Lu Bai

Lin Du, Lu Bai, Jincheng Li et al.

Graph Neural Networks (GNNs) have emerged as a dominant paradigm for graph classification. Specifically, most existing GNNs mainly rely on the message passing strategy between neighbor nodes, where the expressivity is limited by the 1-dimensional Weisfeiler-Lehman (1-WL) test. Although a number of k-WL-based GNNs have been proposed to overcome this limitation, their computational cost increases rapidly with k, significantly restricting the practical applicability. Moreover, since the k-WL models mainly operate on node tuples, these k-WL-based GNNs cannot retain fine-grained node- or edge-level semantics required by attribution methods (e.g., Integrated Gradients), leading to the less interpretable problem. To overcome the above shortcomings, in this paper, we propose a novel Line Graph Aggregation Network (LGAN), that constructs a line graph from the induced subgraph centered at each node to perform the higher-order aggregation. We theoretically prove that the LGAN not only possesses the greater expressive power than the 2-WL under injective aggregation assumptions, but also has lower time complexity. Empirical evaluations on benchmarks demonstrate that the LGAN outperforms state-of-the-art k-WL-based GNNs, while offering better interpretability.

Zhuo Xu, Lu Bai, Lixin Cui et al.

Graph Auto-Encoders (GAEs) are powerful tools for graph representation learning. In this paper, we develop a novel Hierarchical Cluster-based GAE (HC-GAE), that can learn effective structural characteristics for graph data analysis. To this end, during the encoding process, we commence by utilizing the hard node assignment to decompose a sample graph into a family of separated subgraphs. We compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. On the other hand, during the decoding process, we adopt the soft node assignment to reconstruct the original graph structure by expanding the coarsened nodes. By hierarchically performing the above compressing procedure during the decoding process as well as the expanding procedure during the decoding process, the proposed HC-GAE can effectively extract bidirectionally hierarchical structural features of the original sample graph. Furthermore, we re-design the loss function that can integrate the information from either the encoder or the decoder. Since the associated graph convolution operation of the proposed HC-GAE is restricted in each individual separated subgraph and cannot propagate the node information between different subgraphs, the proposed HC-GAE can significantly reduce the over-smoothing problem arising in the classical convolution-based GAEs. The proposed HC-GAE can generate effective representations for either node classification or graph classification, and the experiments demonstrate the effectiveness on real-world datasets.

Lixiang Xu, Xianwei Ding, Xin Yuan et al.

Designed to track changes in students' knowledge status and predict their future answers based on students' historical answer records. Current research on KT modeling focuses on predicting future student performance based on existing, unupdated records of student learning interactions. However, these methods ignore distractions in the response process (such as slipping and guessing) and ignore that static cognitive representations are temporary and limited. Most of them assume that there are no distractions during the answering process, and that the recorded representation fully represents the student's understanding and proficiency in knowledge. This can lead to many dissonant and uncoordinated issues in the original record. Therefore, we propose a knowledge-tracking cognitive representation optimization (CRO-KT) model that uses dynamic programming algorithms to optimize the structure of cognitive representation. This ensures that the structure matches the student's cognitive patterns in terms of practice difficulty. In addition, we use a synergistic optimization algorithm to optimize the cognitive representation of sub-target exercises based on the overall picture of exercise responses by considering all exercises with synergistic relationships as one goal. At the same time, the CRO-KT model integrates the relationship embedding learned in the dichotomous graph with the optimized record representation in a weighted manner, which enhances students' cognitive expression ability. Finally, experiments were conducted on three public datasets to verify the effectiveness of the proposed cognitive representation optimization model.

Feifei Qian, Lixin Cui, Ming Li et al.

In this paper, we propose a new model to learn Adaptive Kernel-based Representations (AKBR) for graph classification. Unlike state-of-the-art R-convolution graph kernels that are defined by merely counting any pair of isomorphic substructures between graphs and cannot provide an end-to-end learning mechanism for the classifier, the proposed AKBR approach aims to define an end-to-end representation learning model to construct an adaptive kernel matrix for graphs. To this end, we commence by leveraging a novel feature-channel attention mechanism to capture the interdependencies between different substructure invariants of original graphs. The proposed AKBR model can thus effectively identify the structural importance of different substructures, and compute the R-convolution kernel between pairwise graphs associated with the more significant substructures specified by their structural attentions. Since each row of the resulting kernel matrix can be theoretically seen as the embedding vector of a sample graph, the proposed AKBR model is able to directly employ the resulting kernel matrix as the graph feature matrix and input it into the classifier for classification (i.e., the SoftMax layer), naturally providing an end-to-end learning architecture between the kernel computation as well as the classifier. Experimental results show that the proposed AKBR model outperforms existing state-of-the-art graph kernels and deep learning methods on standard graph benchmarks.

