Robust graph convolutional networks with directional graph adversarial training

Graph convolutional networks (GCNs), an emerging type of neural network model on graphs, have presented state-of-the-art performance on the node classification task. However, recent studies show that neural networks are vulnerable to the small but deliberate perturbations on input features. And GCNs could be more sensitive to the perturbations since the perturbations from neighbor nodes exacerbate the impact on a target node through the convolution. Adversarial training (AT) is a regularization technique that has been shown capable of improving the robustness of the model against perturbations on image classification. However, directly adopting AT on GCNs is less effective since AT regards examples as independent of each other and does not consider the impact from connected examples. In this work, we explore AT on graph and propose a graph-specific AT method, Directional Graph Adversarial Training (DGAT), which incorporates the graph structure into the adversarial process and automatically identifies the impact of perturbations from neighbor nodes. Concretely, we consider the impact from the connected nodes to define the neighbor perturbation which restricts the perturbation direction on node features towards their neighbor nodes, and additionally introduce an adversarial regularizer to defend the worst-case perturbations. In this way, DGAT can resist the impact of worst-case adversarial perturbations and reduce the impact of perturbations from neighbor nodes. Extensive experiments demonstrate that DGAT can effectively improve the robustness and generalization performance of GCNs. Specially, GCNs with DGAT can provide better performance when there are rare few labels available for training.

     

基于协作推断的正例未标注图学习算法

针对现有正例未标注图学习方法仅提取节点表征信息、独立推断节点类别的问题,提出了一种基于协作推断分类算法,利用节点之间关联信息来帮助推断未标注节点的标签。首先,采用个性化网页排位算法计算每个节点与全体已知正例节点的关联度。其次,采用一个图神经网络学习节点表征信息,与正例关联度联合构造一个局部分类器,预测未标注节点标签;采用另一个图神经网络获取局部节点标签之间依赖关系,与正例关联度联合构造一个关系分类器,协作更新未标注节点标签。然后,借鉴马尔可夫图神经网络方法交替迭代地训练两者,形成多跳步节点标签之间的协作推断;并且,为有效利用正例与未标注节点训练分类器,提出了混合非负无偏风险评估函数。最后,选择两者中任意一个,预测未标注节点的类别。在真实数据集上的实验结果表明,无论是识别单类别正例还是识别多类别合成正例,所述算法均表现出比其他正例未标注学习方法更佳效果,且对正例先验概率误差表现出更好的鲁棒性。     

一种网页分类中基于图的半指导学习算法*

提出一种基于图的半指导学习算法用于网页分类.采用k近邻算法构建一个带权图,图中节点为已标志或未标志的网页,连接边的权重表示类的传播概率,将网页分类问题形式化为图中类的概率传播.为有效利用图中未标志节点辅助分类,结合网页的内容信息和链接信息计算网页间的链接权重,通过已标志节点,类别信息以一定概率从已标志节点推向未标志节点.实验表明,本文提出的算法能有效改进网页分类结果.     

基于图嵌入与支持向量机的社交网络节点分类方法

针对无属性社交网络的节点分类问题,提出了一种基于图嵌入与支持向量机,利用社交网络中节点之间关系特征,对节点进行分类的方法.首先,通过DeepWalk、LINE等多种图嵌入模型挖掘节点隐含关系特征的同时,将高维的社交网络数据转换为低维embedding向量.其次,提取节点度、聚集系数、PageRank值等特征信息,组合构成节点的特征向量.然后,利用支持向量机构建节点分类预测模型对节点进行分类预测.最后,在三个公开的社交网络数据集上实验,与对比方法相比,提出的方法在社交网络节点分类任务中能取得更好的分类效果.     

利用初始残差和解耦操作的自适应深层图卷积

传统的图卷积网络(GCN)及其很多变体都是在浅层时达到最佳的效果,而没有充分利用图中节点的高阶邻居信息.随后产生的深层图卷积模型可以解决以上问题却又不可避免地产生了过平滑的问题,导致模型无法有效区分图中不同类别的节点.针对此问题,提出了一种利用初始残差和解耦操作的自适应深层图卷积模型ID-AGCN.首先,对节点的表示转...     

