Two new spectral algorithms, GDSE and GDE, learn Euclidean embeddings of hypergraphs by optimizing a smoothed reconstruction loss, recovering planted geometry and improving spurious/missing membership detection and clustering.
On spectral partitioning of signed graphs
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abstract
We argue that the standard graph Laplacian is preferable for spectral partitioning of signed graphs compared to the signed Laplacian. Simple examples demonstrate that partitioning based on signs of components of the leading eigenvectors of the signed Laplacian may be meaningless, in contrast to partitioning based on the Fiedler vector of the standard graph Laplacian for signed graphs. We observe that negative eigenvalues are beneficial for spectral partitioning of signed graphs, making the Fiedler vector easier to compute.
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Optimization of geometric hypergraph embedding
Two new spectral algorithms, GDSE and GDE, learn Euclidean embeddings of hypergraphs by optimizing a smoothed reconstruction loss, recovering planted geometry and improving spurious/missing membership detection and clustering.