An empirical method (bootstrap) to differentiate between features that constitute signal versus noise based on the magnitude of their persistence relative to one another. Note: you must have at least 5 features of a given dimension to use this function.
id_significant(features, dim = 1, reps = 100, cutoff = 0.975)
Arguments
| features | 3xn data frame of features; the first column must be dimension, the second birth, and the third death |
|---|---|
| dim | dimension of features of interest |
| reps | number of replicates |
| cutoff | percentile cutoff past which features are considered significant |
Examples
# get dataset (noisy circle) and calculate persistent homology angles <- runif(100, 0, 2 * pi) x <- cos(angles) + rnorm(100, mean = 0, sd = 0.1) y <- sin(angles) + rnorm(100, mean = 0, sd = 0.1) annulus <- cbind(x, y) phom <- calculate_homology(annulus) # find threshold of significance # expecting 1 significant feature of dimension 1 (Betti-1 = 1 for annulus) thresh <- id_significant(features = as.data.frame(phom), dim = 1, reps = 500, cutoff = 0.975) # generate flat persistence diagram # every feature higher than `thresh` is significant plot_persist(phom, flat = TRUE)
