Laplacian

Laplacian.default

Laplacian.matrix

The (symmetric) Laplacian of a graph is a
square matrix with dimention
equal the number of nodes.
It is defined as
$$L_{ij} = n_i \textrm{ if } i=j, -1 \textrm{ if } i\sim j, 0 \textrm{ otherwise}$$
where i~j means that there is an edge
between nodes i and j and
n_i is the number of edges including node i.

Implement some models for
correlation/covariance matrices including two approaches
to model correlation matrices from a graphical structure.
One use latent parent variables as proposed in
Sterrantino et. al. (2024) <doi:10.48550/arXiv.2312.06289>.
The other uses a graph to specify conditional
relations between the variables.
The graphical structure makes correlation matrices
interpretable and avoids the quadratic increase of
parameters as a function of the dimension.
In the first approach a natural sequence of simpler
models along with a complexity penalization is used.
The second penalizes deviations from a base model.
These can be used as prior for model parameters,
considering C code through the 'cgeneric' interface
for the 'INLA' package (<https://www.r-inla.org>).
This allows one to use these models as building
blocks combined and to other latent Gaussian models
in order to build complex data models.

Elias Teixeira Krainski

graphpcor

Models for Correlation Matrices Based on Graphs

Elias Krainski

Denis Rustand

Anna Freni-Sterrantino

Janet van Niekerk

Haavard Rue’

Laplacian function

<dl><dt>graph</dt>
<dd>an object that inherits a matrix class</dd></dl>

Arguments

<ul>
<li><code>Laplacian(default)</code>: The Laplacian default method (none)</li>
<li><code>Laplacian(matrix)</code>: The Laplacian of a matrix</li>
</ul>

Methods (by class)

The Laplacian of a graph — Laplacian

<dl>

<dt>graph</dt>
<dd>an object that inherits a matrix class</dd>

</dl>

Laplacian: The Laplacian of a graph

Description

Usage

Value

Arguments

Methods (by class)