Diffusion profile embedding as a basis for graph vertex similarity
Bibliographic Data
| ID | 6161632 |
|---|---|
| Authors | Scott Payne (0000-0001-5717-6670, West Virginia University), Edgar Fuller (0000-0003-4130-090X, Florida International University, corresponding author), George A Spirou (0000-0001-7677-3585, University of South Florida), George Spirou, Cun‐quan Zhang (0000-0001-5583-4481, West Virginia University), Cun-Quan Zhang |
| Year | 2021 |
| Volume | 9 |
| Issue | 3 |
| Pages | 328-353 |
| Publication date | 2021-09-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Network Science (JOURNAL) |
| Journal identifiers | ISSN: 2050-1250 • E-ISSN: 2050-1242 |
| Publisher | Cambridge University Press (PUBLISHER • US) |
| DOI | 10.1017/nws.2021.11 |
| OpenAlex | W3202636194 |
| Language | EN |
| References cited | 69 |
We describe here a notion of diffusion similarity , a method for defining similarity between vertices in a given graph using the properties of random walks on the graph to model the relationships between vertices. Using the approach of graph vertex embedding, we characterize a vertex v i by considering two types of diffusion patterns: the ways in which random walks emanate from the vertex v i to the remaining graph and how they converge to the vertex v i from the graph. We define the similarity of two vertices v i and v j as the average of the cosine similarity of the vectors characterizing v i and v j . We obtain these vectors by modifying the solution to a differential equation describing a type of continuous time random walk. This method can be applied to any dataset that can be assigned a graph structure that is weighted or unweighted, directed or undirected. It can be used to represent similarity of vertices within community structures of a network while at the same time representing similarity of vertices within layered substructures (e.g., bipartite subgraphs) of the network. To validate the performance of our method, we apply it to synthetic data as well as the neural connectome of the C. elegans worm and a connectome of neurons in the mouse retina. A tool developed to characterize the accuracy of the similarity values in detecting community structures, the uncertainty index , is introduced in this paper as a measure of the quality of similarity methods
Bipartite graph · Cluster analysis · Combinatorics · Cosine similarity · Discrete mathematics · Embedding · Graph · Graph embedding · Random walk · Similarity measure · Vertex (graph theory · Complex Network Analysis Techniques · Computer Science · Functional Brain Connectivity Studies · Mathematics · Mental Health Research Topics · Artificial Intelligence
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| Citation velocity | historical |
|---|---|
| Highly cited | No |