Related papers: Segment representations with small resolution
String diagrams are a graphical language used to represent processes that can be composed sequentially or in parallel, which correspond graphically to horizontal or vertical juxtaposition. In this paper we demonstrate how to compute the…
Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science and technology. Many networks are multipartite, meaning…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
Social and information networks are gaining huge popularity recently due to their various applications. Knowledge representation through graphs in the form of nodes and edges should preserve as many characteristics of the original data as…
We propose a novel subgraph image representation for classification of network fragments with the targets being their parent networks. The graph image representation is based on 2D image embeddings of adjacency matrices. We use this image…
Scene graph generation has emerged as an important problem in computer vision. While scene graphs provide a grounded representation of objects, their locations and relations in an image, they do so only at the granularity of proposal…
A $t$-dimensional orthogonal representation of a hypergraph is an assignment of nonzero vectors in $\mathbb{R}^t$ to its vertices, such that every hyperedge contains two vertices whose vectors are orthogonal. The orthogonality dimension of…
Interval graphs are intersection graphs of closed intervals. A generalization of recognition called partial representation extension was introduced recently. The input gives an interval graph with a partial representation specifying some…
Current image processing methods usually operate on the finest-granularity unit; that is, the pixel, which leads to challenges in terms of efficiency, robustness, and understandability in deep learning models. We present an improved…
A network embedding is a representation of a large graph in a low-dimensional space, where vertices are modeled as vectors. The objective of a good embedding is to preserve the proximity between vertices in the original graph. This way,…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
Graph neural networks (GNNs) have been proposed for medical image segmentation, by predicting anatomical structures represented by graphs of vertices and edges. One such type of graph is predefined with fixed size and connectivity to…
For a set of non-negative integers $L$, the $L$-intersection number of a graph is the smallest number $l$ for which there is an assignment on the vertices to subsets $A_v \subseteq \{1,\dots, l\}$, such that every two vertices $u,v$ are…
Let a \neq b be two positive scalars. A Euclidean representation of a simple graph G in R^r is a mapping of the nodes of G into points in R^r such that the squared Euclidean distance between any two points is a if the corresponding nodes…
Graphlets are subgraphs rooted at a fixed vertex. The number of occurrences of graphlets aligned to a particular vertex, called graphlet degree sequence (gds), gives a topological description of the surrounding of the analyzed vertex.…
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper…
Deep Neural Networks have shown tremendous success in the area of object recognition, image classification and natural language processing. However, designing optimal Neural Network architectures that can learn and output arbitrary graphs…
Structured representations such as scene graphs serve as an efficient and compact representation that can be used for downstream rendering or retrieval tasks. However, existing efforts to generate realistic images from scene graphs perform…
We introduce fractional realizations of a graph degree sequence and a closely associated convex polytope. Simple graph realizations correspond to a subset of the vertices of this polytope. We describe properties of the polytope vertices and…
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…