A Comprehensive Evaluation of Graph Kernels for Unattributed Graphs.

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 well as new datasets. We compare the performance of popular kernels with several baseline methods and study the effect of applying a Gaussian RBF kernel to the metric induced by a graph kernel. In doing so, we find that simple baselines become competitive after this transformation on some datasets. Moreover, we study the extent to which existing graph kernels agree in their predictions (and prediction errors) and obtain a data-driven categorization of kernels as result. Finally, based on our experimental results, we derive a practitioner’s guide to kernel-based graph classification.

Network Intrusion Detection Systems (NIDSs) are an increasingly important tool for the prevention and mitigation of cyber attacks. Over the past years, a lot of research efforts have aimed at leveraging the increasingly powerful models of Machine Learning (ML) for this purpose. A number of labelled synthetic datasets have been generated and made publicly available by researchers, and they have become the benchmarks via which new ML-based NIDS classifiers are being evaluated. Recently published results show excellent classification performance with these datasets, increasingly approaching 100 percent performance across key evaluation metrics such as Accuracy, F1 score, AUC, etc. Unfortunately, we have not yet seen these excellent academic research results translated into practical NIDS systems with such near-perfect performance. This motivated our research presented in this paper, where we analyse the statistical properties of the benign traffic in three of the more recent and relevant NIDS datasets, (CIC_IDS, UNSW_NB15, TON_IOT), by converting them into a common flow format. As a comparison, we consider two datasets obtained from real-world production networks, one from a university network and one from a medium size Internet Service Provider (ISP). Our results show that the two real-world datasets are quite similar among themselves in regards to most of the considered statistical features. Equally, the three synthetic datasets are also relatively similar within their group. However, and most importantly, our results show a distinct difference of most of the considered statistical features between the three synthetic datasets and the two real-world datasets. Since ML relies on the basic assumption of training and test datasets being sampled from the same distribution, this raises the question of how well the performance results of ML-classifiers trained on the considered synthetic datasets can translate and generalise to real-world networks. We believe this is an interesting and relevant question which provides motivation for further research in this space.

Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these substructures. However, most of the existing graph kernels do not have the property of scale-adaptivity, i.e., they cannot compare graphs at multiple levels of granularities. Many real-world graphs such as molecules exhibit structure at varying levels of granularities. To tackle this problem, we propose a new graph kernel called Tree++ in this paper. At the heart of Tree++ is a graph kernel called the path-pattern graph kernel. The path-pattern graph kernel first builds a truncated BFS tree rooted at each vertex and then uses paths from the root to every vertex in the truncated BFS tree as features to represent graphs. The path-pattern graph kernel can only capture graph similarity at fine granularities. In order to capture graph similarity at coarse granularities, we incorporate a new concept called super path into it. The super path contains truncated BFS trees rooted at the vertices in a path. Our evaluation on a variety of real-world graphs demonstrates that Tree++ achieves the best classification accuracy compared with previous graph kernels.

Background: Linear Discriminant Analysis (LDA) is a powerful and widely used technique for classification with correlated variables. Principal Components (PCs) group these variables into linear combinations and produce independent variables. The LDA on these PC’s may provide better classification accuracy in clinical diagnostics than on usual measurements. Methodology: Two datasets were utilized for demonstration: one from a Sudden Sensorineural Hearing Loss (SSNHL) case-control study and the other from a Gall Bladder (GB) case-control study. Linear Discriminant Analysis (LDA) was conducted on the actual correlated measured variables for group classification, as well as on the derived principal component variables, to compare their classification accuracies. Performance metrics including Sensitivity, Specificity, Positive Predictive Value (PPV), Negative Predictive Value (NPV), Classification Accuracy, and F1 Score were assessed. For validation, a third simulated dataset was employed. Additionally, LDA was performed on each dataset using eigenvectors of the control group applied to the cases and vice versa, revealing a strong agreement in classification as measured by the kappa statistic. Results: When LDA was applied to the actual lipid measurements in the SSNHL dataset, the classification accuracy was 57.2%, and the F1 score was 39.7%. However, when LDA was performed using principal components (PCs), the classification accuracy markedly improved to 99.2%, with an F1 score of 98.5%. Similarly, for the GB cancer dataset, the classification accuracy and F1 score were initially 77.2% and 77.3%, respectively. Upon applying LDA with the PCs, these metrics were significantly enhanced to 98.4% and 98.3%, respectively. For the simulated dataset, both the classification accuracy and F1 score were 99.1%. The study also demonstrated that the classification accuracy and F1 score remained consistent regardless of whether the eigenvectors from the cases or controls were used to classify new subjects (Kappa Statistic = 0.962, P < 0.001). Conclusion: In group separation, utilizing principal components significantly improves classification accuracy and overall performance metrics, outperforming the use of the original correlated predictors.

