Graph Kernels: A Survey

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 comprehensive overview of a wide range of graph kernels. Furthermore, we perform an experimental evaluation of several of those kernels on publicly available datasets, and provide a comparative study. Finally, we discuss key applications of graph kernels, and outline some challenges that remain to be addressed.

Predictive modelling of highly multiplexed tumour tissue images by graph neural networks

The progression and treatment response of cancer largely depends on the complex tissue structure that surrounds cancer cells in a tumour, known as the tumour microenvironment (TME). Recent technical advances have led to the development of highly multiplexed imaging techniques such as Imaging Mass Cytometry (IMC), which capture the complexity of the TME by producing spatial tissue maps of dozens of proteins. Combining these multidimensional cell phenotypes with their spatial organization to predict clinically relevant information is a challenging computational task and so far no method has addressed it directly. Here, we propose and evaluate MULTIPLAI, a novel framework to predict clinical biomarkers from IMC data. The method relies on attention-based graph neural networks (GNNs) that integrate both the phenotypic and spatial dimensions of IMC images. In this proof-of-concept study we used MULTIPLAI to predict oestrogen receptor (ER) status, a key clinical variable for breast cancer patients. We trained different architectures of our framework on 240 samples and benchmarked against graph learning via graph kernels. Propagation Attribute graph kernels achieved a class-balanced accuracy of 66.18\% in the development set (N=104) while GNNs achieved a class-balanced accuracy of 90.00\% on the same set when using the best combination of graph convolution and pooling layers. We further validated this architecture in internal (N=112) and external test sets from different institutions (N=281 and N=350), demonstrating the generalizability of the method. Our results suggest that MULTIPLAI captures important TME features with clinical importance. This is the first application of GNNs to this type of data and opens up new opportunities for predictive modelling of highly multiplexed images.

A Comparative Study of Graph Kernels and Clustering Algorithms

Graph kernels have evolved as a promising and popular method for graph clustering over the last decade. In this work, comparative study on the five standard graph kernel techniques for graph clustering has been performed. The graph kernels, namely vertex histogram kernel, shortest path kernel, graphlet kernel, k-step random walk kernel, and Weisfeiler-Lehman kernel have been compared for graph clustering. The clustering methods considered for the kernel comparison are hierarchical, k-means, model-based, fuzzy-based, and self-organizing map clustering techniques. The comparative study of kernel methods over the clustering techniques is performed on MUTAG benchmark dataset. Clustering performance is assessed with internal validation performance parameters such as connectivity, Dunn, and the silhouette index. Finally, the comparative analysis is done to facilitate researchers for selecting the appropriate kernel method for effective graph clustering. The proposed methodology elicits k-step random walk and shortest path kernel have performed best among all graph clustering approaches.