var2_nvd

This function computes the Fréchet variance using exclusively inter-point
distances. As such, it can accommodate any pair of representation and
distance.

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

var2_nvd function

<dl><dt>x</dt>
<dd>An <code>nvd</code> object listing a sample of networks.</dd>
<dt>representation</dt>
<dd>A string specifying the graph representation to be
used. Choices are adjacency, laplacian, modularity, graphon. Default is
adjacency.</dd>
<dt>distance</dt>
<dd>A string specifying the distance to be used. Possible choices
are: hamming, frobenius, spectral or root-euclidean. Default is frobenius.</dd></dl>

Arguments

Fréchet Variance of Network-Valued Data from Inter-Point Distances — var2_nvd

<dl>

<dt>x</dt>
<dd>An <code>nvd</code> object listing a sample of networks.</dd>


<dt>representation</dt>
<dd>A string specifying the graph representation to be
used. Choices are adjacency, laplacian, modularity, graphon. Default is
adjacency.</dd>


<dt>distance</dt>
<dd>A string specifying the distance to be used. Possible choices
are: hamming, frobenius, spectral or root-euclidean. Default is frobenius.</dd>

</dl>

var2_nvd: Fréchet Variance of Network-Valued Data from Inter-Point Distances

Description

Usage

Value

Arguments

Examples