TDA (version 1.3)

plot.maxPersistence: Summary plot for the maxPersistence function

Description

This function plots an object of class maxPersistence, for the selection of the optimal smoothing parameter for persistent homology. For each value of the smoothing parameter, the plot shows the number of detected features, their persistence, and a bootstrap confidence band.

Usage

## S3 method for class 'maxPersistence':
plot(x, features="dimension", colorBand="pink", colorBorder=NA, ...)

Arguments

x

an object of class maxPersistence, as returned by the functions maxPersistence

features

string: if "all" then all the features are plotted; if "dimension" then only the features of the dimension used to compute the confidence band are plotted.

colorBand

the color for filling the confidence band. The default is "pink". (NA leaves the band unfilled)

colorBorder

the color to draw the border of the confidence band. The default is NA and omits the border.

...

additional graphical parameters.

References

Frederic Chazal, Jessi Cisewski, Brittany T. Fasy, Fabrizio Lecci, Bertrand Michel, Alessandro Rinaldo, and Larry Wasserman, (2014), "Robust Topological Inference: distance-to-a-measure and kernel distance" Brittany T. Fasy, Fabrizio Lecci, Alessandro Rinaldo, Larry Wasserman, Sivaraman Balakrishnan, and Aarti Singh. (2013), "Statistical Inference For Persistent Homology", (arXiv:1303.7117). To appear, Annals of Statistics.

See Also

maxPersistence

Examples

## input data: circle with clutter noise
n=600
percNoise=0.1
XX1 = circleUnif(n)
noise=cbind(runif(percNoise*n, -2,2),runif(percNoise*n, -2,2))
X=rbind(XX1,noise)

## limits of the Gird at which the density estimator is evaluated
Xlim=c(-2,2)
Ylim=c(-2,2)
lim=cbind(Xlim,Ylim)
by=0.2

B=80
alpha=0.05

## candidates
parametersKDE=seq(0.1,0.5, by=0.2)

maxKDE=maxPersistence(kde, parametersKDE, X, lim=lim, by=by, 
                  bandFUN="bootstrapBand",B=B, alpha=alpha,
                  parallel=FALSE, printProgress = TRUE)
print(summary(maxKDE))

par(mfrow=c(1,2))
plot(X, pch=16, cex=0.5, main="Circle")
plot(maxKDE)