Related papers: The All-Paths and Cycles Graph Kernel

The kernel method is a potential approach to analyzing structured data such as sequences, trees, and graphs; however, unordered trees have not been investigated extensively. Kimura et al. (2011) proposed a kernel function for unordered…

We propose a new graph-theoretic benchmark in this paper. The benchmark is developed to address shortcomings of an existing widely-used graph benchmark. We thoroughly studied a large number of traditional and contemporary graph algorithms…

A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…

We propose a theoretical framework of multi-way similarity to model real-valued data into hypergraphs for clustering via spectral embedding. For graph cut based spectral clustering, it is common to model real-valued data into graph by…

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…

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…

The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…

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 approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab-initio calculations) and at speeds suitable for molecular dynam- ics simulation. Best…

Graphs are complex objects that do not lend themselves easily to typical learning tasks. Recently, a range of approaches based on graph kernels or graph neural networks have been developed for graph classification and for representation…

Affordable, high-quality whole-genome assemblies have made it possible to construct rich pangenomes that capture haplotype diversity across many species. As these datasets grow, they motivate the development of specialized techniques…

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…

In a directed graph, a kernel is a subset of vertices that is both stable and absorbing. Not all digraphs have a kernel, but a theorem due to Boros and Gurvich guarantees the existence of a kernel in every clique-acyclic orientation of a…

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…

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.…

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,…

Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…

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…

Motivated by chemical applications, we revisit and extend a family of positive definite kernels for graphs based on the detection of common subtrees, initially proposed by Ramon et al. (2003). We propose new kernels with a parameter to…