sklearn.preprocessing.KernelCenterer

class sklearn.preprocessing.KernelCenterer

Center an arbitrary kernel matrix \(K\).

Let define a kernel \(K\) such that:

\[K(X, Y) = \phi(X) . \phi(Y)^{T}\]

\(\phi(X)\) is a function mapping of rows of \(X\) to a Hilbert space and \(K\) is of shape (n_samples, n_samples).

This class allows to compute \(\tilde{K}(X, Y)\) such that:

\[\tilde{K(X, Y)} = \tilde{\phi}(X) . \tilde{\phi}(Y)^{T}\]

\(\tilde{\phi}(X)\) is the centered mapped data in the Hilbert space.

KernelCenterer centers the features without explicitly computing the mapping \(\phi(\cdot)\). Working with centered kernels is sometime expected when dealing with algebra computation such as eigendecomposition for KernelPCA for instance.

Read more in the User Guide.

Attributes

K_fit_rows_ndarray of shape (n_samples,)

Average of each column of kernel matrix.

K_fit_all_float

Average of kernel matrix.

n_features_in_int

Number of features seen during fit.

New in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

New in version 1.0.

See also

sklearn.kernel_approximation.Nystroem

Approximate a kernel map using a subset of the training data.

References

1

Schölkopf, Bernhard, Alexander Smola, and Klaus-Robert Müller. “Nonlinear component analysis as a kernel eigenvalue problem.” Neural computation 10.5 (1998): 1299-1319.

Examples

>>> from sklearn.preprocessing import KernelCenterer
>>> from sklearn.metrics.pairwise import pairwise_kernels
>>> X = [[ 1., -2.,  2.],
...      [ -2.,  1.,  3.],
...      [ 4.,  1., -2.]]
>>> K = pairwise_kernels(X, metric='linear')
>>> K
array([[  9.,   2.,  -2.],
       [  2.,  14., -13.],
       [ -2., -13.,  21.]])
>>> transformer = KernelCenterer().fit(K)
>>> transformer
KernelCenterer()
>>> transformer.transform(K)
array([[  5.,   0.,  -5.],
       [  0.,  14., -14.],
       [ -5., -14.,  19.]])

Methods

fit(K[, y])	Fit KernelCenterer.
fit_transform(X[, y])	Fit to data, then transform it.
get_params([deep])	Get parameters for this estimator.
set_params(**params)	Set the parameters of this estimator.
transform(K[, copy])	Center kernel matrix.

fit(K, y=None)

Fit KernelCenterer.

Parameters

Kndarray of shape (n_samples, n_samples)

Kernel matrix.

yNone

Ignored.

Returns

selfobject

Returns the instance itself.

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters

Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

Additional fit parameters.

Returns

X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

get_params(deep=True)

Get parameters for this estimator.

Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsdict

Parameter names mapped to their values.

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

**paramsdict

Estimator parameters.

Returns

selfestimator instance

Estimator instance.

transform(K, copy=True)

Center kernel matrix.

Parameters

Kndarray of shape (n_samples1, n_samples2)

Kernel matrix.

copybool, default=True

Set to False to perform inplace computation.

Returns

K_newndarray of shape (n_samples1, n_samples2)

Returns the instance itself.