(Hyper)graph Kernels over Simplicial Complexes

Abstract

Graph kernels are one of the mainstream approaches when dealing with measuring similarity between graphs, especially for pattern recognition and machine learning tasks. In turn, graphs gained a lot of attention due to their modeling capabilities for several real-world phenomena ranging from bioinformatics to social network analysis. However, the attention has been recently moved towards hypergraphs, generalization of plain graphs where multi-way relations (other than pairwise relations) can be considered. In this paper, four (hyper)graph kernels are proposed and their efficiency and effectiveness are compared in a twofold fashion. First, by inferring the simplicial complexes on the top of underlying graphs and by performing a comparison among 18 benchmark datasets against state-of-the-art approaches; second, by facing a real-world case study (i.e., metabolic pathways classification) where input data are natively represented by hypergraphs. With this work, we aim at fostering the extension of graph kernels towards hypergraphs and, more in general, bridging the gap between structural pattern recognition and the domain of hypergraphs.

On Information Granulation via Data Clustering for Granular Computing-Based Pattern Recognition: A Graph Embedding Case Study

“…P a t h s S t r a t i f i e d P a t h s C l i q u e s S t r a t i f i e d C l i q u e s In Table 3, we finally show a brief comparison against current approaches for graph classification. Competitors span a variety of techniques, including classifiers working on the top of GEDs [49,67], kernel methods [68][69][70][71] and several embedding techniques [68,72,73], including Granular Computing-based [32,74] and those based on neural networks and deep learning [75][76][77][78][79]. We can see that our method has comparable performances against current approaches in the graph classification literature.…”

An Enhanced Filtering-Based Information Granulation Procedure for Graph Embedding and Classification

“…The comparison is restricted to the five datasets considered in this work, with a dash (-) indicating that a given dataset has not been tested in the literature on the corresponding model. Competitors span a variety of approaches for graph classification, including classifiers working on the top of pure graph matching similarities [72], [74], kernel methods [77], [80] and several embedding techniques [75], [76], including GrC-based [5], [6], [33] and neural ones [78], [79]. As regards subsampling-based implementations, in Table 1 are reported the performances obtained at different subsampling rates in the form of min-max range.…”

Exploring the expressiveness of abstract metabolic networks

“…They have been widely used in a variety of contexts, and some approaches in the literature apply them to represent and compare metabolic networks, see e.g. [ 29 – 31 ]. Here we explore four different kernels: Vertex Histogram (VH), Shortest Path (SP), Weisfeiler-Lehman (WL) and Pyramid Match (PM).…”

“…They have been widely used in a variety of contexts, and some approaches in the literature apply them to represent and compare metabolic networks, see e.g. [29][30][31].…”