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 subgraph kernel based on OT. The positive semidefinite (p.s.d) of graph kernels based on optimal transport distance is not necessarily possible. We further propose regularized graph kernel based on OT where we add the kernel regularization to the original optimal transport distance to obtain p.s.d kernel matrix. We evaluate the proposed graph kernels on several benchmark classification tasks and compare their performance with the existing state-of-the-art graph kernels. In most cases, our proposed graph kernel algorithms outperform the competing methods.
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）；Artificial Intelligence Research Institute（人工智能研究所）
We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To resolve this issue, we introduce kernel weak quadratic costs. We show that they provide improved theoretical guarantees and practical performance. We test NOT with kernel costs on the unpaired image-to-image translation task.
Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）；Microsoft IDC（微软IDC）
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing statistical OT as that of learning the transport plan's kernel mean embedding from sample based estimates of marginal embeddings. The proposed estimator controls overfitting by employing maximum mean discrepancy based regularization, which is complementary to $ϕ$-divergence (entropy) based regularization popularly employed in existing estimators. A key result is t…
Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL, and increase the computational complexity. To improve the accuracy of function approximation and reduce the computational complexity, the present paper studies data-driven selection of kernels from the dictionary that provide satisfactory function approximations. Specifically, based on the similarities among kernels, the novel framework constructs and refines …
Bosch Center for Artificial Intelligence（博世人工智能中心）
Despite recent advances in automated machine learning, model selection is still a complex and computationally intensive process. For Gaussian processes (GPs), selecting the kernel is a crucial task, often done manually by the expert. Additionally, evaluating the model selection criteria for Gaussian processes typically scales cubically in the sample size, rendering kernel search particularly computationally expensive. We propose a novel, efficient search method through a general, structured kernel space. Previous methods solved this task via Bayesian optimization and relied on measuring the di…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutions to the problem and has revamped its practical applications in machine learning. In this paper, we exploit the widely used kernel methods and provide a family of provably positive definite kernels based on the Sliced Wasserstein distance and demonstrate the benefits of these ke…
A novel algorithm is proposed to solve the sample-based optimal transport problem. An adversarial formulation of the push-forward condition uses a test function built as a convolution between an adaptive kernel and an evolving probability distribution $ν$ over a latent variable $b$. Approximating this convolution by its simulation over evolving samples $b^i(t)$ of $ν$, the parameterization of the test function reduces to determining the flow of these samples. This flow, discretized over discrete time steps $t_n$, is built from the composition of elementary maps. The optimal transport also foll…
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective kernel function by appropriate regularization based on graph smoothness. We show that the resulting optimization problem is shown to be convex and pro- pose an accelerated projected gradient descent based solution. Simulation results using real-world graph signals show efficiency…
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Seoul National University College of Medicine（首尔大学医学院）
Deconvolution microscopy has been extensively used to improve the resolution of the wide-field fluorescent microscopy, but the performance of classical approaches critically depends on the accuracy of a model and optimization algorithms. Recently, the convolutional neural network (CNN) approaches have been studied as a fast and high performance alternative. Unfortunately, the CNN approaches usually require matched high resolution images for supervised training. In this paper, we present a novel unsupervised cycle-consistent generative adversarial network (cycleGAN) with a linear blur kernel, w…
LIGM, Université Gustave Eiffel, CNRS（古斯塔夫·埃菲尔大学 LIGM 实验室，法国国家科学研究中心）；INRIA Paris（法国国家信息与自动化研究所巴黎中心）；ENS - Département d’Informatique de l’École Normale Supérieure（巴黎高等师范学院计算机科学系）；PSL Research University（巴黎文理研究大学）
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the object of interest for applications such as generative modeling is the underlying optimal transport map. Hence, computational and statistical guarantees need to be obtained for the estimated maps themselves. In this paper, we propose the first tractable algorithm for which the statistical $L^2$ error on the maps nearly matches the existing minimax lower-bounds…
NICTA（澳大利亚国家信息与通信技术研究院）；University of Cambridge（剑桥大学）
We present a unified framework to study graph kernels, special cases of which include the random walk graph kernel \citep{GaeFlaWro03,BorOngSchVisetal05}, marginalized graph kernel \citep{KasTsuIno03,KasTsuIno04,MahUedAkuPeretal04}, and geometric kernel on graphs \citep{Gaertner02}. Through extensions of linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) and reduction to a Sylvester equation, we construct an algorithm that improves the time complexity of kernel computation from $O(n^6)$ to $O(n^3)$. When the graphs are sparse, conjugate gradient solvers or fixed-point iterations bring …
Center for Machine Learning, Sankt Augustin（机器学习中心，圣奥古斯丁）
The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering graph filtrations: Using meaningful orders on the set of edges, which allow to construct a sequence of nested graphs, we can consider a graph at multiple granularities. For one thing, this provides access to features on different levels of resolution. Furthermore, rather than to simply compare frequencies of features in graphs, it allows for their comparison …
Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer vision and graphics. In this paper, we present extensions of graph kernels for point clouds, which allow to use kernel methods for such ob jects as shapes, line drawings, or any three-dimensional point clouds. In order to design rich and numerically efficient kernels with as few free parameters as possible, we use kernels between covariance matrices and their…
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…
Columbia University（哥伦比亚大学）；Carnegie Mellon University（卡内基梅隆大学）；Adobe Research（Adobe 研究院）；Princeton University（普林斯顿大学）；Duke University（杜克大学）
Many deep learning tasks have to deal with graphs (e.g., protein structures, social networks, source code abstract syntax trees). Due to the importance of these tasks, people turned to Graph Neural Networks (GNNs) as the de facto method for learning on graphs. GNNs have become widely applied due to their convincing performance. Unfortunately, one major barrier to using GNNs is that GNNs require substantial time and resources to train. Recently, a new method for learning on graph data is Graph Neural Tangent Kernel (GNTK) [Du, Hou, Salakhutdinov, Poczos, Wang and Xu 19]. GNTK is an application …
École Polytechnique（巴黎综合理工学院）；Athens University of Economics and Business（雅典经济与商业大学）
Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage approach decouples data representation from learning, which is suboptimal. On the other hand, Convolutional Neural Networks (CNNs) have the capability to learn their own features directly from the raw data during training. Unfortunately, they cannot handle irregular data such as graphs. We address this challenge by using graph kernels to embed meaningful local neig…
University of Bonn（波恩大学）；Fraunhofer IAIS（弗劳恩霍夫智能分析与信息系统研究所）
The Weisfeiler-Lehman graph kernels are among the most prevalent graph kernels due to their remarkable time complexity and predictive performance. Their key concept is based on an implicit comparison of neighborhood representing trees with respect to equality (i.e., isomorphism). This binary valued comparison is, however, arguably too rigid for defining suitable similarity measures over graphs. To overcome this limitation, we propose a generalization of Weisfeiler-Lehman graph kernels which takes into account the similarity between trees rather than equality. We achieve this using a specifical…
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）
A commonly used paradigm for representing graphs is to use a vector that contains normalized frequencies of occurrence of certain motifs or sub-graphs. This vector representation can be used in a variety of applications, such as, for computing similarity between graphs. The graphlet kernel of Shervashidze et al. [32] uses induced sub-graphs of k nodes (christened as graphlets by Przulj [28]) as motifs in the vector representation, and computes the kernel via a dot product between these vectors. One can easily show that this is a valid kernel between graphs. However, such a vector representatio…
With the recent rise in the amount of structured data available, there has been considerable interest in methods for machine learning with graphs. Many of these approaches have been kernel methods, which focus on measuring the similarity between graphs. These generally involving measuring the similarity of structural elements such as walks or paths. Borgwardt and Kriegel proposed the all-paths kernel but emphasized that it is NP-hard to compute and infeasible in practice, favouring instead the shortest-path kernel. In this paper, we introduce a new algorithm for computing the all-paths kernel …
The University of Tokyo（东京大学）；Kyoto University（京都大学）；Alato University（阿尔托大学）
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 agen…
Multi-Relation Graph-Kernel Strengthen Network for Graph-Level Clustering
Hainan University（海南大学）；Northeast Normal University（东北师范大学）；Hebei University of Technology（河北工业大学）；University of Chinese Academy of Science（中国科学院大学）；Hubei University（湖北大学）；The Australian National University（澳大利亚国立大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；Southeast University（东南大学）
University of Notre Dame（圣母大学）；Case Western Reserve University（凯斯西储大学）；Emory University（埃默里大学）
Graph neural networks (GNNs) have demonstrated great success in representation learning for graph-structured data. The layer-wise graph convolution in GNNs is shown to be powerful at capturing graph topology. During this process, GNNs are usually guided by pre-defined kernels such as Laplacian matrix, adjacency matrix, or their variants. However, the adoptions of pre-defined kernels may restrain the generalities to different graphs: mismatch between graph and kernel would entail sub-optimal performance. For example, GNNs that focus on low-frequency information may not achieve satisfactory perf…
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…
Université Paul Sabatier（保罗·萨巴捷大学）；Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Institut de Recherche en Informatique de Toulouse（图卢兹计算机科学研究所）
We present a novel kernel over the space of probability measures based on the dual formulation of optimal regularized transport. We propose an Hilbertian embedding of the space of probabilities using their Sinkhorn potentials, which are solutions of the dual entropic relaxed optimal transport between the probabilities and a reference measure $\mathcal{U}$. We prove that this construction enables to obtain a valid kernel, by using the Hilbert norms. We prove that the kernel enjoys theoretical properties such as universality and some invariances, while still being computationally feasible. Moreo…
While state-of-the-art kernels for graphs with discrete labels scale well to graphs with thousands of nodes, the few existing kernels for graphs with continuous attributes, unfortunately, do not scale well. To overcome this limitation, we present hash graph kernels, a general framework to derive kernels for graphs with continuous attributes from discrete ones. The idea is to iteratively turn continuous attributes into discrete labels using randomized hash functions. We illustrate hash graph kernels for the Weisfeiler-Lehman subtree kernel and for the shortest-path kernel. The resulting novel g…
