We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by a flexible scoring scheme comparing vertex and edge attributes by kernels. We show that subgraph matching kernels generalize several known kernels. To compute the kernel we propose a graph-theoretical algorithm inspired by a classical relation between common subgraphs of two graphs and cliques in their product graph observed by Levi (1973). Encouraging experimental results on a classification task of real-world graphs are presented.
In recent years, kernel methods are widespread in tasks of similarity measuring. Specifically, graph kernels are widely used in fields of bioinformatics, chemistry and financial data analysis. However, existing methods, especially entropy based graph kernels are subject to large computational complexity and the negligence of node-level information. In this paper, we propose a novel labeled subgraph entropy graph kernel, which performs well in structural similarity assessment. We design a dynamic programming subgraph enumeration algorithm, which effectively reduces the time complexity. Speciall…
Heterogeneous Attributed Graph Learning via Neighborhood-Aware Star Kernels
Key Laboratory of System Software (Chinese Academy of Sciences)（系统软件重点实验室（中国科学院））；State Key Laboratory of Computer Science（计算机科学国家重点实验室）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Attributed network embedding aims to learn low-dimensional node representations from both network structure and node attributes. Existing methods can be categorized into two groups: (1) the first group learns two separated node representations from network structure and node attribute respectively and concatenates them together; (2) the other group obtains node representations by translating node attributes into network structure or vice versa. However, both groups have their drawbacks. The first group neglects the correlation between network structure and node attributes, while the second gro…
In this paper, we present subgraph2vec, a novel approach for learning latent representations of rooted subgraphs from large graphs inspired by recent advancements in Deep Learning and Graph Kernels. These latent representations encode semantic substructure dependencies in a continuous vector space, which is easily exploited by statistical models for tasks such as graph classification, clustering, link prediction and community detection. subgraph2vec leverages on local information obtained from neighbourhoods of nodes to learn their latent representations in an unsupervised fashion. We demonstr…
TU Dortmund University（多特蒙德工业大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；TU Darmstadt（达姆施塔特工业大学）
Non-linear kernel methods can be approximated by fast linear ones using suitable explicit feature maps allowing their application to large scale problems. We investigate how convolution kernels for structured data are composed from base kernels and construct corresponding feature maps. On this basis we propose exact and approximative feature maps for widely used graph kernels based on the kernel trick. We analyze for which kernels and graph properties computation by explicit feature maps is feasible and actually more efficient. In particular, we derive approximative, explicit feature maps for …
Central University of Finance and Economics（中央财经大学）；University of York（约克大学）
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 correspondenc…
NLPR&CRIPAC, Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所模式识别与智能控制国家重点实验室（NLPR&CRIPAC））；University of Chinese Academy of Sciences（中国科学院大学）；Tencent AI LAB（腾讯人工智能实验室）；Center for Excellence in Brain Science and Intelligence Technology, CAS（中国科学院脑科学与智能技术卓越创新中心）
Given the input graph and its label/property, several key problems of graph learning, such as finding interpretable subgraphs, graph denoising and graph compression, can be attributed to the fundamental problem of recognizing a subgraph of the original one. This subgraph shall be as informative as possible, yet contains less redundant and noisy structure. This problem setting is closely related to the well-known information bottleneck (IB) principle, which, however, has less been studied for the irregular graph data and graph neural networks (GNNs). In this paper, we propose a framework of Gra…
Indian Institute of Space Science and Technology（印度空间科学技术研究院）；Litmus7 Systems Consulting Pvt Ltd（Litmus7系统咨询私人有限公司）
We describe the design of a reproducing kernel suitable for attributed graphs, in which the similarity between the two graphs is defined based on the neighborhood information of the graph nodes with the aid of a product graph formulation. We represent the proposed kernel as the weighted sum of two other kernels of which one is an R-convolution kernel that processes the attribute information of the graph and the other is an optimal assignment kernel that processes label information. They are formulated in such a way that the edges processed as part of the kernel computation have the same neighb…
Carnegie Mellon Uni.（卡内基梅隆大学）；Michigan State Uni.（密歇根州立大学）；Snap Inc.（Snap公司）
Message Passing Neural Networks (MPNNs) are a common type of Graph Neural Network (GNN), in which each node's representation is computed recursively by aggregating representations (messages) from its immediate neighbors akin to a star-shaped pattern. MPNNs are appealing for being efficient and scalable, how-ever their expressiveness is upper-bounded by the 1st-order Weisfeiler-Lehman isomorphism test (1-WL). In response, prior works propose highly expressive models at the cost of scalability and sometimes generalization performance. Our work stands between these two regimes: we introduce a gen…
