Graph Classification Tasks Research Articles

Biogc: A novel framework for biological network classification via machine learning

Biological network classification is an eminently challenging task in the domain of data mining since the networks contain complex structural information. Conventional biochemical experimental methods and the existing intelligent algorithms still suffer from some limitations such as immense experimental cost and inferior accuracy rate. To solve these problems, in this paper, we propose a novel framework for Biological graph classification named Biogc, which is specifically developed to predict the label of both small-scale and large-scale biological network data flexibly and efficiently. Our framework firstly presents a simplified graph kernel method to capture the structural information of each graph. Then, the obtained informative features are adopted to train different scale biological network data-oriented classifiers to construct the prediction model. Extensive experiments on five benchmark biological network datasets on graph classification task show that the proposed model Biogc outperforms the state-of-the-art methods with an accuracy rate of 98.90% on a larger dataset and 99.32% on a smaller dataset.

Learning graph-level representation from local-structural distribution with Graph Neural Networks

Graph Neural Networks has been proved to be successful in learning the latent vector representation for local structures. While applying this technique to some real-world tasks, such as property prediction for molecules, a graph-level representation generator should be required to integrate all these local-structural embeddings. Limited by varying graph scale and the absence of node order, existing graph-level representation generation approaches usually adopt rough ways, e.g., compressing all local-structural embeddings into a single vector, which cannot simultaneously retain both the local- and global-structural information in graph-level representations. To address this problem, this paper introduces a novel and more powerful approach to learn graph-level representation from local-structural distribution. Firstly, our approach employs a batch strategy to discretize the embeddings of local structures by their structural semantics, which can provide interactive information to approximately align the local-structural embeddings for varying graphs. According to Wasserstein metric, the aligned structural information is beneficial to capture the similarity among graphs. Then, our approach further integrates these aligned local-structural embeddings to construct a resolution-controllable structural histogram as the graph-level representation. Without over-compression, more local-structural information can be preserved. The experimental results show that our approach substantially outperformed the baselines on a range of real-world datasets in both graph classification and regression tasks.

Graph classification based on skeleton and component features

Most existing popular methods for learning graph embedding only consider fixed-order global structural features but lack hierarchical representation for structures. To address this weakness, we propose a novel graph embedding algorithm named GraphCSC that realizes classification leveraging skeleton information from anonymous random walks with fixed-order length, and component information derived from subgraphs with different sizes. Two graphs are similar if their skeletons and components are both similar. Thus in our model, we integrate both of them together into embeddings as graph homogeneity characterization. We demonstrate our model on different datasets in comparison with a comprehensive list of up-to-date state-of-the-art baselines, and experiments show that our work is superior in real-world graph classification tasks.

Learning subtree pattern importance for Weisfeiler-Lehman based graph kernels

Graph is an usual representation of relational data, which are ubiquitous in manydomains such as molecules, biological and social networks. A popular approach to learningwith graph structured data is to make use of graph kernels, which measure the similaritybetween graphs and are plugged into a kernel machine such as a support vector machine.Weisfeiler-Lehman (WL) based graph kernels, which employ WL labeling scheme to extract subtree patterns and perform node embedding, are demonstrated to achieve great performance while being efficiently computable. However, one of the main drawbacks of ageneral kernel is the decoupling of kernel construction and learning process. For moleculargraphs, usual kernels such as WL subtree, based on substructures of the molecules, consider all available substructures having the same importance, which might not be suitable inpractice. In this paper, we propose a method to learn the weights of subtree patterns in the framework of WWL kernels, the state of the art method for graph classification task [14]. To overcome the computational issue on large scale data sets, we present an efficient learning algorithm and also derive a generalization gap bound to show its convergence. Finally, through experiments on synthetic and real-world data sets, we demonstrate the effectiveness of our proposed method for learning the weights of subtree patterns.

