inner-products

ipro_frobenius

This is a collection of functions computing the inner product between two
networks.

A flexible statistical framework for network-valued data analysis.
It leverages the complexity of the space of distributions on graphs by using
the permutation framework for inference as implemented in the 'flipr' package.
Currently, only the two-sample testing problem is covered and generalization
to k samples and regression will be added in the future as well. It is a
4-step procedure where the user chooses a suitable representation of the
networks, a suitable metric to embed the representation into a metric space,
one or more test statistics to target specific aspects of the distributions
to be compared and a formula to compute the permutation p-value. Two types
of inference are provided: a global test answering whether there is a
difference between the distributions that generated the two samples and a
local test for localizing differences on the network structure. The latter
is assumed to be shared by all networks of both samples. References: Lovato,
I., Pini, A., Stamm, A., Vantini, S. (2020) "Model-free two-sample test for
network-valued data" <doi:10.1016/j.csda.2019.106896>; Lovato, I., Pini, A.,
Stamm, A., Taquet, M., Vantini, S. (2021) "Multiscale null hypothesis
testing for network-valued data: Analysis of brain networks of patients with
autism" <doi:10.1111/rssc.12463>.

Aymeric Stamm

nevada

Network-Valued Data Analysis

Ilenia Lovato

Alessia Pini

Simone Vantini

inner-products function

<dl><dt>x</dt>
<dd>An <code><a href="/link/igraph?package=nevada&version=0.2.0" data-mini-rdoc="nevada::igraph">igraph</a></code> object or a matrix representing an
underlying network.</dd>
<dt>y</dt>
<dd>An <code><a href="/link/igraph?package=nevada&version=0.2.0" data-mini-rdoc="nevada::igraph">igraph</a></code> object or a matrix representing an
underlying network. Should have the same number of vertices as <code>x</code>.</dd>
<dt>representation</dt>
<dd>A string specifying the desired type of representation,
among: <code>"adjacency"</code>, <code>"laplacian"</code>, <code>"modularity"</code> or
<code>"graphon"</code>. Default is <code>"laplacian"</code>.</dd></dl>

Arguments

Inner-Products Between Networks — inner-products

<dl>

<dt>x</dt>
<dd>An <code><a href='https://rdrr.io/pkg/igraph/man/aaa-igraph-package.html'>igraph</a></code> object or a matrix representing an
underlying network.</dd>


<dt>y</dt>
<dd>An <code><a href='https://rdrr.io/pkg/igraph/man/aaa-igraph-package.html'>igraph</a></code> object or a matrix representing an
underlying network. Should have the same number of vertices as <code>x</code>.</dd>


<dt>representation</dt>
<dd>A string specifying the desired type of representation,
among: <code>"adjacency"</code>, <code>"laplacian"</code>, <code>"modularity"</code> or
<code>"graphon"</code>. Default is <code>"laplacian"</code>.</dd>

</dl>

inner-products: Inner-Products Between Networks

Description

Usage

Value

Arguments

Examples