一种基于给定目标节点的个性化PageRank算法设计

以往衡量图网络节点重要性时,多基于给定源节点,计算该节点到其余目标节点的个性化PageRank值并推出重要目标节点,运算效率低且存储量大。基于此,提出了一种基于给定目标节点的个性化PageRank算法(TPPR),该算法结合本地更新与优先队列算法,通过计算从所有源节点到给定目标节点的个性化PageRank值来推出重要源节点,相较于传统算法运算精度更高,运行时间大幅减少。     

基于PageRank和谱方法的个性化推荐算法

传统的PageRank推荐算法的可扩展性较差。针对这一问题,提出融合PageRank和谱方法的个性化推荐算法。通过在PageRank算法迭代过程中加入候选集节点数来控制迭代的次数,同时利用阈值来修剪参与迭代的节点个数,从而得到候选节点集;采用谱聚类对候选集进行排序,归一化候选节点邻接矩阵,使用矩阵的特征值与特征向量来评估图中节点与目标节点之间的距离,从而产生最终的推荐列表。实验结果表明,所提推荐算法在保证推荐质量的前提下,提高了处理效率。     

融合全局结构信息的拓扑优化图卷积网络

基于拓扑优化的图卷积网络(TOGCN)是一类图卷积神经网络(GCNN)模型,它通过网络中的辅助信息优化网络拓扑结构,有利于反映节点间的联系程度;然而TOGCN模型仅注重局部节点之间的关联关系,对网络潜在的全局结构信息关注不足.融合全局特征信息,有助于提高模型的性能和处理信息缺失时的鲁棒性.提出了融合全局结构信息的拓扑优...     

Index design and query processing for graph conductance search

Graph conductance queries, also known as personalized PageRank and related to random walks with restarts, were originally proposed to assign a hyperlink-based prestige score to Web pages. More general forms of such queries are also very useful for ranking in entity-relation (ER) graphs used to represent relational, XML and hypertext data. Evaluation of PageRank usually involves a global eigen computation. If the graph is even moderately large, interactive response times may not be possible. Recently, the need for interactive PageRank evaluation has increased. The graph may be fully known only when the query is submitted. Browsing actions of the user may change some inputs to the PageRank computation dynamically. In this paper, we describe a system that analyzes query workloads and the ER graph, invests in limited offline indexing, and exploits those indices to achieve essentially constant-time query processing, even as the graph size scales. Our techniques—data and query statistics collection, index selection and materialization, and query-time index exploitation—have parallels in the extensive relational query optimization literature, but is applied to supporting novel graph data repositories. We report on experiments with five temporal snapshots of the CiteSeer ER graph having 74–702 thousand entity nodes, 0.17–1.16 million word nodes, 0.29–3.26 million edges between entities, and 3.29–32.8 million edges between words and entities. We also used two million actual queries from CiteSeer’s logs. Queries run 3–4 orders of magnitude faster than whole-graph PageRank, the gap growing with graph size. Index size is smaller than a text index. Ranking accuracy is 94–98% with reference to whole-graph PageRank.     

Interpretable learning based Dynamic Graph Convolutional Networks for Alzheimer’s Disease analysis

Graph Convolutional Networks (GCNs) are widely applied in classification tasks by aggregating the neighborhood information of each sample to output robust node embedding. However, conventional GCN methods do not update the graph during the training process so that their effectiveness is always influenced by the quality of the input graph. Moreover, previous GCN methods lack the interpretability to limit their real applications. In this paper, a novel personalized diagnosis technique is proposed for early Alzheimer’s Disease (AD) diagnosis via coupling interpretable feature learning with dynamic graph learning into the GCN architecture. Specifically, the module of interpretable feature learning selects informative features to provide interpretability for disease diagnosis and abandons redundant features to capture inherent correlation of data points. The module of dynamic graph learning adjusts the neighborhood relationship of every data point to output robust node embedding as well as the correlations of all data points to refine the classifier. The GCN module outputs diagnosis results based on the learned inherent graph structure. All three modules are jointly optimized to perform reliable disease diagnosis at an individual level. Experiments demonstrate that our method outputs competitive diagnosis performance as well as provide interpretability for personalized disease diagnosis.     