Semi-supervised learning (SSL), as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data, has been attracting increasing attention in the machine learning community. In particular, the manifold regularization framework has laid solid theoretical foundations for a large family of SSL algorithms, such as Laplacian support vector machine (LapSVM) and Laplacian regularized least squares (LapRLS). However, most of these algorithms are limited to small scale problems due to the high computational cost of the matrix inversion operation involved in the optimization problem. In this paper, we propose a novel framework called Laplacian embedded regression by introducing an intermediate decision variable into the manifold regularization framework. By using ∈-insensitive loss, we obtain the Laplacian embedded support vector regression (LapESVR) algorithm, which inherits the sparse solution from SVR. Also, we derive Laplacian embedded RLS (LapERLS) corresponding to RLS under the proposed framework. Both LapESVR and LapERLS possess a simpler form of a transformed kernel, which is the summation of the original kernel and a graph kernel that captures the manifold structure. The benefits of the transformed kernel are two-fold: (1) we can deal with the original kernel matrix and the graph Laplacian matrix in the graph kernel separately and (2) if the graph Laplacian matrix is sparse, we only need to perform the inverse operation for a sparse matrix, which is much more efficient when compared with that for a dense one. Inspired by kernel principal component analysis, we further propose to project the introduced decision variable into a subspace spanned by a few eigenvectors of the graph Laplacian matrix in order to better reflect the data manifold, as well as accelerate the calculation of the graph kernel, allowing our methods to efficiently and effectively cope with large scale SSL problems. Extensive experiments on both toy and real world data sets show the effectiveness and scalability of the proposed framework.

Effective and accurate diagnosis of Alzheimer's disease (AD), as well as its early stage (mild cognitive impairment, MCI), has attracted more and more attention recently. Researchers have constructed threshold brain function networks and extracted various features for the classification of brain diseases. However, in the construction of the brain function network, the selection of threshold is very important, and the unreasonable setting will seriously affect the final classification results. To address this issue, in this paper, we propose a minimum spanning tree (MST) classification framework to identify Alzheimer's disease (AD), MCI, and normal controls (NCs). The proposed method mainly uses the MST method, graph-based Substructure Pattern mining (gSpan), and graph kernel Principal Component Analysis (graph kernel PCA). Specifically, MST is used to construct the brain functional connectivity network; gSpan, to extract features; and subnetwork selection and graph kernel PCA, to select features. Finally, the support vector machine is used to perform classification. We evaluate our method on MST brain functional networks of 21 AD, 25 MCI, and 22 NC subjects. The experimental results show that our proposed method achieves classification accuracy of 98.3, 91.3, and 77.3%, for MCI vs. NC, AD vs. NC, and AD vs. MCI, respectively. The results show our proposed method can achieve significantly improved classification performance compared to other state-of-the-art methods.

In this paper the use of kernel methods in automatic classification of hierarchical graphs is presented. The classification is used as a basis for evaluation of designs in a computer aided design system. A kernel for hierarchical graphs based on a combination of tree and graph kernels is proposed. Hierarchical graphs-based representation used in design problems is briefly presented. The proposed approach is tested in experiment on a flat layout design task and preliminary result are also presented.

Graph classification is an important problem in many fields, from bioinformatics and neuroscience to computer vision and social network analysis. That said, the task of comparing graphs for the purpose of graph classification faces several major challenges. In particular, an effective graph comparison method must (1) expressively and inductively compare graphs; (2) efficiently compare large graphs; and (3) enable the use of fast machine learning models for graph classification. To address such challenges, we propose Randomized Grid Mapping (RGM), a fast-to-compute feature map that represents a graph via the distribution of its node embeddings in feature space. We justify RGM with close connections to kernel methods: RGM provably approximates the Laplacian kernel mean map and has the multiresolution properties of the pyramid match kernel. We also show that RGM can be extended to incorporate node labels using the Weisfeiler-Lehman framework. Extensive experiments show that graph classification accuracy with RGM feature maps is better than or competitive with many powerful graph kernels, unsupervised graph feature mappings, and deep neural networks. Moreover, comparing graphs based on their node embeddings with RGM is up to an order of magnitude faster than competitive baselines, while maintaining high classification accuracy.

A comprehensive evaluation framework that can assess a wide range of water supply and demand management policy options in terms of economic, social, environmental, risk-based, and functional performance is crucial to ascertain their level of sustainability. However, such a detailed, generic, and holistic policy evaluation framework is not found in the literature. This paper reviews studies to evaluate water supply and/or demand management options conducted during 2000–2016. Primarily, the paper reviews the evaluation criteria used by different studies for decision making given their significant difference and the importance of a comprehensive set of criteria to complete a rigorous evaluation. In addition, a comprehensive set of water supply and demand management options are not considered together for a comparative assessment to prioritise best options for a certain area and time. Further, performance of these options needs to be evaluated for a range of uncertainties arising from changes of spatial and temporal variables of the system. While this paper highlights the important aspects that need to be included in a comprehensive policy evaluation framework, available studies collectively present a rich set of information to support it.

