期刊
JOURNAL OF COMPLEX NETWORKS
卷 8, 期 2, 页码 -出版社
OXFORD UNIV PRESS
DOI: 10.1093/comnet/cnaa007
关键词
graph embedding; graph Laplacian; simplex geometry
资金
- National Science Foundation [IIS-1741197]
- Combat Capabilities Development Command Army Research Laboratory [W911NF-13-2-0045]
- (U.S. Army Research Lab Cyber Security CRA)
Graph embedding seeks to build a low-dimensional representation of a graph G. This low-dimensional representation is then used for various downstream tasks. One popular approach is Laplacian Eigenmaps (LE), which constructs a graph embedding based on the spectral properties of the Laplacian matrix of G. The intuition behind it, and many other embedding techniques, is that the embedding of a graph must respect node similarity: similar nodes must have embeddings that are close to one another. Here, we dispose of this distance-minimization assumption. Instead, we use the Laplacian matrix to find an embedding with geometric properties instead of spectral ones, by leveraging the so-called simplex geometry of G. We introduce a new approach, Geometric Laplacian Eigenmap Embedding, and demonstrate that it outperforms various other techniques (including LE) in the tasks of graph reconstruction and link prediction.
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