fdars (version 0.3.3)

semimetric.hshift: Semi-metric based on Horizontal Shift (Time Warping)

Description

Computes a semi-metric based on the minimum L2 distance after optimal horizontal shifting of curves. This is useful for comparing curves that may have phase differences.

Usage

semimetric.hshift(fdataobj, fdataref = NULL, max_shift = -1, ...)

Value

A distance matrix based on minimum L2 distance after shift.

Arguments

fdataobj

An object of class 'fdata'.

fdataref

An object of class 'fdata'. If NULL, uses fdataobj.

max_shift

Maximum shift in number of grid points. Default is m/4 where m is the number of evaluation points. Use -1 for automatic.

...

Additional arguments (ignored).

Details

For each pair of curves, this function computes: $$d(f, g) = \min_{|h| \le h_{max}} ||f(t) - g(t+h)||$$ where h is the horizontal shift in discrete units.

This semi-metric is useful when comparing curves with phase shifts, such as ECG signals with different heart rates or periodic signals with different phases.

Examples

# Create curves with phase shifts
t <- seq(0, 2*pi, length.out = 100)
X <- matrix(0, 10, 100)
for (i in 1:10) X[i, ] <- sin(t + i*0.2) + rnorm(100, sd = 0.1)
fd <- fdata(X, argvals = t)

# Compute distance accounting for phase shifts
D <- semimetric.hshift(fd, max_shift = 10)