Tokyo Institute of Technology（东京工业大学）；Chalmers University of Technology（查尔姆斯理工大学）
We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification problem, we consider the task of classifying random graphs from two well-known families, by the number of clusters they contain. We verify empirically that the generalized shortest path kernel outperforms the original shortest path kernel on a number of datasets. We give a theoretical analysis for explaining our experimental results. In particular, we estimate …
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
This paper establishes rates of universal approximation for the shallow neural tangent kernel (NTK): network weights are only allowed microscopic changes from random initialization, which entails that activations are mostly unchanged, and the network is nearly equivalent to its linearization. Concretely, the paper has two main contributions: a generic scheme to approximate functions with the NTK by sampling from transport mappings between the initial weights and their desired values, and the construction of transport mappings via Fourier transforms. Regarding the first contribution, the proof …
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We describe and categorize graph kernels based on properties inherent to their design, such as the nature of their extracted graph features, their method of computation and their applicability to problems in practice. In an extensive experimental evaluation, we study the classification accuracy of a large suite of graph kernels on established benchmarks as wel…
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 grap…
IBM Research（IBM研究院）；CMU（卡内基梅隆大学）；WUSTL（华盛顿大学圣路易斯分校）；GMU（乔治梅森大学）；UDEL（特拉华大学）；Huawei（华为）
Graph kernels are widely used for measuring the similarity between graphs. Many existing graph kernels, which focus on local patterns within graphs rather than their global properties, suffer from significant structure information loss when representing graphs. Some recent global graph kernels, which utilizes the alignment of geometric node embeddings of graphs, yield state-of-the-art performance. However, these graph kernels are not necessarily positive-definite. More importantly, computing the graph kernel matrix will have at least quadratic {time} complexity in terms of the number and the s…
Graph kernels have recently emerged as a promising approach for tackling the graph similarity and learning tasks at the same time. In this paper, we propose a general framework for designing graph kernels. The proposed framework capitalizes on the well-known message passing scheme on graphs. The kernels derived from the framework consist of two components. The first component is a kernel between vertices, while the second component is a kernel between graphs. The main idea behind the proposed framework is that the representations of the vertices are implicitly updated using an iterative proced…
Graph-structured data arise in wide applications, such as computer vision, bioinformatics, and social networks. Quantifying similarities among graphs is a fundamental problem. In this paper, we develop a framework for computing graph kernels, based on return probabilities of random walks. The advantages of our proposed kernels are that they can effectively exploit various node attributes, while being scalable to large datasets. We conduct extensive graph classification experiments to evaluate our graph kernels. The experimental results show that our graph kernels significantly outperform exist…
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…
Beijing Normal University（北京师范大学）；Central University of Finance and Economics（中央财经大学）；University of York（约克大学）
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 re…
ETH Zurich（苏黎世联邦理工学院）；Swiss Institute of Bioinformatics（瑞士生物信息学研究所）
Graph-structured data are an integral part of many application domains, including chemoinformatics, computational biology, neuroimaging, and social network analysis. Over the last two decades, numerous graph kernels, i.e. kernel functions between graphs, have been proposed to solve the problem of assessing the similarity between graphs, thereby making it possible to perform predictions in both classification and regression settings. This manuscript provides a review of existing graph kernels, their applications, software plus data resources, and an empirical comparison of state-of-the-art grap…
École Polytechnique（巴黎综合理工学院）；École des Ponts（巴黎高科路桥学院）；Université Gustave Eiffel（古斯塔夫·埃菲尔大学）；CNRS（法国国家科学研究中心）
Graph kernels have attracted a lot of attention during the last decade, and have evolved into a rapidly developing branch of learning on structured data. During the past 20 years, the considerable research activity that occurred in the field resulted in the development of dozens of graph kernels, each focusing on specific structural properties of graphs. Graph kernels have proven successful in a wide range of domains, ranging from social networks to bioinformatics. The goal of this survey is to provide a unifying view of the literature on graph kernels. In particular, we present a comprehensiv…
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…
Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take global graph propertiesinto account may not scale well to large graph databases. Here we propose to start exploring the space between local and global graph kernels, striking the balance between both worlds. Specifically, we introduce a novel graph kernel based on the $k$-dimensional Weisfeiler-Lehman algorithm. Unfortunately, the $k$-dimensional Weisfeiler-…
We propose a new graph kernel for graph classification and comparison using Ollivier Ricci curvature. The Ricci curvature of an edge in a graph describes the connectivity in the local neighborhood. An edge in a densely connected neighborhood has positive curvature and an edge serving as a local bridge has negative curvature. We use the edge curvature distribution to form a graph kernel which is then used to compare and cluster graphs. The curvature kernel uses purely the graph topology and thereby works for settings when node attributes are not available.