Tiantian He, Yew-Soon Ong, Lu Bai

In this paper, we present Conjoint Attentions (CAs), a class of novel learning-to-attend strategies for graph neural networks (GNNs). Besides considering the layer-wise node features propagated within the GNN, CAs can additionally incorporate various structural interventions, such as node cluster embedding, and higher-order structural correlations that can be learned outside of GNN, when computing attention scores. The node features that are regarded as significant by the conjoint criteria are therefore more likely to be propagated in the GNN. Given the novel Conjoint Attention strategies, we then propose Graph conjoint attention networks (CATs) that can learn representations embedded with significant latent features deemed by the Conjoint Attentions. Besides, we theoretically validate the discriminative capacity of CATs. CATs utilizing the proposed Conjoint Attention strategies have been extensively tested in well-established benchmarking datasets and comprehensively compared with state-of-the-art baselines. The obtained notable performance demonstrates the effectiveness of the proposed Conjoint Attentions.

Yue Wang, Zhuo Xu, Lu Bai et al.

Joint-event-extraction, which extracts structural information (i.e., entities or triggers of events) from unstructured real-world corpora, has attracted more and more research attention in natural language processing. Most existing works do not fully address the sparse co-occurrence relationships between entities and triggers, which loses this important information and thus deteriorates the extraction performance. To mitigate this issue, we first define the joint-event-extraction as a sequence-to-sequence labeling task with a tag set composed of tags of triggers and entities. Then, to incorporate the missing information in the aforementioned co-occurrence relationships, we propose a Cross-Supervised Mechanism (CSM) to alternately supervise the extraction of either triggers or entities based on the type distribution of each other. Moreover, since the connected entities and triggers naturally form a heterogeneous information network (HIN), we leverage the latent pattern along meta-paths for a given corpus to further improve the performance of our proposed method. To verify the effectiveness of our proposed method, we conduct extensive experiments on four real-world datasets as well as compare our method with state-of-the-art methods. Empirical results and analysis show that our approach outperforms the state-of-the-art methods in both entity and trigger extraction.

Lu Bai, Lixin Cui, Edwin R. Hancock

In this paper, we develop a new graph kernel, namely the Hierarchical Transitive-Aligned kernel, by transitively aligning the vertices between graphs through a family of hierarchical prototype graphs. Comparing to most existing state-of-the-art graph kernels, the proposed kernel has three theoretical advantages. First, it incorporates the locational correspondence information between graphs into the kernel computation, and thus overcomes the shortcoming of ignoring structural correspondences arising in most R-convolution kernels. Second, it guarantees the transitivity between the correspondence information that is not available for most existing matching kernels. Third, it incorporates the information of all graphs under comparisons into the kernel computation process, and thus encapsulates richer characteristics. By transductively training the C-SVM classifier, experimental evaluations demonstrate the effectiveness of the new transitive-aligned kernel. The proposed kernel can outperform state-of-the-art graph kernels on standard graph-based datasets in terms of the classification accuracy.

Yue Wang, Chenwei Zhang, Shen Wang et al.

We formalize networks with evolving structures as temporal networks and propose a generative link prediction model, Generative Link Sequence Modeling (GLSM), to predict future links for temporal networks. GLSM captures the temporal link formation patterns from the observed links with a sequence modeling framework and has the ability to generate the emerging links by inferring from the probability distribution on the potential future links. To avoid overfitting caused by treating each link as a unique token, we propose a self-tokenization mechanism to transform each raw link in the network to an abstract aggregation token automatically. The self-tokenization is seamlessly integrated into the sequence modeling framework, which allows the proposed GLSM model to have the generalization capability to discover link formation patterns beyond raw link sequences. We compare GLSM with the existing state-of-art methods on five real-world datasets. The experimental results demonstrate that GLSM obtains future positive links effectively in a generative fashion while achieving the best performance (2-10\% improvements on AUC) among other alternatives.

Lu Bai, Lixin Cui, Lixiang Xu et al.

In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand the structural evolution of the financial networks with time. For a set of time-varying financial networks with each vertex representing the individual time series of a different stock and each edge between a pair of time series representing the absolute value of their Pearson correlation, our start point is to compute the commute time matrix associated with the weighted adjacency matrix of the network structures, where each element of the matrix can be seen as the enhanced correlation value between pairwise stocks. For each network, we show how the commute time matrix allows us to identify a reliable set of dominant correlated time series as well as an associated dominant probability distribution of the stock belonging to this set. Furthermore, we represent each original network as a discrete dominant Shannon entropy time series computed from the dominant probability distribution. With the dominant entropy time series for each pair of financial networks to hand, we develop a similarity measure based on the classical dynamic time warping framework, for analyzing the financial time-varying networks. We show that the proposed similarity measure is positive definite and thus corresponds to a kernel measure on graphs. The proposed kernel bridges the gap between graph kernels and the classical dynamic time warping framework for multiple financial time series analysis. Experiments on time-varying networks extracted through New York Stock Exchange (NYSE) database demonstrate the effectiveness of the proposed approach.

