flamelet.band: Bootstrap Band for Persistence Flamelet
In pflamelet: Persistence Flamelets: Computation and Inferential Tools

Description Usage Arguments Value References Examples

View source: R/functions.R

Computes a bootstrap band around the 0 of the Persistence Flamelet. If the input is a list of data points observed at different scales, at each resolution, Persistence Diagrams are built for the sub/superlevel set of an arbitrary function computed on X, and then used to compute the Flamelet.

flamelet.band(
  X,
  B,
  alpha,
  base.type = "landscape",
  base.param = 1,
  dimension = 1,
  tseq,
  diag.fun = distFct,
  sublevel = TRUE,
  h.grid = NULL,
  lim = NULL,
  by = NULL
)

`X`	a list of m matrix/data.frame containing the pointcloud at different resolutions. If `X` is a n-by-d matrix or a data.frame containing a d-dimensional pointcloud, this function computes the Flamelet on the corresponding `diag.fun`.
`B`	number of bootstrap repetitions needed to compute the confidence band over Persistence Diagrams.
`alpha`	the confidence level of the bootstrap confidence bands.
`base.type`	a string specifying whether the Flamelet is built from Persistence Landscapes ("landscape") or Persistence Silhouettes ("silhouettes").
`base.param`	the order k of the Flamelet (if base.type=="landscape") or the power p of the Flamelet (if base.type=="silhouette").
`dimension`	the topological dimension of the flamelet (0 for connected components, 1 for loops, ...)
`tseq`	a vector of values at which the Flamelet function is evaluated for a fixed scale level.
`diag.fun`	the function whose sub/super-level set define the persistent homology groups. Corresponds to the argument `FUN` of the `gridDiag` function in the TDA package.
`sublevel`	a logical indicating whether the Persistent Homology should be computed on sub or superlevel set of the function given as `diag.fun`.
`h.grid`	vector of bandwidths for the KDE, representing the scale parameter of the Flamelet.
`lim`	2-by-d matrix, where the i-th column contains the range of the grid over which the function specified in `diag.fun` is computed for the i-th variable.
`by`	a scalar (or a vector if different values are selected for each dimension). specifying spaces between elements on the grid whose outernmost element are defined by `lim`.

The quantile of level alpha necessary to build the confidence band. More details can be found in Padellini (2017).

T. Padellini and P. Brutti (2017) Persistence Flamelets: multiscale Persistent Homology for kernel density exploration https://arxiv.org/abs/1709.07097

library(TDA)
xx = rbind(circleUnif(50, 1), circleUnif(50, 1.5) + 3)
Xlim = c(-1, 5);  Ylim = c(-1, 5);  by = 0.05
lim = cbind(Xlim, Ylim)
foo.band = flamelet.band(X = xx, B = 10, alpha = 0.95,
                  tseq = seq(0, .75, length.out = 500), diag.fun = kde,
                  h.grid = seq(0.01, 1, length.out = 40), lim = lim, by = by)