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Graph learning methods have been extensively applied in diverse application areas. However, what kind of inherent graph properties e.g. graph proximity, graph structural information has been encoded into graph representation learning for downstream tasks is still under-explored. In this paper, we propose a novel graph probing framework (GraphProbe) to investigate and interpret whether the family of graph learning methods has encoded different levels of knowledge in graph representation learning. Based on the intrinsic properties of graphs, we design three probes to systematically investigate the graph representation learning process from different perspectives, respectively the node-wise level, the path-wise level, and the structural level. We construct a thorough evaluation benchmark with nine representative graph learning methods from random walk based approaches, basic graph neural networks and self-supervised graph methods, and probe them on six benchmark datasets for node classification, link prediction and graph classification. The experimental evaluation verify that GraphProbe can estimate the capability of graph representation learning. Remaking results have been concluded: GCN and WeightedGCN methods are relatively versatile methods achieving better results with respect to different tasks.

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.

Graph Neural Networks (GNNs) are powerful tools for graph classification. One important operation for GNNs is the downsampling or pooling that can learn effective embeddings from the node representations. In this paper, we propose a new hierarchical pooling operation, namely the Edge-Node Attention-based Differentiable Pooling (ENADPool), for GNNs to learn effective graph representations. Unlike the classical hierarchical pooling operation that is based on the unclear node assignment and simply computes the averaged feature over the nodes of each cluster, the proposed ENADPool not only employs a hard clustering strategy to assign each node into an unique cluster, but also compress the node features as well as their edge connectivity strengths into the resulting hierarchical structure based on the attention mechanism after each pooling step. As a result, the proposed ENADPool simultaneously identifies the importance of different nodes within each separated cluster and edges between corresponding clusters, that significantly addresses the shortcomings of the uniform edge-node based structure information aggregation arising in the classical hierarchical pooling operation. Moreover, to mitigate the over-smoothing problem arising in existing GNNs, we propose a Multi-distance GNN (MD-GNN) model associated with the proposed ENADPool operation, allowing the nodes to actively and directly receive the feature information from neighbors at different random walk steps. Experiments demonstrate the effectiveness of the MD-GNN associated with the proposed ENADPool.

Infrared and visible image fusion (IVF) plays an important role in intelligent transportation system (ITS). The early works predominantly focus on boosting the visual appeal of the fused result, and only several recent approaches have tried to combine the high-level vision task with IVF. However, they prioritize the design of cascaded structure to seek unified suitable features and fit different tasks. Thus, they tend to typically bias toward to reconstructing raw pixels without considering the significance of semantic features. Therefore, we propose a novel prior semantic guided image fusion method based on the dual-modality strategy, improving the performance of IVF in ITS. Specifically, to explore the independent significant semantic of each modality, we first design two parallel semantic segmentation branches with a refined feature adaptive-modulation (RFaM) mechanism. RFaM can perceive the features that are semantically distinct enough in each semantic segmentation branch. Then, two pilot experiments based on the two branches are conducted to capture the significant prior semantic of two images, which then is applied to guide the fusion task in the integration of semantic segmentation branches and fusion branches. In addition, to aggregate both high-level semantics and impressive visual effects, we further investigate the frequency response of the prior semantics, and propose a multi-level representation-adaptive fusion (MRaF) module to explicitly integrate the low-frequent prior semantic with the high-frequent details. Extensive experiments on two public datasets demonstrate the superiority of our method over the state-of-the-art image fusion approaches, in terms of either the visual appeal or the high-level semantics.

In this paper, we develop a novel local graph pooling method, namely the Separated Subgraph-based Hierarchical Pooling (SSHPool), for graph classification. We commence by assigning the nodes of a sample graph into different clusters, resulting in a family of separated subgraphs. We individually employ the local graph convolution units as the local structure to further compress each subgraph into a coarsened node, transforming the original graph into a coarsened graph. Since these subgraphs are separated by different clusters and the structural information cannot be propagated between them, the local convolution operation can significantly avoid the over-smoothing problem caused by message passing through edges in most existing Graph Neural Networks (GNNs). By hierarchically performing the proposed procedures on the resulting coarsened graph, the proposed SSHPool can effectively extract the hierarchical global features of the original graph structure, encapsulating rich intrinsic structural characteristics. Furthermore, we develop an end-to-end GNN framework associated with the SSHPool module for graph classification. Experimental results demonstrate the superior performance of the proposed model on real-world datasets.

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.

