landmark_shift_deltas#

skfda.preprocessing.registration.landmark_shift_deltas(fd, landmarks, location=None)[source]#

Return the corresponding shifts to align the landmarks of the curves.

Let \(t^*\) the time where the landmarks of the curves will be aligned, and \(t_i\) the location of the landmarks for each curve. The function will calculate the corresponding \(\delta_i\) shuch that \(t_i = t^* + \delta_i\).

This procedure will work independent of the dimension of the domain and the codomain.

Parameters:

fd (FData) – Functional data object.
landmarks (ArrayLike) – List with the landmarks of the samples.
location (float | Sequence[float] | Callable[[ndarray], float | Sequence[float]] | None) – Defines where the landmarks will be alligned. If a number or list is passed the landmarks will be alligned to it. In case of a callable is passed the location will be the result of the the call, the function should be accept as an unique parameter a numpy array with the list of landmarks. By default it will be used as location the mean of the original locations of the landmarks.

Returns:

Array containing the corresponding shifts.

Raises:

ValueError – If the list of landmarks does not match with the number of samples.

Return type:

ndarray[Any, dtype[float64]]

Examples

>>> from skfda.datasets import make_multimodal_landmarks
>>> from skfda.datasets import make_multimodal_samples
>>> from skfda.preprocessing.registration import landmark_shift_deltas

We will create a data with landmarks as example

>>> fd = make_multimodal_samples(n_samples=3, random_state=1)
>>> landmarks = make_multimodal_landmarks(n_samples=3, random_state=1)
>>> landmarks = landmarks.squeeze()

The function will return the corresponding shifts

>>> shifts = landmark_shift_deltas(fd, landmarks)
>>> shifts.round(3)
array([ 0.327, -0.173, -0.154])

The registered samples can be obtained with a shift

>>> fd.shift(shifts)
FDataGrid(...)