Peak Persistence Analysis

Analyse the persistence of peaks (local maxima) across a range of regularisation strengths. As the regularisation parameter \(\lambda\) increases, aligned curves become smoother and spurious peaks disappear. This function tracks which peaks persist across the regularisation path, providing a multi-scale view of the data's peak structure.

Usage

peak.persistence(fdataobj, lambdas = NULL, max.iter = 10, tol = 1e-04)

Arguments

fdataobj

An object of class 'fdata'.

lambdas

Numeric vector of regularisation values to sweep. If NULL (default), uses seq(0, 5, length.out = 30).

max.iter

Maximum number of Karcher mean iterations at each lambda (default 10).

tol

Convergence tolerance (default 1e-4).

Value

A list with components:

lambdas

the regularisation values used

n_peaks

integer vector of peak counts at each lambda

peak_locations

list of numeric vectors giving peak locations at each lambda

persistence

numeric vector of persistence scores for each peak

References

Tucker, J.D., Wu, W., and Srivastava, A. (2013). Generative models for functional data using phase and amplitude separation. Computational Statistics & Data Analysis, 61:50–66.

See also

karcher.mean

Examples

# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 100)
X <- matrix(0, 15, 100)
for (i in 1:15) X[i, ] <- sin(4 * pi * t + runif(1, -0.3, 0.3))
fd <- fdata(X, argvals = t)
pp <- peak.persistence(fd)
# }