Related papers: FAST: Kernelization based on Graph Modular Decompo…
Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into…
Enumerative kernelization is a recent and promising area sitting at the intersection of parameterized complexity and enumeration algorithms. Its study began with the paper of Creignou et al. [Theory Comput. Syst., 2017], and development in…
A \emph{$t$-treewidth-modulator} of a graph $G$ is a set $X \subseteq V(G)$ such that the treewidth of $G-X$ is at most some constant $t-1$. In this paper, we present a novel algorithm to compute a decomposition scheme for graphs $G$ that…
Graph classification has recently received a lot of attention from various fields of machine learning e.g. kernel methods, sequential modeling or graph embedding. All these approaches offer promising results with different respective…
The main challenge addressed in this paper is to identify individual terms in a superposition of heat kernels on a graph. We establish geometric conditions on the vertices at which these heat kernels are centered and find bounds on the time…
Kernelization algorithms for the {\sc cluster editing} problem have been a popular topic in the recent research in parameterized computation. Thus far most kernelization algorithms for this problem are based on the concept of {\it critical…
Acquiring labels are often costly, whereas unlabeled data are usually easy to obtain in modern machine learning applications. Semi-supervised learning provides a principled machine learning framework to address such situations, and has been…
We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…
A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…
Graph kernels methods are based on an implicit embedding of graphs within a vector space of large dimension. This implicit embedding allows to apply to graphs methods which where until recently solely reserved to numerical data. Within the…
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 introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph primitives. For $m$-edge and $n$-vertex graphs, it is well-known to be solvable in $O(m\sqrt{n})$ time; however, for several applications…
The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. Although a framework for proving kernelization lower bounds has been discovered in 2008 and…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
We introduce a family of multilayer graph kernels and establish new links between graph convolutional neural networks and kernel methods. Our approach generalizes convolutional kernel networks to graph-structured data, by representing…
Causal learning is a beneficial approach to analyze the cause and effect relationships among variables in a dataset. A causal graph can be generated from a dataset using a particular causal algorithm, for instance, the PC algorithm or Fast…
Many scientific datasets are of high dimension, and the analysis usually requires visual manipulation by retaining the most important structures of data. Principal curve is a widely used approach for this purpose. However, many existing…
A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important…
A significant portion of the data today, e.g, social networks, web connections, etc., can be modeled by graphs. A proper analysis of graphs with Machine Learning (ML) algorithms has the potential to yield far-reaching insights into many…