ase {HyperG}

Adjacency spectral embedding.

Description

Using either adjacency or Laplacian spectral embedding, embed a graph into a lower dimensional space.

Usage

ase(g, verbose = FALSE, adjust.diag = FALSE, laplacian = FALSE, 
    normalize = FALSE, scale.by.values = FALSE, vectors = "u", d = 2)
lse(g,...)
hypergraph.spectrum(h, k=3)

Arguments

g, h

A graph (g) or hypergraph (h).

verbose

logical. Control output to terminal.

adjust.diag

logical. For adjacency embedding, whether to add degree/(n-1) to the diagonal of the adjacency matrix.

laplacian

logical. Use the Laplacian rather than the adjacency matrix.

normalize

logical. Whether to normalize by D^1/2.

scale.by.values

logical. Whether to scale the eigen or singular vectors by the square root of the eigen or singular values.

vectors

character. "u", "v" or "uv" indicating which vectors to provide for the embedding.

d, k

dimension of the embedding.

...

arguments passed to ase.

Details

The ase is for graphs, and has the most control over the embedding, as indicated by the arguments. hypergraph.spectrum computes the svd of the incidence matrix for the hypergraph h. lse is Laplacian spectral embedding, and is just a call to ase with laplacian=TRUE and adjust.diag=FALSE. For small hypergraphs (order or size < 3) the base svd function is used and k is ignored.

Value

ase returns a matrix of points, with rows corresponding to vertices and columns to the embedding. There will be either d, or 2*d columns, depending on the value of the variable vectors. For "u" or "v" the dimension is d, for "uv" the dimension is 2*d. hypergraph.spectrum returns the singular value decomposition using the top k singular vectors and values.

Author(s)

David J. Marchette [e-mail]

References

Congyuan Yang, Carey E. Priebe, Youngser Park, David J. Marchette, "Simultaneous Dimensionality and Complexity Model Selection for Spectral Graph Clustering," Journal of Computational and Graphical Statistics, accepted for publication, 2020. arXiv:1904.02926

A. Athreya, V. Lyzinski, D. J. Marchette, C. E. Priebe, D. L. Sussman, and M. Tang, "A limit theorem for scaled eigenvectors of random dot product graphs," Sankhya, vol. 78-A, no. 1, pp 1-18, February 2016.

See Also

svds, eigs.

Examples

 g <- sample_gnp(10,.1)
 ase(g)