Persistent Homology

Computes persistent homology by building simplicial complexes at decreasing weight thresholds and tracking the birth/death of topological features.

Usage

persistent_homology(x, n_steps = 20L, max_dim = 3L)

Arguments

x

A square matrix, tna, or netobject.

n_steps

Number of filtration steps (default 20).

max_dim

Maximum simplex dimension to track (default 3).

Value

A persistent_homology object with:

betti_curve

Data frame: threshold, dimension, betti at each filtration step.

persistence

Data frame of birth-death pairs: dimension, birth, death, persistence.

thresholds

Numeric vector of filtration thresholds.

Examples

# \donttest{
seqs <- data.frame(
  V1 = sample(LETTERS[1:4], 30, TRUE), V2 = sample(LETTERS[1:4], 30, TRUE),
  V3 = sample(LETTERS[1:4], 30, TRUE), V4 = sample(LETTERS[1:4], 30, TRUE)
)
net <- build_network(seqs, method = "relative")
ph <- persistent_homology(net, n_steps = 15)
print(ph)
#> Persistent Homology
#>   15 filtration steps [0.3636 → 0.0036]
#>   Features: b0: 4 (1 persistent) 
#>   Longest-lived:
#>     b0: 0.3636 → 0.0000 (life: 0.3636)
#>     b0: 0.3636 → 0.3122 (life: 0.0514)
#>     b0: 0.3636 → 0.3122 (life: 0.0514)
# }