network analysis and network science, have provided insights into the micro- and macro-level structure of literary texts. Combining these perspectives, in this work we study character networks extracted from a text corpus of J.R.R. Tolkien's Legendarium. We show that this perspective helps us to analyse and visualise the narrative style that characterises Tolkien's works. Addressing character classification, embedding and co-occurrence prediction, we further investigate the advantages of state-of-the-art Graph Neural Networks over a popular word embedding method. Our results highlight the large potential of graph learning in Computational Literary Studies.
APP-installation information is helpful to describe the user's characteristics. The users with similar APPs installed might share several common interests and behave similarly in some scenarios. In this work, we learn a user embedding vector based on each user's APP-installation information. Since the user APP-installation embedding is learnable without dependency on the historical intra-APP behavioral data of the user, it complements the intra-APP embedding learned within each specific APP. Thus, they considerably help improve the effectiveness of the personalized advertising in each APP, and they are particularly beneficial for the cold start of the new users in the APP. In this paper, we formulate the APP-installation user embedding learning into a bipartite graph embedding problem. The main challenge in learning an effective APP-installation user embedding is the imbalanced data distribution. In this case, graph learning tends to be dominated by the popular APPs, which billions of users have installed. In other words, some niche/specialized APPs might have a marginal influence on graph learning. To effectively exploit the valuable information from the niche APPs, we decompose the APP-installation graph into a set of subgraphs. Each subgraph contains only one APP node and the users who install the APP. For each mini-batch, we only sample the users from the same subgraph in the training process. Thus, each APP can be involved in the training process in a more balanced manner. After integrating the learned APP-installation user embedding into our online personal advertising platform, we obtained a considerable boost in CTR, CVR, and revenue.
In the age of big data, the demand for hidden information mining in technological intellectual property is increasing in discrete countries. Definitely, a considerable number of graph learning algorithms for technological intellectual property have been proposed. The goal is to model the technological intellectual property entities and their relationships through the graph structure and use the neural network algorithm to extract the hidden structure information in the graph. However, most of the existing graph learning algorithms merely focus on the information mining of binary relations in technological intellectual property, ignoring the higherorder information hidden in non-binary relations. Therefore, a hypergraph neural network model based on dual channel convolution is proposed. For the hypergraph constructed from technological intellectual property data, the hypergraph channel and the line expanded graph channel of the hypergraph are used to learn the hypergraph, and the attention mechanism is introduced to adaptively fuse the output representations of the two channels. The proposed model outperforms the existing approaches on a variety of datasets.
The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID) that employs more complex feature functions, e.g., distances between data points. Yet, many of these approaches are based on empirical observations, cannot cope with the geometric character of contemporary datasets, and do lack an axiomatic foundation. A different approach was proposed by V. Pestov, who links the intrinsic dimension axiomatically to the mathematical concentration of measure phenomenon. First methods to compute this and related notions for ID were computationally intractable for large-scale real-world datasets. In the present work, we derive a computationally feasible method for determining said axiomatic ID functions. Moreover, we demonstrate how the geometric properties of complex data are accounted for in our modeling. In particular, we propose a principle way to incorporate neighborhood information, as in graph data, into the ID. This allows for new insights into common graph learning procedures, which we illustrate by experiments on the Open Graph Benchmark.
In recent years, graph representation learning has gained significant popularity, which aims to generate node embeddings that capture features of graphs. One of the methods to achieve this is employing a technique called random walks that captures node sequences in a graph and then learns embeddings for each node using a natural language processing technique called Word2Vec. These embeddings are then used for deep learning on graph data for classification tasks, such as link prediction or node classification. Prior work operates on pre-collected temporal graph data and is not designed to handle updates on a graph in real-time. Real world graphs change dynamically and their entire temporal updates are not available upfront. In this paper, we propose an end-to-end graph learning pipeline that performs temporal graph construction, creates low-dimensional node embeddings, and trains multi-layer neural network models in an online setting. The training of the neural network models is identified as the main performance bottleneck as it performs repeated matrix operations on many sequentially connected low-dimensional kernels. We propose to unlock fine-grain parallelism in these low-dimensional kernels to boost performance of model training.