computePS {TDAvec} | R Documentation |
A Vector Summary of the Persistence Silhouette Function
Description
Vectorizes the persistence silhouette (PS) function constructed from a given persistence diagram. The th power silhouette function of a persistence diagram
is defined as
where
Points of with infinite death value are ignored
Usage
computePS(D, homDim, scaleSeq, p=1)
Arguments
D |
matrix with three columns containing the dimension, birth and death values respectively |
homDim |
homological dimension (0 for |
scaleSeq |
numeric vector of increasing scale values used for vectorization |
p |
power of the weights for the silhouette function. By default, |
Value
A numeric vector whose elements are the average values of the th power silhouette function computed between each pair of
consecutive scale points of
scaleSeq
=:
where
Author(s)
Umar Islambekov
References
1. Chazal, F., Fasy, B. T., Lecci, F., Rinaldo, A., & Wasserman, L. (2014). Stochastic convergence of persistence landscapes and silhouettes. In Proceedings of the thirtieth annual symposium on Computational geometry (pp. 474-483).
Examples
N <- 100
set.seed(123)
# sample N points uniformly from unit circle and add Gaussian noise
X <- TDA::circleUnif(N,r=1) + rnorm(2*N,mean = 0,sd = 0.2)
# compute a persistence diagram using the Rips filtration built on top of X
D <- TDA::ripsDiag(X,maxdimension = 1,maxscale = 2)$diagram
scaleSeq = seq(0,2,length.out=11) # sequence of scale values
# compute persistence silhouette (PS) for homological dimension H_0
computePS(D,homDim=0,scaleSeq,p=1)
# compute persistence silhouette (PS) for homological dimension H_1
computePS(D,homDim=1,scaleSeq,p=1)