University of Oxford（牛津大学）；University of Cambridge（剑桥大学）；Man AHL（曼恩AHL公司）；Invenia Labs（Invenia实验室）
Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization framework by treating the graph and feature data as two Hilbert spaces. We also show how numerous kernel-based models on graphs are instances of our design. A kernel defined this way has transductive properties, and this leads to improved ability to learn on fewer training points, as well as better handling of highly non-Euclidean data. We demonstrate these advantag…
In this paper we present a novel graph kernel framework inspired the by the Weisfeiler-Lehman (WL) isomorphism tests. Any WL test comprises a relabelling phase of the nodes based on test-specific information extracted from the graph, for example the set of neighbours of a node. We defined a novel relabelling and derived two kernels of the framework from it. The novel kernels are very fast to compute and achieve state-of-the-art results on five real-world datasets.
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…
We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing graphs as a sequence of kernel feature maps, where each node carries information about local graph substructures. On the one hand, the kernel point of view offers an unsupervised, expressive, and easy-to-regularize data representation, which is useful when limited samples are available. On the other hand, our model can also be trained end-to-end on large-scale da…
The graphlet kernel is a classical method in graph classification. It however suffers from a high computation cost due to the isomorphism test it includes. As a generic proxy, and in general at the cost of losing some information, this test can be efficiently replaced by a user-defined mapping that computes various graph characteristics. In this paper, we propose to leverage kernel random features within the graphlet framework, and establish a theoretical link with a mean kernel metric. If this method can still be prohibitively costly for usual random features, we then incorporate optical rand…
Central University of Finance and Economics（中央财经大学）；Zhejiang Normal University（浙江师范大学）；Beijing Normal University（北京师范大学）；University of York（约克大学）
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…
Rutgers University（罗格斯大学）；University of Delaware（特拉华大学）
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is still ill-posed and the state-of-the-art methods are heavily based on heuristics. Here, we present a novel theoretical kernel-based framework for node classification that can bridge the gap between these two representation learning problems on graphs. Our approach is motivated by graph kernel methodology but extended to learn the node representations capturin…
Amazon（亚马逊）；RIKEN AIP（理化学研究所先进智能项目中心）；Kyoto University（京都大学）；University of Oxford（牛津大学）
Neural architecture search (NAS) automates the design of deep neural networks. One of the main challenges in searching complex and non-continuous architectures is to compare the similarity of networks that the conventional Euclidean metric may fail to capture. Optimal transport (OT) is resilient to such complex structure by considering the minimal cost for transporting a network into another. However, the OT is generally not negative definite which may limit its ability to build the positive-definite kernels required in many kernel-dependent frameworks. Building upon tree-Wasserstein (TW), whi…
University of Electronic Science and Technology of China（电子科技大学）
Constructing the adjacency graph is fundamental to graph-based clustering. Graph learning in kernel space has shown impressive performance on a number of benchmark data sets. However, its performance is largely determined by the chosen kernel matrix. To address this issue, the previous multiple kernel learning algorithm has been applied to learn an optimal kernel from a group of predefined kernels. This approach might be sensitive to noise and limits the representation ability of the consensus kernel. In contrast to existing methods, we propose to learn a low-rank kernel matrix which exploits …
Huazhong University of Science and Technology（华中科技大学）；Nanyang Technological University（南洋理工大学）
Graph convolutional network (GCN) is now an effective tool to deal with non-Euclidean data, such as social networks in social behavior analysis, molecular structure analysis in the field of chemistry, and skeleton-based action recognition. Graph convolutional kernel is one of the most significant factors in GCN to extract nodes' feature, and some improvements of it have reached promising performance theoretically and experimentally. However, there is limited research about how exactly different data types and graph structures influence the performance of these kernels. Most existing methods us…