GPPR：跨域环境下的个性化PageRank算法

个性化PageRank作为大图分析中的的基本算法,在搜索引擎、社交推荐、社区检测等领域具有广泛的应用,一直是研究者们关注的热点问题.现有的分布式个性化PageRank算法均假设所有数据位于同一地理位置,且数据所在的计算节点之间具有相同的网络环境.然而,在现实世界中,这些数据可能分布在跨洲际的多个数据中心中,这些跨域分布（Geo-Distributed）的数据中心之间通过广域网连接,存在网络带宽异构、硬件差异巨大、通信费用高昂等特点.而分布式个性化PageRank算法需要多轮迭代,并在全局图上进行随机游走.因此,现有的分布式个性化PageRank算法不适用于跨域环境.针对此问题,本研究提出了GPPR（Geo-Distributed Personalized PageRank）算法.该算法首先对跨域环境中的大图数据进行预处理,通过采用启发式算法映射图数据,以降低网络带宽异构对算法迭代速度的影响.其次,GPPR改进了随机游走方式,提出了基于概率的push算法,通过减少工作节点之间传输数据的带宽负载,进一步减少算法所需的迭代次数.我们基于Spark框架实现了GPPR算法,并在阿里云中构建真实的跨域环境,在8个开源大图数据上与现有的多个代表性分布式个性化PageRank算法进行了对比实验.结果显示,GPPR的通信数据量在跨域环境中较其他算法平均减少30%.在算法运行效率方面,GPPR较其他算法平均提升2.5倍.     

基于图编码网络的社交网络节点分类方法

针对如何融合节点自身属性以及网络结构信息实现社交网络节点分类的问题,提出了一种基于图编码网络的社交网络节点分类算法。首先,每个节点向邻域节点传播其携带的信息;其次,每个节点通过神经网络挖掘其与邻域节点之间可能隐含的关系,并且将这些关系进行融合;最后,每个节点根据自身信息以及与邻域节点关系的信息提取更高层次的特征,作为节点的表示,并且根据该表示对节点进行分类。在微博数据集上,与经典的深度随机游走模型、逻辑回归算法有以及最近提出的图卷积网络算法相比,所提算法分类准确率均有大于8%的提升;在DBLP数据集上,与多层感知器相比分类准确率提升4.83%,与图卷积网络相比分类准确率提升0.91%。     

Graph theoretic closure properties of the family of boundary NLC graph languages

Summary Node label controlled (NLC) grammars are graph grammars (operating on node labeled undirected graphs) which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only. They define (possibly infinite) languages of undirected node labeled graphs (or, if we just omit the labels, languages of unlabeled graphs). Boundary NLC (BNLC) grammars are NLC grammars with the property that whenever — in a graph already generated — two nodes may be rewritten, then these nodes are not adjacent. The graph languages generated by this type of grammars are called BNLC languages. The present paper continues the investigations of basic properties of BNLC grammars and languages where the central question is the following: If L is a BNLC language and P is a graph theoretic property, is the set of all graphs from L satisfying P again a BNLC language? We demonstrate that the class of BNLC languages is very stable in the sense that for almost all properties we consider the resulting languages are BNLC. In particular, the above question gets an affirmative answer, if the property P is: being k-colorable, being connected, having a subgraph homeomorphic to a given graph, and being nonplanar.This research was carried out during the second author's stay at the Rijksuniversiteit Leiden, The Netherlands     

结合图自编码器与聚类的半监督表示学习方法

节点标签是复杂网络中广泛存在的监督信息,对网络表示学习具有重要作用。基于此,提出了一种结合图自编码器与聚类的半监督表示学习方法（GAECSRL）。首先,以图卷积网络（GCN）和内积函数分别作为编码器和解码器,并构建图自编码器以形成信息传播框架;然后,在编码器生成的低维表示基础上增加k-means聚类模块,从而使图自编码器的训练过程和节点的类别分布划分形成自监督机制;最后,利用节点标签的判别信息对网络低维表示的类别划分进行指导,将网络表示生成、类别划分以及图自编码器的训练构建在一个统一的优化模型中,并获得融合节点标签信息的有效网络表示结果。在仿真实验中,将GAECSRL用于节点分类和链接预测任务。实验结果表明,相比DeepWalk、node2vec、全局结构信息图表示学习（GraRep）、结构化深度网络嵌入（SDNE）和用数据的转导式或归纳式嵌入预测标签和邻居（Planetoid）,在节点分类任务中GAECSRL的Micro?F1指标提高了0.9~24.46个百分点,Macro?F1指标提高了0.76~24.20个百分点;在链接预测任务中,GAECSRL的AUC指标提高了0.33~9.06个百分点,说明GAECSRL获得的网络表示结果能有效提高节点分类和链接预测任务的性能。     

