Graph convolutional networks (GCNs) have gained popularity due to high performance achievable on several downstream tasks including node classification. Several architectural variants of these networks have been proposed and investigated with experimental studies in the literature. Motivated by a recent work on simplifying GCNs, we study the problem of designing other variants and propose a framework to compose networks using building blocks of GCN. The framework offers flexibility to compose and evaluate different networks using feature and/or label propagation networks, linear or non-linear networks, with each composition having different computational complexity. We conduct a detailed experimental study on several benchmark datasets with many variants and present observations from our evaluation. Our empirical experimental results suggest that several newly composed variants are useful alternatives to consider because they are as competitive as, or better than the original GCN.
We present a multi-filtering Graph Convolution Neural Network (GCN) framework for network embedding task. It uses multiple local GCN filters to do feature extraction in every propagation layer. We show this approach could capture different important aspects of node features against the existing attribute embedding based method. We also show that with multi-filtering GCN approach, we can achieve significant improvement against baseline methods when training data is limited. We also perform many empirical experiments and demonstrate the benefit of using multiple filters against single filter as well as most current existing network embedding methods for both the link prediction and node classification tasks.
Network embedding aims to learn low-dimensional representations of nodes while capturing structure information of networks. It has achieved great success on many tasks of network analysis such as link prediction and node classification. Most of existing network embedding algorithms focus on how to learn static homogeneous networks effectively. However, networks in the real world are more complex, e.g., networks may consist of several types of nodes and edges (called heterogeneous information) and may vary over time in terms of dynamic nodes and edges (called evolutionary patterns). Limited work has been done for network embedding of dynamic heterogeneous networks as it is challenging to learn both evolutionary and heterogeneous information simultaneously. In this paper, we propose a novel dynamic heterogeneous network embedding method, termed as DyHATR, which uses hierarchical attention to learn heterogeneous information and incorporates recurrent neural networks with temporal attention to capture evolutionary patterns. We benchmark our method on four real-world datasets for the task of link prediction. Experimental results show that DyHATR significantly outperforms several state-of-the-art baselines.
Network embedding is an effective method to learn low-dimensional representations of nodes, which can be applied to various real-life applications such as visualization, node classification, and link prediction. Although significant progress has been made on this problem in recent years, several important challenges remain, such as how to properly capture temporal information in evolving networks. In practice, most networks are continually evolving. Some networks only add new edges or nodes such as authorship networks, while others support removal of nodes or edges such as internet data routing. If patterns exist in the changes of the network structure, we can better understand the relationships between nodes and the evolution of the network, which can be further leveraged to learn node representations with more meaningful information. In this paper, we propose the Embedding via Historical Neighborhoods Aggregation (EHNA) algorithm. More specifically, we first propose a temporal random walk that can identify relevant nodes in historical neighborhoods which have impact on edge formations. Then we apply a deep learning model which uses a custom attention mechanism to induce node embeddings that directly capture temporal information in the underlying feature representation. We perform extensive experiments on a range of real-world datasets, and the results demonstrate the effectiveness of our new approach in the network reconstruction task and the link prediction task.
Oversmoothing has been assumed to be the major cause of performance drop in deep graph convolutional networks (GCNs). In this paper, we propose a new view that deep GCNs can actually learn to anti-oversmooth during training. This work interprets a standard GCN architecture as layerwise integration of a Multi-layer Perceptron (MLP) and graph regularization. We analyze and conclude that before training, the final representation of a deep GCN does over-smooth, however, it learns anti-oversmoothing during training. Based on the conclusion, the paper further designs a cheap but effective trick to improve GCN training. We verify our conclusions and evaluate the trick on three citation networks and further provide insights on neighborhood aggregation in GCNs.
