Periodic Rotation for Functional Data — periodic.rotate • fdars

Circularly rotate each curve to a canonical position before elastic alignment of periodic functional data (e.g., data on $[0, 2\pi]$ where $f(0) = f(2\pi)$).

Usage

periodic.rotate(
  fdataobj,
  target.pos = NULL,
  method = c("peak", "xcorr", "landmark", "iterative"),
  reference = NULL,
  landmark.func = NULL,
  max.iter = 5,
  ...
)

Arguments

fdataobj: An object of class 'fdata'.
target.pos: Target grid index for the feature position. If NULL (default), uses floor(ncol(fdataobj$data) / 4).
method: Rotation method: "peak" (default), "xcorr", "landmark", or "iterative".
reference: Reference curve for cross-correlation methods. A numeric vector or single-curve fdata. If NULL, uses the cross-sectional mean.
landmark.func: A function taking a numeric vector (one curve) and returning a single integer grid index. Required when method = "landmark".
max.iter: Maximum number of rotation-alignment iterations for method = "iterative". Default 5.
...: Additional arguments (ignored).

Value

A list with components:

fdataobj: fdata of rotated curves
shifts: integer vector of circular shifts applied to each curve

Details

Four methods are available:

"peak": Shift each curve's global maximum to target.pos using which.max. Fast and simple, but fragile when curves have multiple peaks of similar height.
"xcorr": Circular cross-correlation with a reference curve (via stats::convolve). The lag maximising cross-correlation is the optimal shift. Robust to multi-peak shapes.
"landmark": Like "peak", but uses a user-supplied function landmark.func(curve) -> index to locate the feature of interest (e.g., steepest rise, first zero crossing).
"iterative": Alternate cross-correlation rotation and elastic alignment for up to max.iter iterations. Useful when the optimal rotation depends on the alignment and vice versa.

References

Srivastava, A. and Klassen, E. (2016). Functional and Shape Data Analysis. Springer.

Examples

# Periodic sinusoidal curves with random circular shifts
argvals <- seq(0, 2 * pi, length.out = 100)
data <- matrix(0, 10, 100)
for (i in 1:10) {
  shift <- sample(0:99, 1)
  idx <- ((seq_len(100) - 1 + shift) %% 100) + 1
  data[i, ] <- sin(argvals[idx])
}
fd <- fdata(data, argvals = argvals)
rot <- periodic.rotate(fd)

# Cross-correlation method (robust to multi-peak curves)
rot_xcorr <- periodic.rotate(fd, method = "xcorr")