Predicting anticancer hyperfoods with graph convolutional networks

BackgroundRecent efforts in the field of nutritional science have allowed the discovery of disease-beating molecules within foods based on the commonality of bioactive food molecules to FDA-approved drugs. The pioneering work in this field used an unsupervised network propagation algorithm to learn the systemic-wide effect on the human interactome of 1962 FDA-approved drugs and a supervised algorithm to predict anticancer therapeutics using the learned representations. Then, a set of bioactive molecules within foods was fed into the model, which predicted molecules with cancer-beating potential.The employed methodology consisted of disjoint unsupervised feature generation and classification tasks, which can result in sub-optimal learned drug representations with respect to the classification task. Additionally, due to the disjoint nature of the tasks, the employed approach proved cumbersome to optimize, requiring testing of thousands of hyperparameter combinations and significant computational resources.To overcome the technical limitations highlighted above, we represent each drug as a graph (human interactome) with its targets as binary node features on the graph and formulate the problem as a graph classification task. To solve this task, inspired by the success of graph neural networks in graph classification problems, we use an end-to-end graph neural network model operating directly on the graphs, which learns drug representations to optimize model performance in the prediction of anticancer therapeutics.ResultsThe proposed model outperforms the baseline approach in the anticancer therapeutic prediction task, achieving an F1 score of 67.99%±2.52% and an AUPR of 73.91%±3.49%. It is also shown that the model is able to capture knowledge of biological pathways to predict anticancer molecules based on the molecules’ effects on cancer-related pathways.ConclusionsWe introduce an end-to-end graph convolutional model to predict cancer-beating molecules within food. The introduced model outperforms the existing baseline approach, and shows interpretability, paving the way to the future of a personalized nutritional science approach allowing the development of nutrition strategies for cancer prevention and/or therapeutics.

Graph-based neural network models with multiple self-supervised auxiliary tasks

• Graph-based neural network models exploiting multiple self-supervised auxiliary tasks. • We propose three new self-supervised auxiliary tasks for graph-based neural networks. • Vertex features autoencoding. • Corrupted vertex features reconstruction. • Corrupted vertex embeddings reconstruction. Self-supervised learning is currently gaining a lot of attention, as it allows neural networks to learn robust representations from large quantities of unlabeled data. Additionally, multi-task learning can further improve representation learning by training networks simultaneously on related tasks, leading to significant performance improvements. In this paper, we propose three novel self-supervised auxiliary tasks to train graph-based neural network models in a multi-task fashion. Since Graph Convolutional Networks are among the most promising approaches for capturing relationships among structured data points, we use them as a building block to achieve competitive results on standard semi-supervised graph classification tasks.

Graph characterisation using graphlet-based entropies

Abstract In this paper, we present a general framework to estimate the network entropy that is represented by means of an undirected graph and subsequently employ this framework for graph classification tasks. The proposed framework is based on local information functionals which are defined using induced connected subgraphs of different sizes. These induced subgraphs are termed graphlets. Specifically, we extract the set of all graphlets of a specific sizes and compute the graph entropy using our proposed framework. To classify the network into different categories, we construct a feature vector whose components are obtained by computing entropies of different graphlet sizes. We apply the proposed framework to two different tasks, namely view-based object recognition and biomedical datasets with binary outcomes classification. Finally, we report and compare the classification accuracies of the proposed method and compare against some of the state-of-the-art methods.

Topology-Aware Graph Pooling Networks.

Pooling operations have shown to be effective on computer vision and natural language processing tasks. One challenge of performing pooling operations on graph data is the lack of locality that is not well-defined on graphs. Previous studies used global ranking methods to sample some of the important nodes, but most of them are not able to incorporate graph topology. In this work, we propose the topology-aware pooling (TAP) layer that explicitly considers graph topology. Our TAP layer is a two-stage voting process that selects more important nodes in a graph. It first performs local voting to generate scores for each node by attending each node to its neighboring nodes. The scores are generated locally such that topology information is explicitly considered. In addition, graph topology is incorporated in global voting to compute the importance score of each node globally in the entire graph. Altogether, the final ranking score for each node is computed by combining its local and global voting scores. To encourage better graph connectivity in the sampled graph, we propose to add a graph connectivity term to the computation of ranking scores. Results on graph classification tasks demonstrate that our methods achieve consistently better performance than previous methods.