GPPR: Geo-distributed Personalized PageRank Algorithm

Personalized PageRank, as a basic algorithm in large graph analysis, has a wide range of applications in search engines, social recommendation, community detection, and other fields and it has been a hot problem of interest to researchers. The existing distributed personalized PageRank algorithms assume that all data are located in the same geographic location and the network environment is the same among the computing nodes where the data are located. However, in the real world, these data may be distributed in multiple data centers across continents, and these geo-distributed data centers are connected to each other through WANs, which are characterized by heterogeneous network bandwidth, huge hardware differences, and high communication costs. Moreover, the distributed personalized PageRank algorithm requires multiple iterations and random walk on the global graph. Therefore, the existing distributed personalized PageRank algorithms are not applicable to the geo-distributed environment. To address this problem, the GPPR (Geo-distributed Personalized PageRank) algorithm is proposed in this paper. The algorithm first preprocesses the big graph data in the geo-distributed environment and maps the graph data by using a heuristic algorithm to reduce the impact of network bandwidth heterogeneity on the iteration speed of the algorithm. Secondly, GPPR improves the random walk approach and proposes a probability-based push algorithm to further lower the number of iterations required by the algorithm by reducing the bandwidth load of data transmission between working nodes. We implement the GPPR algorithm based on the Spark framework and build a real geo-distributed environment in AliCloud to conduct experiments comparing the GPPR algorithm with several existing representative distributed personalized PageRank algorithms on eight open-source big graph datasets. The results show that the communication data volume of GPPR is reduced by 30% on average in the geo-distributed environment compared with that of other algorithms. In terms of algorithm running efficiency, GPPR improves by an average 2.5 factor compared with other algorithms.     

Image retrieval based on augmented relational graph representation

The “semantic gap” problem is one of the main difficulties in image retrieval tasks. Semi-supervised learning, typically integrated with the relevance feedback techniques, is an effective method to narrow down the semantic gap. However, in semi-supervised learning, the amount of unlabeled data is usually much greater than that of labeled data. Therefore, the performance of a semi-supervised learning algorithm relies heavily on its effectiveness of using the relationships between the labeled and unlabeled data. This paper proposes a novel algorithm to better explore those relationships by augmenting the relational graph representation built on the entire data set, expected to increase the intra-class weights while decreasing the inter-class weights and linking the potential intra-class data. The augmented relational matrix can be directly used in any semi-supervised learning algorithms. The experimental results in a range of feedback-based image retrieval tasks show that the proposed algorithm not only achieves good generality, but also outperforms other algorithms in the same semi-supervised learning framework.     

自注意力超图池化网络

近年来,将卷积神经网络推广到图数据上的图卷积神经网络引起了广泛关注,主要包括重新定义图的卷积和池化操作.由于图数据只能表达二元关系的局限性,使其在实际应用中表现欠佳.相比之下,超图能够捕获数据的高阶相关性,利用其灵活的超边易于处理复杂的数据表示.然而,现有的超图卷积神经网络还不够成熟,目前尚无有效的超图池化操作.因此,提出了带有自注意机制的超图池化网络,使用超图结构建模,通过引入自注意力的超图卷积操作学习带有高阶数据信息的节点隐藏层特征,再经过超图池化操作选择并保留在结构和内容上的重要节点,进而得到更准确的超图表示.在文本分类、菜肴分类和蛋白质分类任务上的实验结果表明:与目前多种主流方法相比,该方法均取得了更好的效果.     

Drawing maps with advice

We study the problem of the amount of information required to draw a complete or a partial map of a graph with unlabeled nodes and arbitrarily labeled ports. A mobile agent, starting at any node of an unknown connected graph and walking in it, has to accomplish one of the following tasks: draw a complete map of the graph, i.e., find an isomorphic copy of it including port numbering, or draw a partial map, i.e., a spanning tree, again with port numbering. The agent executes a deterministic algorithm and cannot mark visited nodes in any way. None of these map drawing tasks is feasible without any additional information, unless the graph is a tree. Hence we investigate the minimum number of bits of information (minimum size of advice  ) that has to be given to the agent to complete these tasks. It turns out that this minimum size of advice depends on the number n$n$ of nodes or the number m$m$ of edges of the graph, and on a crucial parameter μ$\mu$, called the multiplicity of the graph, which measures the number of nodes that have an identical view of the graph.