Related papers: Graph embeddings into Hamming spaces

We study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph $G=(V,E)$, we define a "good" $G$-matrix as a $V\times V$ matrix…

Graph similarity computation is one of the core operations in many graph-based applications, such as graph similarity search, graph database analysis, graph clustering, etc. Since computing the exact distance/similarity between two graphs…

The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…

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…

Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…

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…

In this paper we consider the problem of embedding almost-spanning, bounded degree graphs in a random graph. In particular, let $\Delta\geq 5$, $\varepsilon > 0$ and let $H$ be a graph on $(1-\varepsilon)n$ vertices and with maximum degree…

Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…

A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…

Graph embedding methods aim at finding useful graph representations by mapping nodes to a low-dimensional vector space. It is a task with important downstream applications, such as link prediction, graph reconstruction, data visualization,…

Heterogeneous graphs (HGs) also known as heterogeneous information networks have become ubiquitous in real-world scenarios; therefore, HG embedding, which aims to learn representations in a lower-dimension space while preserving the…

Learning useful representations is a key ingredient to the success of modern machine learning. Currently, representation learning mostly relies on embedding data into Euclidean space. However, recent work has shown that data in some domains…

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…

We introduce the {\em pair-cut cone $PCUT_n$} of metrics on sets with $n\ge 3$ elements, that correspond to linear combinations with non-negative coefficients of the cut-metrics resulting from cuts that are pairs. Given a metric, we fully…

Much recent work in bilingual lexicon induction (BLI) views word embeddings as vectors in Euclidean space. As such, BLI is typically solved by finding a linear transformation that maps embeddings to a common space. Alternatively, word…

Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…

A simple graph G is said to be representable in a real vector space of dimension m if there is an embedding of the vertex set in the vector space such that the Euclidean distance between any two distinct vertices is one of only two distinct…

Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…

Network embedding techniques aim at representing structural properties of graphs in geometric space. Those representations are considered useful in downstream tasks such as link prediction and clustering. However, the number of graph…

Graph embedding techniques have attracted growing interest since they convert the graph data into continuous and low-dimensional space. Effective graph analytic provides users a deeper understanding of what is behind the data and thus can…