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Persistence landscape of a persistence diagram

Source: R/simplicial_wrappers.R
hg_landscape.Rd

The persistence landscape: at every filtration value t, the k-th largest of the tent functions \(\max(0, \min(t - b, d - t))\) of the diagram's (birth, death) pairs in one homology dimension. Essential classes, which never die, are left out.

Usage

hg_landscape(ph, k_max = 5L, dimension = 1L, t_grid = NULL)

Arguments

ph

A hg_homology() result, or a data.frame with columns dimension, birth, death.

k_max

Highest landscape level. Default 5.

dimension

Homology dimension. Default 1.

t_grid

Evaluation points. NULL uses 200 points spanning the pairs.

Value

A persistence_landscape object. Read it with hg_get(): one row per level and grid point (what = "landscape").

References

Bubenik, P. (2015). Statistical topological data analysis using persistence landscapes. Journal of Machine Learning Research, 16, 77–102.

See also

hg_homology()

Examples

set.seed(1)
w <- matrix(runif(36), 6, 6, dimnames = list(letters[1:6], letters[1:6]))
w <- (w + t(w)) / 2
diag(w) <- 0
pl <- hg_landscape(hg_homology(w, n_steps = 10), dimension = 0)
hg_get(pl, k = 1, top = 5)
#>   k         t        value
#> 1 1 0.5838612 0.0000000000
#> 2 1 0.5846595 0.0007983042
#> 3 1 0.5854578 0.0015966085
#> 4 1 0.5862561 0.0023949127
#> 5 1 0.5870544 0.0031932170