English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Graph embeddings, wherein the nodes of the graph are represented by points ina continuous space, are used in a broad range of Graph ML applications. Thequality of such embeddings crucially depends on whether the geometry of thespace matches that of the graph. Euclidean spaces are often a poor choice formany types of real-world graphs, where hierarchical structure and a power-lawdegree distribution are linked to negative curvature. In this regard, it hasrecently been shown that hyperbolic spaces and more general manifolds, such asproducts of constant-curvature spaces and matrix manifolds, are advantageous toapproximately match nodes pairwise distances. However, all these classes ofmanifolds are homogeneous, implying that the curvature distribution is the sameat each point, making them unsuited to match the local curvature (and relatedstructural properties) of the graph. In this paper, we study graph embeddingsin a broader class of heterogeneous rotationally-symmetric manifolds. By addinga single extra radial dimension to any given existing homogeneous model, we canboth account for heterogeneous curvature distributions on graphs and pairwisedistances. We evaluate our approach on reconstruction tasks on synthetic andreal datasets and show its potential in better preservation of high-orderstructures and heterogeneous random graphs generation.

Heterogeneous manifolds for curvature-aware graph embedding