Calculate Persistent Homology via a Vietoris-Rips Complex

This function is an R wrapper for the Ripser C++ library to calculate persistent homology. For more information on the C++ library, see https://github.com/Ripser/ripser. For more information on how objects of different classes are evaluated by vietoris_rips, read the Details section below.

vietoris_rips(dataset, ...)

# S3 method for data.frame
vietoris_rips(dataset, ...)

# S3 method for matrix
vietoris_rips(dataset, max_dim = 1L, threshold = -1, p = 2L, ...)

# S3 method for dist
vietoris_rips(dataset, max_dim = 1L, threshold = -1, p = 2L, ...)

# S3 method for numeric
vietoris_rips(
  dataset,
  data_dim = 2L,
  dim_lag = 1L,
  sample_lag = 1L,
  method = "qa",
  ...
)

# S3 method for ts
vietoris_rips(dataset, ...)

# S3 method for default
vietoris_rips(dataset, ...)

Arguments

dataset	object on which to calculate persistent homology
...	other relevant parameters
max_dim	maximum dimension of persistent homology features to be calculated
threshold	maximum simplicial complex diameter to explore
p	prime field in which to calculate persistent homology
data_dim	desired end data dimension
dim_lag	time series lag factor between dimensions
sample_lag	time series lag factor between samples (rows)
method	currently only allows "qa" (quasi-attractor method)

Value

PHom object

Details

vietoris_rips.data.frame assumes dataset is a point cloud, with each row representing a point and each column representing a dimension.

vietoris_rips.matrix currently assumes dataset is a point cloud (similar to vietoris_rips.data.frame). Currently in the process of adding network representation to this method.

vietoris_rips.dist takes a dist object and calculates persistent homology based on pairwise distances. The dist object could have been calculated from a point cloud, network, or any object containing elements from a finite metric space.

vietoris_rips.numeric and vietoris_rips.ts both calculate persistent homology of a time series object. The time series object is converted to a matrix using the quasi-attractor method detailed in Umeda (2017) doi:10.1527/tjsai.D-G72. Persistent homology of the resulting matrix is then calculated.

Examples

# create a 2-d point cloud of a circle (100 points)
num.pts <- 100
rand.angle <- runif(num.pts, 0, 2*pi)
pt.cloud <- cbind(cos(rand.angle), sin(rand.angle))

# calculate persistent homology (num.pts by 3 numeric matrix)
pers.hom <- vietoris_rips(pt.cloud)