Manifold structure in graph embeddings

06/09/2020
by   Patrick Rubin-Delanchy, et al.
0

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is often available. In spectral embedding, this dimension may be very high. However, this paper shows that existing random graph models, including graphon and other latent position models, predict the data should live near a much lower dimensional set. One may therefore circumvent the curse of dimensionality by employing methods which exploit hidden manifold structure.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

09/06/2017

A Quasi-isometric Embedding Algorithm

The Whitney embedding theorem gives an upper bound on the smallest embed...
06/02/2021

Matrix factorisation and the interpretation of geodesic distance

Given a graph or similarity matrix, we consider the problem of recoverin...
08/12/2020

A Bayesian Approach to Spherical Factor Analysis for Binary Data

Factor models are widely used across diverse areas of application for pu...
07/04/2021

Latent structure blockmodels for Bayesian spectral graph clustering

Spectral embedding of network adjacency matrices often produces node rep...
01/03/2020

Scalability and robustness of spectral embedding: landmark diffusion is all you need

While spectral embedding is a widely applied dimension reduction techniq...
12/15/2021

Fast Computation of Generalized Eigenvectors for Manifold Graph Embedding

Our goal is to efficiently compute low-dimensional latent coordinates fo...
01/05/2020

Multi-Objective Genetic Programming for Manifold Learning: Balancing Quality and Dimensionality

Manifold learning techniques have become increasingly valuable as data c...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.