Association for Artificial Intelligence 2021, Jiang, Yuan, Ting, Kai Ming et al. · Underline Science Inc. · 2021
A recent Wasserstein Weisfeiler-Lehman (WWL) Graph Kernel has a distinctive feature: Representing the distribution of Weisfeiler-Lehman (WL)-embedded node vectors of a graph in a histogram that enables a dissimilarity measurement of two graphs using Wasserstein distance. It has been shown to produce better classification accuracy than other graph kernels which do not employ such distribution and Wasserstein distance. This paper introduces an alternative called Isolation Graph Kernel (IGK) that measures the similarity between two attributed graphs. IGK is unique in two aspects among existing graph kernels. First, it is the first graph kernel which employs a distributional kernel in the framework of kernel mean embedding. This avoids the need to use the computationally expensive Wasserstein distance. Second, it is the first graph kernel that incorporates the distribution of attributed nodes (ignoring the edges) in a dataset of graphs. We reveal that this distributional information, extracted in the form of a feature map of Isolation Kernel, is crucial in building an efficient and effective graph kernel. We show that IGK is better than WWL in terms of classification accuracy, and it runs orders of magnitude faster in large datasets when used in the context of SVM classification.
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David Kohan Marzagão, Trung Dong Huynh, Ayah Helal et al. · IEEE Transactions on Knowledge and Data Engineering · 2025
Provenance is a standardised record that describes how entities, activities, and agents have influenced a piece of data; it is commonly represented as graphs with relevant labels on both their nodes and edges. With the growing adoption of provenance in a wide range of application domains, users are increasingly confronted with an abundance of graph data, which may prove challenging to process. Graph kernels, on the other hand, have been successfully used to efficiently analyse graphs. In this paper, we introduce a novel graph kernel called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">provenance kernel</i>, which is inspired by and tailored for provenance data. We employ provenance kernels to classify provenance graphs from three application domains. Our evaluation shows that they perform well in terms of classification accuracy and yield competitive results when compared against existing graph kernel methods and the provenance network analytics method while more efficient in computing time. Moreover, the provenance types used by provenance kernels are a symbolic representation of a tree pattern which can, in turn, be described using the domain-agnostic vocabulary of provenance. Therefore, provenance types thus allow for the creation of explanations of predictive models built on them.
Cited by 1
David Kohan Marzag˜ao (20726219), Trung Dong Huynh (17921012), Aya Helal (20726222) et al. · Figshare · 2025
Provenance is a standardised record that describes how entities, activities, and agents have influenced a piece of data; it is commonly represented as graphs with relevant labels on both their nodes and edges. With the growing adoption of provenance in a wide range of application domains, users are increasingly confronted with an abundance of graph data, which may prove challenging to process. Graph kernels, on the other hand, have been successfully used to efficiently analyse graphs. In this paper, we introduce a novel graph kernel called provenance kernel, which is inspired by and tailored for provenance data. We employ provenance kernels to classify provenance graphs from three application domains. Our evaluation shows that they perform well in terms of classification accuracy and yield competitive results when compared against existing graph kernel methods and the provenance network analytics method while more efficient in computing time. Moreover, the provenance types used by provenance kernels are a symbolic representation of a tree pattern which can, in turn, be described using the domain-agnostic vocabulary of provenance. Therefore, provenance types thus allow for the creation of explanations of predictive models built on them.
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David Kohan Marzagão, Trung Dong Huynh, Ayah Helal et al. · arXiv (Cornell University) · 2020
Provenance is a record that describes how entities, activities, and agents have influenced a piece of data; it is commonly represented as graphs with relevant labels on both their nodes and edges. With the growing adoption of provenance in a wide range of application domains, users are increasingly confronted with an abundance of graph data, which may prove challenging to process. Graph kernels, on the other hand, have been successfully used to efficiently analyse graphs. In this paper, we introduce a novel graph kernel called provenance kernel, which is inspired by and tailored for provenance data. It decomposes a provenance graph into tree-patterns rooted at a given node and considers the labels of edges and nodes up to a certain distance from the root. We employ provenance kernels to classify provenance graphs from three application domains. Our evaluation shows that they perform well in terms of classification accuracy and yield competitive results when compared against existing graph kernel methods and the provenance network analytics method while more efficient in computing time. Moreover, the provenance types used by provenance kernels also help improve the explainability of predictive models built on them.