Graph convolutional neural networks with node transition probability-based message passing and DropNode regularization

Graph convolutional neural networks (GCNNs) have received much attention recently, owing to their capability in handling graph-structured data. Among the existing GCNNs, many methods can be viewed as instances of a neural message passing motif; features of nodes are passed around their neighbors, aggregated and transformed to produce better nodes’ representations. Nevertheless, these methods seldom use node transition probabilities, a measure that has been found useful in exploring graphs. Furthermore, when the transition probabilities are used, their transition direction is often improperly considered in the feature aggregation step, resulting in an inefficient weighting scheme. In addition, although a great number of GCNN models with increasing level of complexity have been introduced, the GCNNs often suffer from over-fitting when being trained on small graphs. Another issue of the GCNNs is over-smoothing, which tends to make nodes’ representations indistinguishable. This work presents a new method to improve the message passing process based on node transition probabilities by properly considering the transition direction, leading to a better weighting scheme in nodes’ features aggregation compared to the existing counterpart. Moreover, we propose a novel regularization method termed DropNode to address the over-fitting and over-smoothing issues simultaneously. DropNode randomly discards part of a graph, thus it creates multiple deformed versions of the graph, leading to data augmentation regularization effect. Additionally, DropNode lessens the connectivity of the graph, mitigating the effect of over-smoothing in deep GCNNs. Extensive experiments on eight benchmark datasets for node and graph classification tasks demonstrate the effectiveness of the proposed methods in comparison with the state of the art.

Toward graph classification on structure property using adaptive motif based on graph convolutional network

Graph convolutional network (GCN) has been widely used in handling various graph data analysis tasks. For graph classification tasks, existing work on graph classification mainly focuses on two aspects of graph similarity: physical structure and practical property. In this paper, we consider the problem of graph classification from a new perspective, namely structural properties. Graph similarity is defined based on structural properties such as maximum clique, minimum vertex coverage, and minimum dominating set of graphs. To capture these structural features, we design an adaptive motif to mine the higher-order connectivity information among nodes. Furthermore, to obtain the unique down-sampling in graph pooling stage, we propose a de-correlation pooling approach. Our extensive experiments on several artificially generated datasets show that our proposed model can effectively classify graphs with similar structural property. It is also experimentally compared with the baseline approach to demonstrate the effectiveness of our adaptive motif GCNs.

Line Graph Neural Networks for Link Prediction.

We consider the graph link prediction task, which is a classic graph analytical problem with many real-world applications. With the advances of deep learning, current link prediction methods commonly compute features from subgraphs centered at two neighboring nodes and use the features to predict the label of the link between these two nodes. In this formalism, a link prediction problem is converted to a graph classification task. In order to extract fixed-size features for classification, graph pooling layers are necessary in the deep learning model, thereby incurring information loss. To overcome this key limitation, we propose to seek a radically different and novel path by making use of the line graphs in graph theory. In particular, each node in a line graph corresponds to a unique edge in the original graph. Therefore, link prediction problems in the original graph can be equivalently solved as a node classification problem in its corresponding line graph, instead of a graph classification task. Experimental results on fourteen datasets from different applications demonstrate that our proposed method consistently outperforms the state-of-the-art methods, while it has fewer parameters and high training efficiency.