Lu Bail, Lixin Cui, Yuhang Jiao et al.

In this paper, we develop a novel Backtrackless Aligned-Spatial Graph Convolutional Network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed BASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based Graph Convolutional Network (GCN) models, but also bridges the theoretical gap between traditional Convolutional Neural Network (CNN) models and spatially-based GCN models. Furthermore, the proposed BASGCN model can both adaptively discriminate the importance between specified vertices during the convolution process and reduce the notorious tottering problem of existing spatially-based GCNs related to the Weisfeiler-Lehman algorithm, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.

Lu Bai, Lixin Cui, Yue Wang et al.

Feature selection has been proven a powerful preprocessing step for high-dimensional data analysis. However, most state-of-the-art methods tend to overlook the structural correlation information between pairwise samples, which may encapsulate useful information for refining the performance of feature selection. Moreover, they usually consider candidate feature relevancy equivalent to selected feature relevancy, and some less relevant features may be misinterpreted as salient features. To overcome these issues, we propose a new feature selection method using structural correlation between pairwise samples. Our idea is based on converting the original vectorial features into structure-based feature graph representations to incorporate structural relationship between samples, and defining a new evaluation measure to compute the joint significance of pairwise feature combinations in relation to the target feature graph. Furthermore, we formulate the corresponding feature subset selection problem into a least square regression model associated with a fused lasso regularizer to simultaneously maximize the joint relevancy and minimize the redundancy of the selected features. To effectively solve the optimization problem, an iterative algorithm is developed to identify the most discriminative features. Experiments demonstrate the effectiveness of the proposed approach.

Lu Bai, Lixin Cui, Shu Wu et al.

In this paper, we develop a new aligned vertex convolutional network model to learn multi-scale local-level vertex features for graph classification. Our idea is to transform the graphs of arbitrary sizes into fixed-sized aligned vertex grid structures, and define a new vertex convolution operation by adopting a set of fixed-sized one-dimensional convolution filters on the grid structure. We show that the proposed model not only integrates the precise structural correspondence information between graphs but also minimises the loss of structural information residing on local-level vertices. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model.

Lixin Cui, Lu Bai, Zhihong Zhang et al.

Feature selection can efficiently identify the most informative features with respect to the target feature used in training. However, state-of-the-art vector-based methods are unable to encapsulate the relationships between feature samples into the feature selection process, thus leading to significant information loss. To address this problem, we propose a new graph-based structurally interacting elastic net method for feature selection. Specifically, we commence by constructing feature graphs that can incorporate pairwise relationship between samples. With the feature graphs to hand, we propose a new information theoretic criterion to measure the joint relevance of different pairwise feature combinations with respect to the target feature graph representation. This measure is used to obtain a structural interaction matrix where the elements represent the proposed information theoretic measure between feature pairs. We then formulate a new optimization model through the combination of the structural interaction matrix and an elastic net regression model for the feature subset selection problem. This allows us to a) preserve the information of the original vectorial space, b) remedy the information loss of the original feature space caused by using graph representation, and c) promote a sparse solution and also encourage correlated features to be selected. Because the proposed optimization problem is non-convex, we develop an efficient alternating direction multiplier method (ADMM) to locate the optimal solutions. Extensive experiments on various datasets demonstrate the effectiveness of the proposed methods.

Lu Bai, Yuhang Jiao, Luca Rossi et al.

This paper proposes a new Quantum Spatial Graph Convolutional Neural Network (QSGCNN) model that can directly learn a classification function for graphs of arbitrary sizes. Unlike state-of-the-art Graph Convolutional Neural Network (GCNN) models, the proposed QSGCNN model incorporates the process of identifying transitive aligned vertices between graphs, and transforms arbitrary sized graphs into fixed-sized aligned vertex grid structures. In order to learn representative graph characteristics, a new quantum spatial graph convolution is proposed and employed to extract multi-scale vertex features, in terms of quantum information propagation between grid vertices of each graph. Since the quantum spatial convolution preserves the grid structures of the input vertices (i.e., the convolution layer does not change the original spatial sequence of vertices), the proposed QSGCNN model allows to directly employ the traditional convolutional neural network architecture to further learn from the global graph topology, providing an end-to-end deep learning architecture that integrates the graph representation and learning in the quantum spatial graph convolution layer and the traditional convolutional layer for graph classifications. We demonstrate the effectiveness of the proposed QSGCNN model in relation to existing state-of-the-art methods. The proposed QSGCNN model addresses the shortcomings of information loss and imprecise information representation arising in existing GCN models associated with the use of SortPooling or SumPooling layers. Experiments on benchmark graph classification datasets demonstrate the effectiveness of the proposed QSGCNN model.