Cited by 1Open access
Stephen Dokroug Kolog, Jun Wang · SSRN Electronic Journal · 2024
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Runze Yang, Hao Peng, Angsheng Li et al. · IEEE Transactions on Knowledge and Data Engineering · 2024
Graph kernels have been regarded as a successful tool for handling a variety of graph applications since they were proposed. However, most of the proposed graph kernels are based on the R-convolution framework, which decomposes graphs into a set of substructures at the same abstraction level and compares all substructure pairs equally; these methods inherently overlook the utility of the hierarchical structural information embedded in graphs. In this paper, we propose <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</b>ierarchical <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b>bstracting <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</b>raph <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</b>ernels (HAGK), a novel set of graph kernels that compare graphs’ hierarchical substructures to capture and utilize the latent hierarchical structural information fully. Instead of generating non-structural substructures, we reveal each graph’s hierarchical substructures by constructing its <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hierarchical abstracting</i>, specifically, the hierarchically organized nested node sets adhering to the principle of structural entropy minimization. To compare a pair of hierarchical abstractings, we propose two novel substructure matching approaches, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Local Optimal Matching</i> (LOM) and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Priority Ordering Matching</i> (POM), to find appropriate matching between the substructures by different strategies recursively. Extensive experiments demonstrate that the proposed kernels are highly competitive with the existing state-of-the-art graph kernels, and verify that the hierarchical abstracting plays a significant role in the improvement of the kernel performance.
Cited by 4
Liang Zhang, Longqiang Yi, Yu Liu et al. · Pattern Recognition · 2023
Cited by 4
Cao, Yang, Yichuan Deng, Wenyu Jin et al. · arXiv (Cornell University) · 2022
A geometric graph associated with a set of points $P= \{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$ and a fixed kernel function $\mathsf{K}:\mathbb{R}^d\times \mathbb{R}^d\to\mathbb{R}_{\geq 0}$ is a complete graph on $P$ such that the weight of edge $(x_i, x_j)$ is $\mathsf{K}(x_i, x_j)$. We present a fully-dynamic data structure that maintains a spectral sparsifier of a geometric graph under updates that change the locations of points in $P$ one at a time. The update time of our data structure is $n^{o(1)}$ with high probability, and the initialization time is $n^{1+o(1)}$. Under certain assumption, our data structure can be made robust against adaptive adversaries, which makes our sparsifier applicable in iterative optimization algorithms. We further show that the Laplacian matrices corresponding to geometric graphs admit a randomized sketch for maintaining matrix-vector multiplication and projection in $n^{o(1)}$ time, under sparse updates to the query vectors, or under modification of points in $P$.
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Jicong Fan, Zhihao Wu, Zhao Zhang · 2023
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Lixiang Xu, Wei Ge, Feiping Nie et al. · Pattern Recognition · 2026
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Mingxuan Ju, Shifu Hou, Yujie Fan et al. · Proceedings of the AAAI Conference on Artificial Intelligence · 2022
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 performance when high-frequency information is significant for the graphs, and vice versa. To solve this problem, in this paper, we propose a novel framework - i.e., namely Adaptive Kernel Graph Neural Network (AKGNN) - which learns to adapt to the optimal graph kernel in a unified manner at the first attempt. In the proposed AKGNN, we first design a data-driven graph kernel learning mechanism, which adaptively modulates the balance between all-pass and low-pass filters by modifying the maximal eigenvalue of the graph Laplacian. Through this process, AKGNN learns the optimal threshold between high and low frequency signals to relieve the generality problem. Later, we further reduce the number of parameters by a parameterization trick and enhance the expressive power by a global readout function. Extensive experiments are conducted on acknowledged benchmark datasets and promising results demonstrate the outstanding performance of our proposed AKGNN by comparison with state-of-the-art GNNs. The source code is publicly available at: https://github.com/jumxglhf/AKGNN.
Cited by 1Open access
Jun Suzuki, Tsutomu Hirao, Yutaka Sasaki et al. · 2003
This paper proposes the "Hierarchical Directed Acyclic Graph (HDAG) Kernel" for structured natural language data. The HDAG Kernel directly accepts several levels of both chunks and their relations, and then efficiently computes the weighed sum of the number of common attribute sequences of the HDAGs. We applied the proposed method to question classification and sentence alignment tasks to evaluate its performance as a similarity measure and a kernel function. The results of the experiments demonstrate that the HDAG Kernel is superior to other kernel functions and baseline methods.
