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.

Added 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.

Added 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.]])

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_feature_names_out(input_features=None)

get output feature names for transformation.

The feature names out will prefixed by the lowercased class name. For example, if the transformer outputs 3 features, then the feature names out are: ["class_name0", "class_name1", "class_name2"].

Parameters:

input_featuresarray-like of str or None, default=None

Only used to validate feature names with the names seen in fit.

Returns:

feature_names_outndarray of str objects

Transformed feature names.

get_metadata_routing()

get metadata routing of this object.

Please check User guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

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_fit_request(*, K: bool | None | str = '$UNCHANgED$') → KernelCenterer

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to fit.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANgED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

Kstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANgED

Metadata routing for K parameter in fit.

Returns:

selfobject

The updated object.

set_output(*, transform=None)

Set output container.

See Introducing the set_output API for an example on how to use the API.

Parameters:

transform{“default”, “pandas”, “polars”}, default=None

Configure output of transform and fit_transform.

• "default": Default output format of a transformer

• "pandas": DataFrame output

• "polars": Polars output

• None: Transform configuration is unchanged

Added in version 1.4: "polars" option was added.

Returns:

selfestimator instance

Estimator instance.

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&gt;__<parameter&gt; so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

set_transform_request(*, K: bool | None | str = '$UNCHANgED$', copy: bool | None | str = '$UNCHANgED$') → KernelCenterer

Request metadata passed to the transform method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to transform if provided. The request is ignored if metadata is not provided.

• False: metadata is not requested and the meta-estimator will not pass it to transform.

• None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

• str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANgED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

Kstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANgED

Metadata routing for K parameter in transform.

copystr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANgED

Metadata routing for copy parameter in transform.

Returns:

selfobject

The updated object.

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.