End-to-end multimodal learning on knowledge graphs has been left largely unaddressed. Instead, most end-to-end models such as message passing networks learn solely from the relational information encoded in graphs' structure: raw values, or literals, are either omitted completely or are stripped from their values and treated as regular nodes. In either case we lose potentially relevant information which could have otherwise been exploited by our learning methods. To avoid this, we must treat literals and non-literals as separate cases. We must also address each modality separately and accordingly: numbers, texts, images, geometries, et cetera. We propose a multimodal message passing network which not only learns end-to-end from the structure of graphs, but also from their possibly divers set of multimodal node features. Our model uses dedicated (neural) encoders to naturally learn embeddings for node features belonging to five different types of modalities, including images and geometries, which are projected into a joint representation space together with their relational information. We demonstrate our model on a node classification task, and evaluate the effect that each modality has on the overall performance. Our result supports our hypothesis that including information from multiple modalities can help our models obtain a better overall performance.
Graph convolutional networks have been successful in addressing graph-based tasks such as semi-supervised node classification. Existing methods use a network structure defined by the user based on experimentation with fixed number of layers and neurons per layer and employ a layer-wise propagation rule to obtain the node embeddings. Designing an automatic process to define a problem-dependant architecture for graph convolutional networks can greatly help to reduce the need for manual design of the structure of the model in the training process. In this paper, we propose a method to automatically build compact and task-specific graph convolutional networks. Experimental results on widely used publicly available datasets show that the proposed method outperforms related methods based on convolutional graph networks in terms of classification performance and network compactness.
Graph Neural Networks (GNNs) have recently been used for node and graph classification tasks with great success, but GNNs model dependencies among the attributes of nearby neighboring nodes rather than dependencies among observed node labels. In this work, we consider the task of inductive node classification using GNNs in supervised and semi-supervised settings, with the goal of incorporating label dependencies. Because current GNNs are not universal (i.e., most-expressive) graph representations, we propose a general collective learning approach to increase the representation power of any existing GNN. Our framework combines ideas from collective classification with self-supervised learning, and uses a Monte Carlo approach to sampling embeddings for inductive learning across graphs. We evaluate performance on five real-world network datasets and demonstrate consistent, significant improvement in node classification accuracy, for a variety of state-of-the-art GNNs.
This paper aims at revisiting Graph Convolutional Neural Networks by bridging the gap between spectral and spatial design of graph convolutions. We theoretically demonstrate some equivalence of the graph convolution process regardless it is designed in the spatial or the spectral domain. The obtained general framework allows to lead a spectral analysis of the most popular ConvGNNs, explaining their performance and showing their limits. Moreover, the proposed framework is used to design new convolutions in spectral domain with a custom frequency profile while applying them in the spatial domain. We also propose a generalization of the depthwise separable convolution framework for graph convolutional networks, what allows to decrease the total number of trainable parameters by keeping the capacity of the model. To the best of our knowledge, such a framework has never been used in the GNNs literature. Our proposals are evaluated on both transductive and inductive graph learning problems. Obtained results show the relevance of the proposed method and provide one of the first experimental evidence of transferability of spectral filter coefficients from one graph to another. Our source codes are publicly available at: https://github.com/balcilar/Spectral-Designed-Graph-Convolutions
Graph convolutional networks (GCNs) have shown promising results in processing graph data by extracting structure-aware features. This gave rise to extensive work in geometric deep learning, focusing on designing network architectures that ensure neuron activations conform to regularity patterns within the input graph. However, in most cases the graph structure is only accounted for by considering the similarity of activations between adjacent nodes, which limits the capabilities of such methods to discriminate between nodes in a graph. Here, we propose to augment conventional GCNs with geometric scattering transforms and residual convolutions. The former enables band-pass filtering of graph signals, thus alleviating the so-called oversmoothing often encountered in GCNs, while the latter is introduced to clear the resulting features of high-frequency noise. We establish the advantages of the presented Scattering GCN with both theoretical results establishing the complementary benefits of scattering and GCN features, as well as experimental results showing the benefits of our method compared to leading graph neural networks for semi-supervised node classification, including the recently proposed GAT network that typically alleviates oversmoothing using graph attention mechanisms.
