Related papers: GLEE: Geometric Laplacian Eigenmap Embedding
A method for embedding graphs in Euclidean space is suggested. The method connects nodes to their geographically closest neighbors and economizes on the total physical length of links. The topological and geometrical properties of…
Modern graph embedding procedures can efficiently process graphs with millions of nodes. In this paper, we propose GEMSEC -- a graph embedding algorithm which learns a clustering of the nodes simultaneously with computing their embedding.…
Manifold Learning occupies a vital role in the field of nonlinear dimensionality reduction and its ideas also serve for other relevant methods. Graph-based methods such as Graph Convolutional Networks (GCN) show ideas in common with…
Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the…
Analysis of signals defined on complex topologies modeled by graphs is a topic of increasing interest. Signal decomposition plays a crucial role in the representation and processing of such information, in particular, to process graph…
Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE…
Graph Representation Learning (GRL) has become essential for modern graph data mining and learning tasks. GRL aims to capture the graph's structural information and exploit it in combination with node and edge attributes to compute…
Let G be a graph on n vertices. The Laplacian matrix of G, denoted by L(G), is defined as L(G) = D(G) - A(G), where A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the vertex degrees of G. A graph G is said to be…
Recent works on representation learning for graph structured data predominantly focus on learning distributed representations of graph substructures such as nodes and subgraphs. However, many graph analytics tasks such as graph…
Node embedding is the task of extracting concise and informative representations of certain entities that are connected in a network. Various real-world networks include information about both node connectivity and certain node attributes,…
Graph representation learning is a fast-growing field where one of the main objectives is to generate meaningful representations of graphs in lower-dimensional spaces. The learned embeddings have been successfully applied to perform various…
Traditional Graph Neural Network (GNN), as a graph representation learning method, is constrained by label information. However, Graph Contrastive Learning (GCL) methods, which tackle the label problem effectively, mainly focus on the…
Unsupervised graph representation learning aims to distill various graph information into a downstream task-agnostic dense vector embedding. However, existing graph representation learning approaches are designed mainly under the node…
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…
Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
With the rising interest in graph representation learning, a variety of approaches have been proposed to effectively capture a graph's properties. While these approaches have improved performance in graph machine learning tasks compared to…
Graph embedding techniques are useful to characterize spectral signature relations for hyperspectral images. However, such images consists of disjoint classes due to spatial details that are often ignored by existing graph computing tools.…
The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…
Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…