Department of Computer Science and Technology（计算机科学与技术系）；MIIT Key Laboratory of Pattern Analysis and Machine Intelligence（工业和信息化部模式分析与机器智能重点实验室）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Jiangsu Province（江苏省）
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph hierarchical structure information, we propose pyramid graph kernel based on optimal transport (OT). Each graph is embedded into hierarchical structures of the pyramid. Then, the OT distance is utilized to measure the similarity between graphs in hierarchical structures. We also utilize the OT distance to measure the similarity between subgraphs and propose sub…
Noah’s Ark Lab Paris, Huawei Technologies Ltd（华为技术有限公司诺亚方舟实验室巴黎分部）；London School of Economics（伦敦政治经济学院）
We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where edges are created over time, which induces an order. Combining convolutional subgraph kernels and string kernels, we design new scalable algorithms for generation of explicit graph feature maps using sketching techniques. We obtain precise bounds for the approximation accuracy and computational complexity of the proposed approaches and demonstrate their applica…
Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation learning on graphs in general. As the developed methodologies become more sophisticated, it is important to understand which components of the increasingly complex methods are necessary or most effective. As a first step, we develop a simple yet meaningful graph representation, and explore its effectiveness in graph classification. We test our baseline represen…
We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage early-stage distributions from propagation schemes such as random walks to capture structural information encoded in node labels, attributes, and edge information. This has two benefits. First, off-the-shelf propagation schemes can be used to naturally construct kernels for many graph types, including labeled, partially labeled, unlabeled, directed, and att…
We study large-scale kernel methods for acoustic modeling and compare to DNNs on performance metrics related to both acoustic modeling and recognition. Measuring perplexity and frame-level classification accuracy, kernel-based acoustic models are as effective as their DNN counterparts. However, on token-error-rates DNN models can be significantly better. We have discovered that this might be attributed to DNN's unique strength in reducing both the perplexity and the entropy of the predicted posterior probabilities. Motivated by our findings, we propose a new technique, entropy regularized perp…
Graph kernels are usually defined in terms of simpler kernels over local substructures of the original graphs. Different kernels consider different types of substructures. However, in some cases they have similar predictive performances, probably because the substructures can be interpreted as approximations of the subgraphs they induce. In this paper, we propose to associate to each feature a piece of information about the context in which the feature appears in the graph. A substructure appearing in two different graphs will match only if it appears with the same context in both graphs. We p…
University of Chicago（芝加哥大学）；Argonne National Laboratory（阿贡国家实验室）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
Gaussian processes (GPs) are an attractive class of machine learning models because of their simplicity and flexibility as building blocks of more complex Bayesian models. Meanwhile, graph neural networks (GNNs) emerged recently as a promising class of models for graph-structured data in semi-supervised learning and beyond. Their competitive performance is often attributed to a proper capturing of the graph inductive bias. In this work, we introduce this inductive bias into GPs to improve their predictive performance for graph-structured data. We show that a prominent example of GNNs, the grap…
OmniGraph, a novel representation to support a range of NLP classification tasks, integrates lexical items, syntactic dependencies and frame semantic parses into graphs. Feature engineering is folded into the learning through convolution graph kernel learning to explore different extents of the graph. A high-dimensional space of features includes individual nodes as well as complex subgraphs. In experiments on a text-forecasting problem that predicts stock price change from news for company mentions, OmniGraph beats several benchmarks based on bag-of-words, syntactic dependencies, and semantic…
ETH Zurich（苏黎世联邦理工学院）；SIB Swiss Institute of Bioinformatics（SIB瑞士生物信息学研究所）
Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of the final set of substructures, usually a sum or average, thereby potentially discarding valuable information about the distribution of individual components. Furthermore, only a limited instance of these approaches can be extended to continuously attributed graphs. We propose a novel method that relies on the Wasserstein distance between the node feature vec…
University of Bonn（波恩大学）；University of Vienna（维也纳大学）
We introduce the \emph{temporal graphlet kernel} for classifying dissemination processes in labeled temporal graphs. Such dissemination processes can be spreading (fake) news, infectious diseases, or computer viruses in dynamic networks. The networks are modeled as labeled temporal graphs, in which the edges exist at specific points in time, and node labels change over time. The classification problem asks to discriminate dissemination processes of different origins or parameters, e.g., infectious diseases with different infection probabilities. Our new kernel represents labeled temporal graph…