Variants of Graph Neural Networks (GNNs) for representation learning have been proposed recently and achieved fruitful results in various fields. Among them, Graph Attention Network (GAT) first employs a self-attention strategy to learn attention weights for each edge in the spatial domain. However, learning the attentions over edges can only focus on the local information of graphs and greatly increases the computational costs. In this paper, we first introduce the attention mechanism in the spectral domain of graphs and present Spectral Graph Attention Network (SpGAT) that learns representations for different frequency components regarding weighted filters and graph wavelets bases. In this way, SpGAT can better capture global patterns of graphs in an efficient manner with much fewer learned parameters than that of GAT. Further, to reduce the computational cost of SpGAT brought by the eigen-decomposition, we propose a fast approximation variant SpGAT-Cheby. We thoroughly evaluate the performance of SpGAT and SpGAT-Cheby in semi-supervised node classification tasks and verify the effectiveness of the learned attentions in the spectral domain.
Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction, and graph clustering. However, they expose uncertainty and unreliability against the well-designed inputs, i.e., adversarial examples. Accordingly, a line of studies has emerged for both attack and defense addressed in different graph analysis tasks, leading to the arms race in graph adversarial learning. Despite the booming works, there still lacks a unified problem definition and a comprehensive review. To bridge this gap, we investigate and summarize the existing works on graph adversarial learning tasks systemically. Specifically, we survey and unify the existing works w.r.t. attack and defense in graph analysis tasks, and give appropriate definitions and taxonomies at the same time. Besides, we emphasize the importance of related evaluation metrics, investigate and summarize them comprehensively. Hopefully, our works can provide a comprehensive overview and offer insights for the relevant researchers. Latest advances in graph adversarial learning are summarized in our GitHub repository https://github.com/EdisonLeeeee/Graph-Adversarial-Learning.
We present Karate Club a Python framework combining more than 30 state-of-the-art graph mining algorithms which can solve unsupervised machine learning tasks. The primary goal of the package is to make community detection, node and whole graph embedding available to a wide audience of machine learning researchers and practitioners. We designed Karate Club with an emphasis on a consistent application interface, scalability, ease of use, sensible out of the box model behaviour, standardized dataset ingestion, and output generation. This paper discusses the design principles behind this framework with practical examples. We show Karate Club's efficiency with respect to learning performance on a wide range of real world clustering problems, classification tasks and support evidence with regards to its competitive speed.
Graph autoencoders (GAEs) are powerful tools in representation learning for graph embedding. However, the performance of GAEs is very dependent on the quality of the graph structure, i.e., of the adjacency matrix. In other words, GAEs would perform poorly when the adjacency matrix is incomplete or be disturbed. In this paper, two novel unsupervised graph embedding methods, unsupervised graph embedding via adaptive graph learning (BAGE) and unsupervised graph embedding via variational adaptive graph learning (VBAGE) are proposed. The proposed methods expand the application range of GAEs on graph embedding, i.e, on the general datasets without graph structure. Meanwhile, the adaptive learning mechanism can initialize the adjacency matrix without be affected by the parameter. Besides that, the latent representations are embedded in the laplacian graph structure to preserve the topology structure of the graph in the vector space. Moreover, the adjacency matrix can be self-learned for better embedding performance when the original graph structure is incomplete. With adaptive learning, the proposed method is much more robust to the graph structure. Experimental studies on several datasets validate our design and demonstrate that our methods outperform baselines by a wide margin in node clustering, node classification, and graph visualization tasks.
Knowledge Graphs (KGs) represent real-world noisy raw information in a structured form, capturing relationships between entities. However, for dynamic real-world applications such as social networks, recommender systems, computational biology, relational knowledge representation has emerged as a challenging research problem where there is a need to represent the changing nodes, attributes, and edges over time. The evolution of search engine responses to user queries in the last few years is partly because of the role of KGs such as Google KG. KGs are significantly contributing to various AI applications from link prediction, entity relations prediction, node classification to recommendation and question answering systems. This article is an attempt to summarize the journey of KG for AI.
We study the problem of representation learning in heterogeneous networks. Its unique challenges come from the existence of multiple types of nodes and links, which limit the feasibility of the conventional network embedding techniques. We develop two scalable representation learning models, namely metapath2vec and metapath2vec++. The metapath2vec model formalizes meta-path-based random walks to construct the heterogeneous neighborhood of a node and then leverages a heterogeneous skip-gram model to perform node embeddings. The metapath2vec++ model further enables the simultaneous modeling of structural and semantic correlations in heterogeneous networks. Extensive experiments show that metapath2vec and metapath2vec++ are able to not only outperform state-of-the-art embedding models in various heterogeneous network mining tasks, such as node classification, clustering, and similarity search, but also discern the structural and semantic correlations between diverse network objects.
