相关论文: Graph Information Ratio
A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. We study the approximability properties of the Weighted Maximum H-Colourable Subgraph problem (MAX H-COL). The instances of this…
In the study of random structures we often face a trade-off between realism and tractability, the latter typically enabled by assuming some form of independence. In this work we initiate an effort to bridge this gap by developing tools that…
Information theoretic quantities play an important role in various settings in machine learning, including causality testing, structure inference in graphical models, time-series problems, feature selection as well as in providing privacy…
This report concerns the information content of a graph, optionally conditional on one or more background, "common knowledge" graphs. It describes an algorithm to estimate this information content, and includes some examples based on…
How do social networks differ across platforms? How do information networks change over time? Answering questions like these requires us to compare two or more graphs. This task is commonly treated as a measurement problem, but numerical…
In this article we introduce and study the intersection graph of graded ideals of graded rings. The intersection graph of $G-$graded ideals of a graded ring $(R,G)$ is a simple graph, denoted by $Gr_G(R)$, whose vertices are the nontrivial…
Graph signal processing uses the graph eigenvector basis to analyze signals. However, these graph eigenvectors are typically linearly ordered (by total variation), which may not be reasonable for many graph structures. There have been…
Reliable propagation of information through large networks, e.g., communication networks, social networks or sensor networks is very important in many applications concerning marketing, social networks, and wireless sensor networks.…
In this paper we investigate the extremal relationship between two well-studied graph parameters: the order of the largest homogeneous set in a graph $G$ and the maximal number of distinct degrees appearing in an induced subgraph of $G$,…
The information transmission rate (ITR), or effective bit rate, is a popular and widely used information measurement metric, particularly popularized for SSVEP-based Brain-Computer (BCI) interfaces. By combining speed and accuracy into a…
In this paper, we prove the existence of fundamental relations between information theory and estimation theory for network-coded flows. When the network is represented by a directed graph G=(V, E) and under the assumption of uncorrelated…
Recommender systems are fundamental information filtering techniques to recommend content or items that meet users' personalities and potential needs. As a crucial solution to address the difficulty of user identification and unavailability…
With the emerging needs of creating fairness-aware solutions for search and recommendation systems, a daunting challenge exists of evaluating such solutions. While many of the traditional information retrieval (IR) metrics can capture the…
The capacity of a graph is defined as the rate of exponential growth of independent sets in the strong powers of the graph. In the strong power an edge connects two sequences if at each position their letters are equal or adjacent. We…
For graphs $G$ and $H$, an $H$-colouring of $G$ is a map $\psi:V(G)\rightarrow V(H)$ such that $ij\in E(G)\Rightarrow\psi(i)\psi(j)\in E(H)$. The number of $H$-colourings of $G$ is denoted by $\hom(G,H)$. We prove the following: for all…
We propose a novel image representation, termed Attribute-Graph, to rank images by their semantic similarity to a given query image. An Attribute-Graph is an undirected fully connected graph, incorporating both local and global image…
The spectral theory of graphs provides a bridge between classical signal processing and the nascent field of graph signal processing. In this paper, a spectral graph analogy to Heisenberg's celebrated uncertainty principle is developed.…
Information projections have found important applications in probability theory, statistics, and related areas. In the field of hypothesis testing in particular, the reverse information projection (RIPr) has recently been shown to lead to…
Let $P$ be a set of $n$ points in the plane where each point $p$ of $P$ is associated with a radius $r_p>0$.The transmission graph $G=(P,E)$ of $P$ is defined as the directed graph such that $E$ contains an edge from $p$ to $q$ if and only…
Given a graph $G=(V,E)$, an integer $k$, and a function $f_G:V^k \times V^k \to {0,1}$, the $k^{th}$ graph product of $G$ w.r.t $f_G$ is the graph with vertex set $V^k$, and an edge between two vertices $x=(x_1,...,x_k)$ and…