New York University（纽约大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
The ability to detect and count certain substructures in graphs is important for solving many tasks on graph-structured data, especially in the contexts of computational chemistry and biology as well as social network analysis. Inspired by this, we propose to study the expressive power of graph neural networks (GNNs) via their ability to count attributed graph substructures, extending recent works that examine their power in graph isomorphism testing and function approximation. We distinguish between two types of substructure counting: induced-subgraph-count and subgraph-count, and establish b…
Beihang University（北京航空航天大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Many real-world problems can be represented as graph-based learning problems. In this paper, we propose a novel framework for learning spatial and attentional convolution neural networks on arbitrary graphs. Different from previous convolutional neural networks on graphs, we first design a motif-matching guided subgraph normalization method to capture neighborhood information. Then we implement subgraph-level self-attentional layers to learn different importances from different subgraphs to solve graph classification problems. Analogous to image-based attentional convolution networks that oper…
Beijing Normal University（北京师范大学）；Central University of Finance and Economics（中央财经大学）；Zhejiang Normal University（浙江师范大学）；University of York（约克大学）
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 r…
Graduate School of Fundamental Science and Engineering, WASEDA University（早稻田大学基础理工学研究生院）；Department of Computer Science and Communication Engineering, WASEDA University（早稻田大学计算机科学与通信工程系）
For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems, the graph class depends on not only the topological similarity of the whole graph, but also constituent subgraph patterns. To this end, we propose a novel graph embedding method using a multi-layer adjacent point merging model. This embedding method allows us to extract different subgraph patterns from train-data. Then we present a flexible loss function for …
University of Bucharest（布加勒斯特大学）；The Research Institute University of Bucharest (ICUB)（布加勒斯特大学研究院（ICUB））
In general, anomaly detection is the problem of distinguishing between normal data samples with well defined patterns or signatures and those that do not conform to the expected profiles. Financial transactions, customer reviews, social media posts are all characterized by relational information. In these networks, fraudulent behaviour may appear as a distinctive graph edge, such as spam message, a node or a larger subgraph structure, such as when a group of clients engage in money laundering schemes. Most commonly, these networks are represented as attributed graphs, with numerical features c…
Yale University（耶鲁大学）；IBM T. J. Watson Research Center（IBM T. J. 沃森研究中心）
Graph kernels are historically the most widely-used technique for graph classification tasks. However, these methods suffer from limited performance because of the hand-crafted combinatorial features of graphs. In recent years, graph neural networks (GNNs) have become the state-of-the-art method in downstream graph-related tasks due to their superior performance. Most GNNs are based on Message Passing Neural Network (MPNN) frameworks. However, recent studies show that MPNNs can not exceed the power of the Weisfeiler-Lehman (WL) algorithm in graph isomorphism test. To address the limitations of…
Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；University at Buffalo（布法罗大学）
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric structure, and natural inclusion of uncertainty quantification. Unfortunately, the use of exact GPs is prohibitively expensive for large datasets due to their unfavorable numerical complexity of $O(N^3)$ in computation and $O(N^2)$ in storage. All existing methods addressing this issue utilize some form of approximation -- usually considering subsets of the …
Malware analysis techniques are divided into static and dynamic analysis. Both techniques can be bypassed by circumvention techniques such as obfuscation. In a series of works, the authors have promoted the use of symbolic executions combined with machine learning to avoid such traps. Most of those works rely on natural graph-based representations that can then be plugged into graph-based learning algorithms such as Gspan. There are two main problems with this approach. The first one is in the cost of computing the graph. Indeed, working with graphs requires one to compute and representing the…
Convolutional Neural Networks have become the standard for image classification tasks, however, these architectures are not invariant to translations of the input image. This lack of invariance is attributed to the use of stride which ignores the sampling theorem, and fully connected layers which lack spatial reasoning. We show that stride can greatly benefit translation invariance given that it is combined with sufficient similarity between neighbouring pixels, a characteristic which we refer to as local homogeneity. We also observe that this characteristic is dataset-specific and dictates th…
Filtration-Based Representation Learning for Temporal Graphs
Indian Institute of Science Education and Research Tirupati（印度科学教育与研究学院 Tirupati）；Chennai Mathematical Institute（钦奈数学研究所）；Institut Polytechnique de Paris（巴黎高等技术学院）