Unsupervised homogeneous network embedding (NE) represents every vertex of networks into a low-dimensional vector and meanwhile preserves the network information. Adjacency matrices retain most of the network information, and directly charactrize the first-order proximity. In this work, we devote to mining valuable information in adjacency matrices at a deeper level. Under the same objective, many NE methods calculate high-order proximity by the powers of adjacency matrices, which is not accurate and well-designed enough. Instead, we propose to redefine high-order proximity in a more intuitive manner. Besides, we design a novel algorithm for calculation, which alleviates the scalability problem in the field of accurate calculation for high-order proximity. Comprehensive experiments on real-world network datasets demonstrate the effectiveness of our method in downstream machine learning tasks such as network reconstruction, link prediction and node classification.
Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between classes, these methods crucially depend on knowing the compatibility matrix that must be provided by either domain experts or heuristics. Can we instead directly estimate the correct compatibilities from a sparsely labeled graph in a principled and scalable way? We answer this question affirmatively and suggest a method called distant compatibility estimation that works even on extremely sparsely labeled graphs (e.g., 1 in 10,000 nodes is labeled) in a fraction of the time it later takes to label the remaining nodes. Our approach first creates multiple factorized graph representations (with size independent of the graph) and then performs estimation on these smaller graph sketches. We define algebraic amplification as the more general idea of leveraging algebraic properties of an algorithm's update equations to amplify sparse signals. We show that our estimator is by orders of magnitude faster than an alternative approach and that the end-to-end classification accuracy is comparable to using gold standard compatibilities. This makes it a cheap preprocessing step for any existing label propagation method and removes the current dependence on heuristics.
Message passing neural networks have recently evolved into a state-of-the-art approach to representation learning on graphs. Existing methods perform synchronous message passing along all edges in multiple subsequent rounds and consequently suffer from various shortcomings: Propagation schemes are inflexible since they are restricted to $k$-hop neighborhoods and insensitive to actual demands of information propagation. Further, long-range dependencies cannot be modeled adequately and learned representations are based on correlations of fixed locality. These issues prevent existing methods from reaching their full potential in terms of prediction performance. Instead, we consider a novel asynchronous message passing approach where information is pushed only along the most relevant edges until convergence. Our proposed algorithm can equivalently be formulated as a single synchronous message passing iteration using a suitable neighborhood function, thus sharing the advantages of existing methods while addressing their central issues. The resulting neural network utilizes a node-adaptive receptive field derived from meaningful sparse node neighborhoods. In addition, by learning and combining node representations over differently sized neighborhoods, our model is able to capture correlations on multiple scales. We further propose variants of our base model with different inductive bias. Empirical results are provided for semi-supervised node classification on five real-world datasets following a rigorous evaluation protocol. We find that our models outperform competitors on all datasets in terms of accuracy with statistical significance. In some cases, our models additionally provide faster runtime.
To take full advantage of fast-growing unlabeled networked data, this paper introduces a novel self-supervised strategy for graph representation learning by exploiting natural supervision provided by the data itself. Inspired by human social behavior, we assume that the global context of each node is composed of all nodes in the graph since two arbitrary entities in a connected network could interact with each other via paths of varying length. Based on this, we investigate whether the global context can be a source of free and effective supervisory signals for learning useful node representations. Specifically, we randomly select pairs of nodes in a graph and train a well-designed neural net to predict the contextual position of one node relative to the other. Our underlying hypothesis is that the representations learned from such within-graph context would capture the global topology of the graph and finely characterize the similarity and differentiation between nodes, which is conducive to various downstream learning tasks. Extensive benchmark experiments including node classification, clustering, and link prediction demonstrate that our approach outperforms many state-of-the-art unsupervised methods and sometimes even exceeds the performance of supervised counterparts.