Utilizing domain knowledge to improve the classification of intravenous contrast phase of CT scans

With the development of computer technique, performance evaluation of complex products is playing an increasingly critical role in ensuring product quality and improving development process. An extensible comprehensive performance evaluation framework with the integration of effective group decision-making algorithms could be a supporting tool to achieve an efficient evaluation process and reduce comprehensive evaluation difficulty. This paper aims to provide a evaluation framework with friendly interactive operation and extensive expansibility, which adopts a multi-expert evaluation approach based on fuzzy, analytical hierarchy process (FAHP) and Dempstere–Shafer (DS) theory (FADS) in order to consider experts’ relative importance degree. In addition, an extensible evaluation process and related auxiliary functions are implemented in the framework, including the establishment of an assessment index system, integration and calls of multiple types of testing data preprocessing methods and index assessment methods suitable for small sample data, graphical result display and data analysis, etc. Finally, performance evaluation cases of two models of airborne radar anti-jamming are presented to verify the feasibility and expansibility of our assessment framework. The group decision-making method shows its effectiveness compared with the experimental evaluation results by the FAHP researched method.

This research focuses on rational pesticide design, using graph machine learning to accelerate the development of safer, eco-friendly agrochemicals, inspired by in silico methods in drug discovery. With an emphasis on ecotoxicology, the initial contributions include the creation of ApisTox, the largest curated dataset on pesticide toxicity to honey bees. We conducted a broad evaluation of machine learning (ML) models for molecular graph classification, including molecular fingerprints, graph kernels, GNNs, and pretrained transformers. The results show that methods successful in medicinal chemistry often fail to generalize to agrochemicals, underscoring the need for domain-specific models and benchmarks. Future work will focus on developing a comprehensive benchmarking suite and designing ML models tailored to the unique challenges of pesticide discovery.

In this paper we present a fast subgraph kernel based on Jensen-Shannon divergence and depth-based representations. For graphs with n vertices and m edges, the worst-case time complexity for our kernel is O(n 3 + mn), in contrast to O(n 6) for the classic graph kernel. Key to this efficiency is that we manage to compute the Jensen-Shannon divergence involved in our kernel with O(n 2) operations. This computational strategy enables our subgraph kernel to easily scale up to graphs of reasonably large sizes and thus overcome the size limits arising in state of the art graph kernels. Experiments on standard bioinformatics graph datasets together with graph datasets extracted from images demonstrate the effectiveness and efficiency of our subgraph kernel.KeywordsShannon EntropyShort Path LengthMachine Learn ResearchGraph KernelAlgebraic Graph TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Decoding brain states using backward edge elimination and graph kernels in fMRI connectivity networks

Many practical problems (frequency assignement, register allocation, timetables) may be formulated as graph (vertex-)coloring problems, but finding solutions for them is difficult as long as they are treated in the most general case (where the graph is arbitrary), since vertex coloring has been proved to be NP-complete. The problem becomes much easier to solve if the graph resulting from the modelisation of the practical application belongs to some particular class of graphs, for which solutions to the problem are known. Meyniel graphs form such a class (a fast coloring algorithm can be found in [9]), for which an efficient recognizing algorithm is therefore needed. A graph G=(V,E) is said to be a Meyniel graph if every odd cycle of G on at least five vertices contains at least two chords. Meyniel graphs generalize both i-triangulated and parity graphs, two well known classes of perfect graphs that will be present in our paper in Section 7. In [2], Burlet and Fonlupt propose a characterization of Meyniel graphs which relies on the following property: the class of Meyniel graphs may be obtained from some basic Meyniel graphs using a binary operation called amalgam. Besides the theoretical interest of this result, a practical interest arises because of the polynomial recognition algorithm which can be obtained. Unfortunately, it is quite expensive to verify if a given graph is the amalgam of two graphs (therefore the complexity of the whole algorithm is in O(n7)), and this supports the idea that a new point of view is needed to find a more efficient algorithm. Our approach of Meyniel graphs will be directed through the search of a general structure. Intuitively, a Meyniel graph either will be simple (i.e. with no hole or domino), or will have a skeleton around which the rest of the graph will be regularly organized. As suggested, the first type of Meyniel graphs is simple to identify. For the second type, a deeper analysis is necessary; it yields a characterization theorem, which is used to deduce the O(m2+mn) recognition algorithm.