certificate: Mapper graph certificates

In appliedtopology/certifiedTDAmapper: Implements the Certified Mapper Method

Description

Calculates certificates of non-obstruction for TDAmapper::mapper1d graphs

Usage

certificate(mapper, data, graph = NULL, type = c("interleaving",
  "probabilistic"), cl = NULL, N.sim = 100)

Arguments

mapper	A TDAmapper::mapper1d output object.
data	The underlying data for the Mapper graph.
graph	The adjacency matrix igraph::graph of the Mapper graph. Will be calculated if missing.
type	Which kind(s) of certificate to calculate: interleaving distance or probabilistic test. Takes a character vector and calculates either or both depending on the presence or absense of interleaving or probabilistic as strings in the vector.
cl	A parallel cluster object. If present, will use parLapply to speed up calculations.
N.sim	The number of entries in the simulation testing for the probabilistic certificate.

Details

Based on Vejdemo-Johansson and Leshchenko, this is an implementation of computing certificates for 1-dimensional mapper graphs. Here, a certificate is a quantification of the absence or indication of the presence of an obstruction to a nerve lemma for the graph, which would imply that the graph is close in persistent homology to the true shape of the point cloud.

This function implements the global method from Vejdemo-Johansson and Leshchenko for probabilistic certificates.

Value

A list with entries depending on the type of certificate chosen: If calculating an interleaving certificate

interleaving.epsilon

The interleaving distance according to the persistent interleaving results by Govc and Skraba.

persistences

The actual persistence values used to calculate interleaving.epsilon

If calculating an probabilistic certificate

z.scores

The Z-scores calculated.

p.value

The estimated p-value derived.

appliedtopology/certifiedTDAmapper documentation built on May 5, 2019, 4:49 p.m.