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Title: GLEE: Geometric Laplacian Eigenmap Embedding
Abstract 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.  more » « less
Award ID(s):
1741197
PAR ID:
10181338
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of Complex Networks
Volume:
8
Issue:
2
ISSN:
2051-1310
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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