local_averages#

skfda.preprocessing.feature_construction.local_averages(data, *, domains)[source]#

Calculate the local averages of given data in the desired domains.

It takes functional data and performs the following map:

\[\begin{split}f_1(X) = \frac{1}{|T_1|} \int_{T_1} X(t) dt,\dots, \\ f_p(X) = \frac{1}{|T_p|} \int_{T_p} X(t) dt\end{split}\]

where \(T_1, \dots, T_p\) are subregions of the original domain.

Parameters:

data (FData) – FDataGrid or FDataBasis where we want to calculate the local averages.
domains (int | Sequence[int] | Sequence[DomainRangeLike]) – Domains for each local average. It is possible to pass a number or a list of numbers to automatically split each dimension in that number of intervals and use them for the averages.

Returns:

ndarray of shape (n_samples, n_domains, codomain_dimension) with the transformed data.

Return type:

NDArrayFloat

See also

LocalAveragesTransformer

Examples

We import the Berkeley Growth Study dataset. We will use only the first 3 samples to make the example easy

>>> from skfda.datasets import fetch_growth
>>> dataset = fetch_growth(return_X_y=True)[0]
>>> X = dataset[:3]

We can choose the intervals used for the local averages. For example, we could in this case use the averages at different stages of development of the child: from 1 to 3 years, from 3 to 10 and from 10 to 18:

>>> import numpy as np
>>> from skfda.preprocessing.feature_construction import local_averages
>>> averages = local_averages(
...     X,
...     domains=[(1, 3), (3, 10), (10, 18)],
... )
>>> np.around(averages, decimals=2)
array([[[  91.37],
        [ 126.52],
        [ 179.02]],
       [[  87.51],
        [ 120.71],
        [ 158.81]],
       [[  86.36],
        [ 115.04],
        [ 156.37]]])

A different possibility is to decide how many intervals we want to consider. For example, we could want to split the domain in 2 intervals of the same length.

>>> np.around(local_averages(X, domains=2), decimals=2)
array([[[ 116.94],
        [ 177.26]],
       [[ 111.86],
        [ 157.62]],
       [[ 107.29],
        [ 154.97]]])