computeECC {TDAvec} | R Documentation |
A Vector Summary of the Euler Characteristic Curve
Description
Vectorizes the Euler characteristic curve
where are the Betti curves corresponding to persistence diagrams
of dimeansions
respectively, all computed from the same filtration
Usage
computeECC(D, maxhomDim, scaleSeq)
Arguments
D |
matrix with three columns containing the dimension, birth and death values respectively |
maxhomDim |
maximum homological dimension considered (0 for |
scaleSeq |
numeric vector of increasing scale values used for vectorization |
Value
A numeric vector whose elements are the average values of the Euler characteristic curve computed between each pair of
consecutive scale points of scaleSeq
=:
where
Author(s)
Umar Islambekov
References
1. Richardson, E., & Werman, M. (2014). Efficient classification using the Euler characteristic. Pattern Recognition Letters, 49, 99-106.
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 ECC
computeECC(D,maxhomDim=1,scaleSeq)
[Package TDAvec version 0.1.3 Index]