Related papers: Uniform Embeddings for Robinson Similarity Matrice…
Let $G=(V,E)$ be a finite, connected graph. We consider a greedy selection of vertices: given a list of vertices $x_1, \dots, x_k$, take $x_{k+1}$ to be any vertex maximizing the sum of distances to the existing vertices and iterate: we…
I start with a scenario where the universe is an abstract space $\mathcal{M}$ having $d$ dimensions. There is a two dimensional surface embedded in it. Embedding is a map from the embedded surface to $\mathcal{M}$ that has a field theory…
Graph encoder embedding, a recent technique for graph data, offers speed and scalability in producing vertex-level representations from binary graphs. In this paper, we extend the applicability of this method to a general graph model, which…
The $n$-$book ~embedding$ of a graph $G$ is an embedding of the graph $G$ in an $n$-book with the vertices of $G$ on the spine and each edge to the pages without crossing each other. If the degree of vertices of $G$ at most one in each…
Graph embedding approaches attempt to project graphs into geometric entities, i.e, manifolds. The idea is that the geometric properties of the projected manifolds are helpful in the inference of graph properties. However, if the choice of…
This paper is concerned with long-time interest of us, especially, the author, in realizing graphs as Reeb graphs of real algebraic functions of certain nice classes. The Reeb graph of a differentiable function is the set consisting of all…
Let $D$ be an $n \times n$ Euclidean distance matrix (EDM) with embedding dimension $r$; and let $d \in R^n$ be a given vector. In this note, we consider the problem of finding a vector $y \in R^n$, that is closest to d in Euclidean norm,…
We study the problem of edit similarity joins, where given a set of strings and a threshold value $K$, we want to output all pairs of strings whose edit distances are at most $K$. Edit similarity join is a fundamental problem in data…
In this paper we give a lower bound for the least distortion embedding of a distance regular graph into Euclidean space. We use the lower bound for finding the least distortion for Hamming graphs, Johnson graphs, and all strongly regular…
A graph is called (generically) rigid in $\mathbb{R}^d$ if, for any choice of sufficiently generic edge lengths, it can be embedded in $\mathbb{R}^d$ in a finite number of distinct ways, modulo rigid transformations. Here we deal with the…
Heterogeneous graphs are ubiquitous in real-world applications because they can represent various relationships between different types of entities. Therefore, learning embeddings in such graphs is a critical problem in graph machine…
Our goal is to efficiently compute low-dimensional latent coordinates for nodes in an input graph -- known as graph embedding -- for subsequent data processing such as clustering. Focusing on finite graphs that are interpreted as uniform…
The space of graphs is often characterised by a non-trivial geometry, which complicates learning and inference in practical applications. A common approach is to use embedding techniques to represent graphs as points in a conventional…
Random intersection graphs have received much attention recently and been used in a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. For these graphs, each node is equipped…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying…
Embedding graphs in a geographical or latent space, i.e.\ inferring locations for vertices in Euclidean space or on a smooth manifold or submanifold, is a common task in network analysis, statistical inference, and graph visualization. We…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
In the graph node embedding problem, embedding spaces can vary significantly for different data types, leading to the need for different GNN model types. In this paper, we model the embedding update of a node feature as a Hamiltonian orbit…
By definition, a rigid graph in $\mathbb{R}^d$ (or on a sphere) has a finite number of embeddings up to rigid motions for a given set of edge length constraints. These embeddings are related to the real solutions of an algebraic system.…