In this work, we develop an Aligned Entropic Reproducing Kernel (AERK) for graph classification. We commence by performing the Continuous-time Quantum Walk (CTQW) on each graph structure, and computing the Averaged Mixing Matrix (AMM) to describe how the CTQW visit all vertices from a starting vertex. More specifically, we show how this AMM matrix allows us to compute a quantum Shannon entropy for each vertex of a graph. For pairwise graphs, the proposed AERK kernel is defined by computing a reproducing kernel based similarity between the quantum Shannon entropies of their each pair of aligned vertices. The analysis of theoretical properties reveals that the proposed AERK kernel cannot only address the shortcoming of neglecting the structural correspondence information between graphs arising in most existing R-convolution graph kernels, but also overcome the problem of neglecting the structural differences between pairs of aligned vertices arising in existing vertex-based matching kernels. Moreover, unlike existing classical graph kernels that only focus on the global or local structural information of graphs, the proposed AERK kernel can simultaneously capture both global and local structural information through the quantum Shannon entropies, reflecting more precise kernel based similarity measures between pairs of graphs. The above theoretical properties explain the effectiveness of the proposed kernel. The experimental evaluation on standard graph datasets demonstrates that the proposed AERK kernel is able to outperform state-of-the-art graph kernels for graph classification tasks., Comment: Corresponding author: Lu Bai, bailu@bnu.edu.cn; bailucs@cufe.edu.cn

In this paper, we propose a novel graph kernel, namely the Quantum-based Entropic Subtree Kernel (QESK), for Graph Classification. To this end, we commence by computing the Average Mixing Matrix (AMM) of the Continuous-time Quantum Walk (CTQW) evolved on each graph structure. Moreover, we show how this AMM matrix can be employed to compute a series of entropic subtree representations associated with the classical Weisfeiler-Lehman (WL) algorithm. For a pair of graphs, the QESK kernel is defined by computing the exponentiation of the negative Euclidean distance between their entropic subtree representations, theoretically resulting in a positive definite graph kernel. We show that the proposed QESK kernel not only encapsulates complicated intrinsic quantum-based structural characteristics of graph structures through the CTQW, but also theoretically addresses the shortcoming of ignoring the effects of unshared substructures arising in state-of-the-art R-convolution graph kernels. Moreover, unlike the classical R-convolution kernels, the proposed QESK can discriminate the distinctions of isomorphic subtrees in terms of the global graph structures, theoretically explaining the effectiveness. Experiments indicate that the proposed QESK kernel can significantly outperform state-of-the-art graph kernels and graph deep learning methods for graph classification problems.

In this work, we propose a family of novel quantum kernels, namely the Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed graphs. Different from most existing classical graph kernels, the proposed HAQJSK kernels can incorporate hierarchical aligned structure information between graphs and transform graphs of random sizes into fixed-sized aligned graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of vertices and the Hierarchical Transitive Aligned Density Matrix of the Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the resulting HAQJSK kernels are defined by measuring the Quantum Jensen-Shannon Divergence (QJSD) between their transitive aligned graph structures. We show that the proposed HAQJSK kernels not only reflect richer intrinsic global graph characteristics in terms of the CTQW, but also address the drawback of neglecting structural correspondence information arising in most existing R-convolution kernels. Furthermore, unlike the previous Quantum Jensen-Shannon Kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can simultaneously guarantee the properties of permutation invariant and positive definiteness, explaining the theoretical advantages of the HAQJSK kernels. Experiments indicate the effectiveness of the proposed kernels.

To alleviate the challenges of building Knowledge Graphs (KG) from scratch, a more general task is to enrich a KG using triples from an open corpus, where the obtained triples contain noisy entities and relations. It is challenging to enrich a KG with newly harvested triples while maintaining the quality of the knowledge representation. This paper proposes a system to refine a KG using information harvested from an additional corpus. To this end, we formulate our task as two coupled sub-tasks, namely join event extraction (JEE) and knowledge graph fusion (KGF). We then propose a Collaborative Knowledge Graph Fusion Framework to allow our sub-tasks to mutually assist one another in an alternating manner. More concretely, the explorer carries out the JEE supervised by both the ground-truth annotation and an existing KG provided by the supervisor. The supervisor then evaluates the triples extracted by the explorer and enriches the KG with those that are highly ranked. To implement this evaluation, we further propose a Translated Relation Alignment Scoring Mechanism to align and translate the extracted triples to the prior KG. Experiments verify that this collaboration can both improve the performance of the JEE and the KGF., Comment: Under review by IEEE Transactions on Knowledge and Data Engineering (TKDE)

Event extraction, the technology that aims to automatically get the structural information from documents, has attracted more and more attention in many fields. Most existing works discuss this issue with the token-level multi-label classification framework by distinguishing the tokens as different roles while ignoring the writing styles of documents. The writing style is a special way of content organizing for documents and it is relative fixed in documents with a special field (e.g. financial, medical documents, etc.). We argue that the writing style contains important clues for judging the roles for tokens and the ignorance of such patterns might lead to the performance degradation for the existing works. To this end, we model the writing style in documents as a distribution of argument roles, i.e., Role-Rank Distribution, and propose an event extraction model with the Role-Rank Distribution based Supervision Mechanism to capture this pattern through the supervised training process of an event extraction task. We compare our model with state-of-the-art methods on several real-world datasets. The empirical results show that our approach outperforms other alternatives with the captured patterns. This verifies the writing style contains valuable information that could improve the performance of the event extraction task., Comment: This paper has been submitted to Pattern Recognition Letters

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., Comment: Accepted by ICPR 2020

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.