Cited by 62Open access
Shohei Hido, Hisashi Kashima · 2009
The design of a good kernel is fundamental for knowledge discovery from graph-structured data. Existing graph kernels exploit only limited information about the graph structures but are still computationally expensive. We propose a novel graph kernel based on the structural characteristics of graphs. The key is to represent node labels as binary arrays and characterize each node using logical operations on the label set of the connected nodes. Our kernel has a linear time complexity with respect to the number of nodes times the average number of neighboring nodes in the given graphs. The experimental result shows that the proposed kernel performs comparable and much faster than a state-of-the-art graph kernel for benchmark data sets and shows high scalability for new applications with large graphs.
Cited by 110
Aaron Smalter · KU ScholarWorks (The University of Kansas) · 2008
Graphs are information-rich structures, but their complexity makes them difficult to analyze. Given their broad and powerful representation capacity, the classification of graphs has become an intense area of research. Many established classifiers represent objects with vectors of explicit features. When the number of features grows, however, these vector representations suffer from typical problems of high dimensionality such as overfitting and high computation time. This work instead focuses on using kernel functions to map graphs into implicity defined spaces that avoid the difficulties of vector representations. The introduction of kernel classifiers has kindled great interest in kernel functions for graph data. By using kernels the problem of graph classification changes from finding a good classifier to finding a good kernel function. This work explores several novel uses of kernel functions for graph classification. The first technique is the use of structure based features to add structural information to the kernel function. A strength of this approach is the ability to identify specific structure features that contribute significantly to the classification process. Discriminative structures can then be passed off to domain-specific researchers for additional analysis. The next approach is the use of wavelet functions to represent graph topology as simple real-valued features. This approach achieves order-of-magnitude decreases in kernel computation time by eliminating costly topological comparisons, while retaining competitive classification accuracy. Finally, this work examines the use of even simpler graph representations and their utility for classification. The models produced from the kernel functions presented here yield excellent performance with respect to both efficiency and accuracy, as demonstrated in a variety of experimental studies.
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U Kang, Hanghang Tong, Jimeng Sun · 2012
Random walk graph kernel has been used as an important tool for various data mining tasks including classification and similarity computation. Despite its usefulness, however, it suffers from the expensive computational cost which is at least O(n3) or O(m2) for graphs with n nodes and m edges. In this paper, we propose ARK, a set of fast algorithms for random walk graph kernel computation. ARK is based on the observation that real graphs have much lower intrinsic ranks, compared with the orders of the graphs. ARK exploits the low rank structure to quickly compute random walk graph kernels in O(n2) or O(m) time. Experimental results show that our method is up to 97,865× faster than the existing algorithms, while providing more than 91.3% of the accuracies.
Cited by 120
Hichem Sahbi · HAL (Le Centre pour la Communication Scientifique Directe) · 2021
International audience
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Yannick Kuhar, Uroš Čibej · Proceedings of the International Conference on Information Systems Development · 2024
This paper presents a novel way to conduct machine learning analysis on graphs and empirically evaluates it. We can not perform such analysis on non-fixed length feature vectors, so first, we must find a way to represent graphs as such. We propose a graph kernel based on graph automorphisms, also known as graph symmetries. We then empirically evaluate the classification accuracy of three machine learning algorithms, SVM, Random Forest, and AdaBoost, using this novel graph kernel against two existing graph kernels and a naive baseline. The models reach a higher classification accuracy on some datasets using our Symmetry kernels than the graphlet kernel and Weisfeiler-Lehman kernel despite our kernel constructing far smaller feature vectors than the existing approaches.
Cited by 0
Simon S. Du, Kangcheng Hou, Barnabás Póczos et al. · arXiv (Cornell University) · 2019
While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better practical performance, as GNNs use multi-layer architectures and non-linear activation functions to extract high-order information of graphs as features. However, due to the large number of hyper-parameters and the non-convex nature of the training procedure, GNNs are harder to train. Theoretical guarantees of GNNs are also not well-understood. Furthermore, the expressive power of GNNs scales with the number of parameters, and thus it is hard to exploit the full power of GNNs when computing resources are limited. The current paper presents a new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to infinitely wide multi-layer GNNs trained by gradient descent. GNTKs enjoy the full expressive power of GNNs and inherit advantages of GKs. Theoretically, we show GNTKs provably learn a class of smooth functions on graphs. Empirically, we test GNTKs on graph classification datasets and show they achieve strong performance.
Cited by 74Open access
Lixiang Xu, Jin Peng, Xiaoyi Jiang et al. · Pattern Recognition · 2024
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Yuchen Zhou (1601536), Hongtao Huo (14774084), Zhiwen Hou (14774087) et al. · Figshare · 2023
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