TDAvec (version 0.1.41)

computeLimits: Compute the Extreme Values of Birth, Death, and Persistence Across Multiple Persistence Diagrams

Description

Given a list of persistence diagrams, computeLimits() computes the extreme values of birth, death, and persistence across all diagrams for a specified homological dimension. Points with infinite death values are ignored.

Usage

computeLimits(Dlist, homDim)

Value

A (named) numeric vector containing:

• minB: the minimum birth value across all diagrams.

• maxB: the maximum birth value across all diagrams.

• maxD: the maximum death value across all diagrams.

• minP: the minimum persistence value across all diagrams.

• maxP: the maximum persistence value across all diagrams.

Arguments

Dlist

a list of persistence diagrams, where each diagram is a matrix containing three columns representing homological dimension, birth, and death values.

homDim

the homological dimension (0 for \(H_0\), 1 for \(H_1\), etc.). Rows of the diagrams are filtered based on this value.

Author

Umar Islambekov

Examples

set.seed(123)
N <- 100 # The size of point clouds
nD <- 50 # The number of persistence diagrams
Dlist <- list()
for (i in 1:nD){
  # sample N points uniformly from the unit circle and add Gaussian noise
  theta <- runif(N, min = 0, max = 2 * pi)
  X <- cbind(cos(theta), sin(theta)) + rnorm(2 * N, mean = 0, sd = 0.2)

  # Compute the persistence diagram using the Rips filtration built on top of X
  # The 'threshold' parameter specifies the maximum distance for building simplices
  Dlist[[i]] <- TDAstats::calculate_homology(X, threshold = 2)
}

# Compute the extreme values of birth, death, and persistence across 
# all 50 diagrams for homological dimension H_0
computeLimits(Dlist, homDim = 0)

# Compute the extreme values of birth, death, and persistence across 
# all 50 diagrams for homological dimension H_1
computeLimits(Dlist, homDim = 1)