KNeighborsHatMatrix#

class skfda.misc.hat_matrix.KNeighborsHatMatrix(*, n_neighbors=None, kernel=<function uniform>)[source]#

K-nearest neighbour kernel method.

Creates the matrix \(\hat{H}\), used in the kernel smoothing and kernel regression algorithms, as explained below.

\[\hat{H}_{i,j} = \frac{K\left(\frac{d(x_j-x_i')}{h_i}\right)} {\sum_{k=1}^{n}K\left(\frac{d(x_k-x_i')}{h_{i}}\right)}\]

For smoothing, \(\{x_1, ..., x_n\}\) are the points with known value and \(\{x_1', ..., x_m'\}\) are the points for which it is desired to estimate the smoothed value. The distance \(d\) is the absolute value.

For regression, \(\{x_1, ..., x_n\}\) are the functional data and \(\{x_1', ..., x_m'\}\) are the functions for which it is desired to estimate the scalar value. Here, \(d\) is some functional distance.

In both cases, \(K(\cdot)\) is a kernel function and \(h_{i}\) is calculated as the distance from \(x_i'\) to its n_neighbors-th nearest neighbor in \(\{x_1, ..., x_n\}\) [1].

Used with the uniform kernel, it takes the average of the closest n_neighbors points to a given point.

Parameters:

n_neighbors (int | None) – Number of nearest neighbours. By default it takes the 5% closest elements.
kernel (Callable[[NDArrayFloat], NDArrayFloat]) – Kernel function. By default a uniform kernel to perform a ‘usual’ k nearest neighbours estimation.

References

Methods

`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`set_params`(**params)	Set the parameters of this estimator.

get_metadata_routing()#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:: routing – A MetadataRequest encapsulating routing information.
Return type:: MetadataRequest

get_params(deep=True)#

Get parameters for this estimator.

Parameters:: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:: params – Parameter names mapped to their values.
Return type:: dict

set_params(**params)#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance

Examples using `skfda.misc.hat_matrix.KNeighborsHatMatrix`#

Kernel Regression

Kernel Smoothing

KNeighborsHatMatrix#

Examples using skfda.misc.hat_matrix.KNeighborsHatMatrix#

Examples using `skfda.misc.hat_matrix.KNeighborsHatMatrix`#