Related papers: Kernels, Truth and Satisfaction
Fact Verification requires fine-grained natural language inference capability that finds subtle clues to identify the syntactical and semantically correct but not well-supported claims. This paper presents Kernel Graph Attention Network…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
Entity resolution, the problem of identifying the underlying entity of references found in data, has been researched for many decades in many communities. A common theme in this research has been the importance of incorporating relational…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
A nut graph is a simple graph whose kernel is spanned by a single full vector (i.e. the adjacency matrix has a single zero eigenvalue and all non-zero kernel eigenvectors have no zero entry). We classify generalisations of nut graphs to nut…
Let $D$ be a digraph. We call a subset $N$ of $V(D)$ $k$-independent if for every pair of vertices $u,v \in N$, $d(u,v) \geq k$; and we call it $\ell$-absorbent if for every vertex $u \in V(D) \setminus N$, there exists $v \in N$ such that…
We explore the concept of a graph homomorphism through the lens of C$^*$-algebras and operator systems. We start by studying the various notions of a quantum graph homomorphism and examine how they are related to each other. We then define…
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…
In many networks, including networks of protein-protein interactions, interdisciplinary collaboration networks, and semantic networks, connections are established between nodes with complementary rather than similar properties. While…
Separation kernels are fundamental software of safety and security-critical systems, which provide to their hosted applications spatial and temporal separation as well as controlled information flows among partitions. The application of…
Soft set theory and rough set theory are mathematical tools to deal with uncertainties. In [3], authors combined these concepts and introduced soft rough sets. In this paper, we introduce the concepts of soft rough graphs, vertex and edge…
In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…
It has been shown that the maximum stable set problem in some infinite graphs, and the kissing number problem in particular, reduces to a minimization problem over the cone of copositive kernels. Optimizing over this infinite dimensional…
We give a self-contained derivation of the Stinespring and Kraus structure theorems for completely positive maps using only scalar positive-definite kernels.
In this paper, we generalize the notions of perfect matchings, perfect 2-matchings to perfect k-matchings and give a necessary and sufficient condition for existence of perfect k-matchings. For bipartite graphs, we show that this k-matching…
The $P_2$-packing problem asks for whether a graph contains $k$ vertex-disjoint paths each of length two. We continue the study of its kernelization algorithms, and develop a $5k$-vertex kernel.
Markov kernels play a decisive role in probability and mathematical statistics theories, and are an extension of the concepts of sigma-field and statistic. Concepts such as independence, sufficiency, completeness, ancillarity or conditional…
We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of…
In this survey, we explore recent literature on finding the cores of higher graphs using geometric and topological means. We study graphs, hypergraphs, and simplicial complexes, all of which are models of higher graphs. We study the notion…
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…