eigs_sym.undirected_factor_model

Compute the eigendecomposition of the expected adjacency matrix of an undirected factor model

Samples generalized random product graphs, a generalization of
a broad class of network models. Given matrices X, S, and Y with with
non-negative entries, samples a matrix with expectation X S Y^T and
independent Poisson or Bernoulli entries using the fastRG algorithm of
Rohe et al. (2017) <https://www.jmlr.org/papers/v19/17-128.html>. The
algorithm first samples the number of edges and then puts them down
one-by-one. As a result it is O(m) where m is the number of edges, a
dramatic improvement over element-wise algorithms that which require
O(n^2) operations to sample a random graph, where n is the number of
nodes.

Alex Hayes

fastRG

Sample Generalized Random Dot Product Graphs in Linear Time

Karl Rohe

Jun Tao

Xintian Han

Norbert Binkiewicz

eigs_sym.undirected_factor_model function

<dl><dt>A</dt>
<dd>An <code>undirected_factor_model()</code>.</dd>
<dt>k</dt>
<dd>Desired rank of decomposition.</dd>
<dt>which</dt>
<dd>Selection criterion. See Details below.</dd>
<dt>sigma</dt>
<dd>Shift parameter. See section Shift-And-Invert Mode.</dd>
<dt>opts</dt>
<dd>Control parameters related to the computing
algorithm. See Details below.</dd>
<dt>...</dt>
<dd>Unused, included only for consistency with generic signature.</dd></dl>

Arguments

Compute the eigendecomposition of the expected adjacency matrix of an undirected factor model — eigs_sym.undirected_factor_model

<dl>

<dt>A</dt>
<dd>An <code>undirected_factor_model()</code>.</dd>


<dt>k</dt>
<dd>Desired rank of decomposition.</dd>


<dt>which</dt>
<dd>Selection criterion. See Details below.</dd>


<dt>sigma</dt>
<dd>Shift parameter. See section Shift-And-Invert Mode.</dd>


<dt>opts</dt>
<dd>Control parameters related to the computing
algorithm. See Details below.</dd>


<dt>...</dt>
<dd>Unused, included only for consistency with generic signature.</dd>

</dl>

"LM"	The \(k\) eigenvalues with largest magnitude. Here the magnitude means the Euclidean norm of complex numbers.
"SM"	The \(k\) eigenvalues with smallest magnitude.
"LR"	The \(k\) eigenvalues with largest real part.
"SR"	The \(k\) eigenvalues with smallest real part.
"LI"	The \(k\) eigenvalues with largest imaginary part.
"SI"	The \(k\) eigenvalues with smallest imaginary part.
"LA"	The \(k\) largest (algebraic) eigenvalues, considering any negative sign.
"SA"	The \(k\) smallest (algebraic) eigenvalues, considering any negative sign.
"BE"	Compute \(k\) eigenvalues, half from each end of the spectrum. When \(k\) is odd, compute more from the high and then from the low end.

eigs_sym.undirected_factor_model: Compute the eigendecomposition of the expected adjacency matrix of an undirected factor model

Description

Usage

Arguments

Details