Calculate Persistent Homology of a Point Cloud

Calculates the persistent homology of a point cloud, as represented by a Vietoris-Rips complex. This function is an R wrapper for Ulrich Bauer's Ripser C++ library for calculating persistent homology. For more information on the C++ library, see <https://github.com/Ripser/ripser>.

calculate_homology(mat, dim = 1, threshold = -1, format = "cloud",
  standardize = FALSE, return_df = FALSE)

Arguments

mat	numeric matrix containing point cloud or distance matrix
dim	maximum dimension of features to calculate
threshold	maximum diameter for computation of Vietoris-Rips complexes
format	format of `mat`, either "cloud" for point cloud or "distmat" for distance matrix
standardize	boolean determining whether point cloud size should be standardized
return_df	defaults to `FALSE`, returning a matrix; if `TRUE`, returns a data frame

Value

3-column matrix or data frame, with each row representing a TDA feature

Details

The `mat` parameter should be a numeric matrix with each row corresponding to a single point, and each column corresponding to a single dimension. Thus, if `mat` has 50 rows and 5 columns, it represents a point cloud with 50 points in 5 dimensions. The `dim` parameter should be a positive integer. Alternatively, the `mat` parameter could be a distance matrix (upper triangular half is ignored); note: `format` should be specified as "ldm".

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 <- calculate_homology(pt.cloud)