Note
Go to the end to download the full example code or to run this example in your browser via Binder
Neighbors Functional Regression#
Shows the usage of the nearest neighbors regressor with functional response.
# Author: Pablo Marcos Manchón
# License: MIT
# sphinx_gallery_thumbnail_number = 4
from sklearn.model_selection import train_test_split
import skfda
from skfda.ml.regression import KNeighborsRegressor
from skfda.representation.basis import FourierBasis
In this example we are going to show the usage of the nearest neighbors
regressors with functional response. There is available a K-nn version,
KNeighborsRegressor
, and other one based in
the radius, RadiusNeighborsRegressor
.
As in the scalar response example, we will fetch the Canadian weather dataset, which contains the daily temperature and precipitation at 35 different locations in Canada averaged over 1960 to 1994. The following figure shows the different temperature and precipitation curves.
data = skfda.datasets.fetch_weather()
fd = data['data']
# Split dataset, temperatures and curves of precipitation
X, y = fd.coordinates
Temperatures
X.plot()
<Figure size 640x480 with 1 Axes>
Precipitation
y.plot()
<Figure size 640x480 with 1 Axes>
We will try to predict the precipitation curves. First of all we are going to make a smoothing of the precipitation curves using a basis representation, employing for it a fourier basis with 5 elements.
y = y.to_basis(FourierBasis(n_basis=5))
y.plot()
<Figure size 640x480 with 1 Axes>
We will split the dataset in two partitions, for training and test,
using the sklearn function
train_test_split()
.
X_train, X_test, y_train, y_test = train_test_split(
X,
y,
test_size=0.1,
random_state=28,
)
We will try make a prediction using 5 neighbors and the \(\mathbb{L}^2\) distance. In this case, to calculate the response we will use a mean of the response, weighted by their distance to the test sample.
knn = KNeighborsRegressor(n_neighbors=5, weights='distance')
knn.fit(X_train, y_train)
We can predict values for the test partition using
predict()
. The
following figure shows the real precipitation curves, in dashed line, and
the predicted ones.
y_pred = knn.predict(X_test)
# Plot prediction
fig = y_pred.plot()
fig.axes[0].set_prop_cycle(None) # Reset colors
y_test.plot(fig=fig, linestyle='--')
<Figure size 640x480 with 1 Axes>
We can quantify how much variability it is explained by the model
using the
score()
method,
which computes the value
where \(y_i\) are the real responses and \(\hat{y}_i\) the predicted ones.
0.9149923776656351
More detailed information about the canadian weather dataset can be obtained in the following references.
Ramsay, James O., and Silverman, Bernard W. (2006). Functional Data Analysis, 2nd ed. , Springer, New York.
Ramsay, James O., and Silverman, Bernard W. (2002). Applied Functional Data Analysis, Springer, New Yorkn’
Total running time of the script: (0 minutes 0.794 seconds)