GLEE: Geometric Laplacian Eigenmap Embeddingleotrs.com/static/GLEE_lanet19.pdf · Rows of S point...
Transcript of GLEE: Geometric Laplacian Eigenmap Embeddingleotrs.com/static/GLEE_lanet19.pdf · Rows of S point...
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GLEE: Geometric Laplacian Eigenmap Embedding
Leo TorresKevin S. Chan and Tina Eliassi-Rad
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The problem of embedding
ML
ClassificationRegressionLink prediction….
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Laplacian Eigenmaps
Solution given by the eigenvectors of the normalized Laplacian D⁻1L.
[1] M. Belkin and P. Niyogi. Laplacian eigenmaps for dimensionality reduction and data representation.Neural Computation, 15(6):1373–1396, 2003
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GLEE: Geometric Laplacian Eigenmap Embedding
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GLEE: Geometric Laplacian Eigenmap Embedding
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Rows of S point to the vertices of an (n-1)-D simplex.
GLEE: Geometric Laplacian Eigenmap Embedding
[2] K. Devriendt and P. Van Mieghem. The simplex geometry of graphs.The Journal of Complex Networks, 2019.
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GLEE: Geometric Laplacian Eigenmap Embedding
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Graph Reconstruction
Pre
cisi
on a
t k
k
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Link Prediction: common neighborsIn many networks (e.g. social networks), the number of common neighbors is an excellent predictor of links because of triadic closure.
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¡Gracias!
Supported by NSF CNS-1314603, NSF IIS-1741197, Army Research Laboratory Cooperative Agreement W911NF-13-2-0045.
Code: github.com/leotrs/glee Paper: arxiv.org/abs/1905.09763Contact: [email protected]