Propagation Enhanced Neural Message Passing for Graph Representation Learning

Graph Neural Network (GNN) is capable of applying deep neural networks to graph domains. Recently, Message Passing Neural Networks (MPNNs) have been proposed to generalize several existing graph neural networks into a unified framework. For graph representation learning, MPNNs firstly generate discriminative node representations using the message passing function and then read from the node representation space to generate a graph representation using the readout function. In this paper, we analyze the representation capacity of the MPNNs for aggregating graph information and observe that the existing approaches ignore the self-loop for graph representation learning, leading to limited representation capacity. To alleviate this issue, we introduce a simple yet effective propagation enhanced extension, Self-Connected Neural Message Passing (SC-NMP), which aggregates the node representations of the current step and the graph representation of the previous step. To further improve the information flow, we also propose a Densely Self-Connected Neural Message Passing that connects each layer to every other layer in a feed-forward fashion. Extensive experiments on various benchmark datasets strongly demonstrate the effectiveness, leading to superior performance for graph classification and regression tasks.

Graph U-Nets.

We consider the problem of representation learning for graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied to image pixel-wise prediction tasks, similar methods are lacking for graph data. This is because pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling and unpooling operations. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values. We further propose the gUnpool layer as the inverse operation of the gPool layer. Based on our proposed methods, we develop an encoder-decoder model, known as the graph U-Nets. Experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models. Along this direction, we extend our methods by integrating attention mechanisms. Based on attention operators, we proposed attention-based pooling and unpooling layers, which can better capture graph topology information. The empirical results on graph classification tasks demonstrate the promising capability of our methods.

An End-to-End Multiplex Graph Neural Network for Graph Representation Learning

Research on graph classification tasks based on graph neural networks has attracted wide attention. The graphs to be classified may have various graph sizes (i.e., different numbers of nodes and edges) and have various graph properties (e.g., average node degree, diameter, and clustering coefficient). The diverse property of graphs has imposed significant challenges on existing graph learning techniques since diverse graphs have different best-fit hyperparameters. Consequently, it is unreasonable to learn graph representation from a set of diverse graphs by a unified graph neural network. Inspired by this, we design an end-to-end Multiplex Graph Neural Network (MxGNN) that learns graph representations with multiple GNNs, and combines them with a learnable method. The main challenge lies with the combination of multiple representation results. Our new findings show that the a priori graph properties do have an effect on the quality of representation learning, which can be used to guide the learning. Our experiments on graph classification with multiple data sets show that the performance of MxGNN is better than the existing graph representation learning methods.

NetKI: A kirchhoff index based statistical graph embedding in nearly linear time

Recent advancements in learning from graph-structured data have shown promising results on the graph classification task. However, due to their high time complexities, making them scalable on large graphs, with millions of nodes and edges, remains a challenge. In this paper, we propose NetKI, an algorithm to extract sparse representation from a given graph with n nodes and m edges in O(m∊-2log4n) time. Our approach follows the notion of Kirchhoff index that encodes the structure of the graph by estimating effective resistance - relying on this approach yields nearly linear time graph representation method that allows scalability on sufficiently large graphs. Through extensive experiments, we show that NetKI provides improved results in terms of running time on large networks and the classification accuracy is within range 2% from the state-of-the-art results.

The spring bounces back: introducing the strain elevation tension spring embedding algorithm for network representation

This paper introduces the strain elevation tension spring embedding (SETSe) algorithm. SETSe is a novel graph embedding method that uses a physical model to project feature-rich networks onto a manifold with semi-Euclidean properties. Due to its method, SETSe avoids the tractability issues faced by traditional force-directed graphs, having an iteration time and memory complexity that is linear to the number of edges in the network. SETSe is unusual as an embedding method as it does not reduce dimensionality or explicitly attempt to place similar nodes close together in the embedded space. Despite this, the algorithm outperforms five common graph embedding algorithms, on graph classification and node classification tasks, in low-dimensional space. The algorithm is also used to embed 100 social networks ranging in size from 700 to over 40,000 nodes and up to 1.5 million edges. The social network embeddings show that SETSe provides a more expressive alternative to the popular assortativity metric and that even on large complex networks, SETSe’s classification ability outperforms the naive baseline and the other embedding methods in low-dimensional representation. SETSe is a fast and flexible unsupervised embedding algorithm that integrates node attributes and graph topology to produce interpretable results.