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., Comment: accepted by World Wide Web Journal

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., Comment: Previously, the original version of this manuscript appeared as arXiv:1902.09947v2, that was submitted as a replacement by a mistake. Now, that article has been replaced to correct the error, and this manuscript is distinct from that article

Counterfactual thinking describes a psychological phenomenon that people re-infer the possible results with different solutions about things that have already happened. It helps people to gain more experience from mistakes and thus to perform better in similar future tasks. This paper investigates the counterfactual thinking for agents to find optimal decision-making strategies in multi-agent reinforcement learning environments. In particular, we propose a multi-agent deep reinforcement learning model with a structure which mimics the human-psychological counterfactual thinking process to improve the competitive abilities for agents. To this end, our model generates several possible actions (intent actions) with a parallel policy structure and estimates the rewards and regrets for these intent actions based on its current understanding of the environment. Our model incorporates a scenario-based framework to link the estimated regrets with its inner policies. During the iterations, our model updates the parallel policies and the corresponding scenario-based regrets for agents simultaneously. To verify the effectiveness of our proposed model, we conduct extensive experiments on two different environments with real-world applications. Experimental results show that counterfactual thinking can actually benefit the agents to obtain more accumulative rewards from the environments with fair information by comparing to their opponents while keeping high performing efficiency., Comment: This paper is accepted by ICDM'19 as a short paper

We develop a novel method for measuring the similarity between complete weighted graphs, which are probed by means of discrete-time quantum walks. Directly probing complete graphs using discrete-time quantum walks is intractable due to the cost of simulating the quantum walk. We overcome this problem by extracting a commute-time minimum spanning tree from the complete weighted graph. The spanning tree is probed by a discrete time quantum walk which is initialised using a weighted version of the Perron-Frobenius operator. This naturally encapsulates the edge weight information for the spanning tree extracted from the original graph. For each pair of complete weighted graphs to be compared, we simulate a discrete-time quantum walk on each of the corresponding commute time minimum spanning trees, and then compute the associated density matrices for the quantum walks. The probability of the walk visiting each edge of the spanning tree is given by the diagonal elements of the density matrices. The similarity between each pair of graphs is then computed using either a) the inner product or b) the negative exponential of the Jensen-Shannon divergence between the probability distributions. We show that in both cases the resulting similarity measure is positive definite and therefore corresponds to a kernel on the graphs. We perform a series of experiments on publicly available graph datasets from a variety of different domains, together with time-varying financial networks extracted from data for the New York Stock Exchange. Our experiments demonstrate the effectiveness of the proposed similarity measures.

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., Comment: This is an extension work for journals based on the previous work of arXiv:1904.04238v1

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., Comment: arXiv admin note: text overlap with arXiv:1809.01090

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.

Most recent works model the market structure of the stock market as a correlation network of the stocks. They apply pre-defined patterns to extract correlation information from the time series of stocks. Without considering the influences of the evolving market structure to the market index trends, these methods hardly obtain the market structure models which are compatible with the market principles. Advancements in deep learning have shown their incredible modeling capacity on various finance-related tasks. However, the learned inner parameters, which capture the essence of the finance time series, are not further exploited about their representation in the financial fields. In this work, we model the financial market structure as a deep co-investment network and propose a Deep Co-investment Network Learning (DeepCNL) method. DeepCNL automatically learns deep co-investment patterns between any pairwise stocks, where the rise-fall trends of the market index are used for distance supervision. The learned inner parameters of the trained DeepCNL, which encodes the temporal dynamics of deep co-investment patterns, are used to build the co-investment network between the stocks as the investment structure of the corresponding market. We verify the effectiveness of DeepCNL on the real-world stock data and compare it with the existing methods on several financial tasks. The experimental results show that DeepCNL not only has the ability to better reflect the stock market structure that is consistent with widely-acknowledged financial principles but also is more capable to approximate the investment activities which lead to the stock performance reported in the real news or research reports than other alternatives., Comment: accepted by ICBK 2018

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., Comment: Neurocomputing (Accept/In Press), ISSN: 0925-2312

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.