GNEA: A Graph Neural Network with ELM Aggregator for Brain Network Classification

Brain networks provide essential insights into the diagnosis of functional brain disorders, such as Alzheimer’s disease (AD). Many machine learning methods have been applied to learn from brain images or networks in Euclidean space. However, it is still challenging to learn complex network structures and the connectivity of brain regions in non-Euclidean space. To address this problem, in this paper, we exploit the study of brain network classification from the perspective of graph learning. We propose an aggregator based on extreme learning machine (ELM) that boosts the aggregation ability and efficiency of graph convolution without iterative tuning. Then, we design a graph neural network named GNEA (Graph Neural Network with ELM Aggregator) for the graph classification task. Extensive experiments are conducted using a real-world AD detection dataset to evaluate and compare the graph learning performances of GNEA and state-of-the-art graph learning methods. The results indicate that GNEA achieves excellent learning performance with the best graph representation ability in brain network classification applications.

M-Evolve: Structural-Mapping-Based Data Augmentation for Graph Classification

Graph classification, which aims to identify the category labels of graphs, plays a significant role in drug classification, toxicity detection, protein analysis etc. However, the limitation of scale in the benchmark datasets makes it easy for graph classification models to fall into over-fitting and undergeneralization. To improve this, we introduce data augmentation on graphs (i.e. graph augmentation) and present four methods:random mapping, vertex-similarity mapping, motif-random mapping and motif-similarity mapping, to generate more weakly labeled data for small-scale benchmark datasets via heuristic transformation of graph structures. Furthermore, we propose a generic model evolution framework, named M-Evolve, which combines graph augmentation, data filtration and model retraining to optimize pre-trained graph classifiers. Experiments on six benchmark datasets demonstrate that the proposed framework helps existing graph classification models alleviate over-fitting and undergeneralization in the training on small-scale benchmark datasets, which successfully yields an average improvement of 3 - 13% accuracy on graph classification tasks.

Uniform Pooling for Graph Networks

The graph convolution network has received a lot of attention because it extends the convolution to non-Euclidean domains. However, the graph pooling method is still less concerned, which can learn coarse graph embedding to facilitate graph classification. Previous pooling methods were based on assigning a score to each node and then pooling only the highest-scoring nodes, which might throw away whole neighbourhoods of nodes and therefore information. Here, we proposed a novel pooling method UGPool with a new point-of-view on selecting nodes. UGPool learns node scores based on node features and uniformly pools neighboring nodes instead of top nodes in the score-space, resulting in a uniformly coarsened graph. In multiple graph classification tasks, including the protein graphs, the biological graphs and the brain connectivity graphs, we demonstrated that UGPool outperforms other graph pooling methods while maintaining high efficiency. Moreover, we also show that UGPool can be integrated with multiple graph convolution networks to effectively improve performance compared to no pooling.

Second-Order Pooling for Graph Neural Networks.

Graph neural networks have achieved great success in learning node representations for graph tasks such as node classification and link prediction. Graph representation learning requires graph pooling to obtain graph representations from node representations. It is challenging to develop graph pooling methods due to the variable sizes and isomorphic structures of graphs. In this work, we propose to use second-order pooling as graph pooling, which naturally solves the above challenges. In addition, compared to existing graph pooling methods, second-order pooling is able to use information from all nodes and collect second-order statistics, making it more powerful. We show that direct use of second-order pooling with graph neural networks leads to practical problems. To overcome these problems, we propose two novel global graph pooling methods based on second-order pooling; namely, bilinear mapping and attentional second-order pooling. In addition, we extend attentional second-order pooling to hierarchical graph pooling for more flexible use in GNNs. We perform thorough experiments on graph classification tasks to demonstrate the effectiveness and superiority of our proposed methods. Experimental results show that our methods improve the performance significantly and consistently.