sklearn.decomposition.KernelPCA

class sklearn.decomposition.KernelPCA(n_components=None, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, alpha=1.0, fit_inverse_transform=False, eigen_solver='auto', tol=0, max_iter=None, remove_zero_eig=False, random_state=None, copy_X=True, n_jobs=None)[source]

Kernel Principal component analysis (KPCA)

Non-linear dimensionality reduction through the use of kernels (see Pairwise metrics, Affinities and Kernels).

Read more in the User Guide.

Parameters
n_componentsint, default=None

Number of components. If None, all non-zero components are kept.

kernel“linear” | “poly” | “rbf” | “sigmoid” | “cosine” | “precomputed”

Kernel. Default=”linear”.

gammafloat, default=1/n_features

Kernel coefficient for rbf, poly and sigmoid kernels. Ignored by other kernels.

degreeint, default=3

Degree for poly kernels. Ignored by other kernels.

coef0float, default=1

Independent term in poly and sigmoid kernels. Ignored by other kernels.

kernel_paramsmapping of string to any, default=None

Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.

alphaint, default=1.0

Hyperparameter of the ridge regression that learns the inverse transform (when fit_inverse_transform=True).

fit_inverse_transformbool, default=False

Learn the inverse transform for non-precomputed kernels. (i.e. learn to find the pre-image of a point)

eigen_solverstring [‘auto’|’dense’|’arpack’], default=’auto’

Select eigensolver to use. If n_components is much less than the number of training samples, arpack may be more efficient than the dense eigensolver.

tolfloat, default=0

Convergence tolerance for arpack. If 0, optimal value will be chosen by arpack.

max_iterint, default=None

Maximum number of iterations for arpack. If None, optimal value will be chosen by arpack.

remove_zero_eigboolean, default=False

If True, then all components with zero eigenvalues are removed, so that the number of components in the output may be < n_components (and sometimes even zero due to numerical instability). When n_components is None, this parameter is ignored and components with zero eigenvalues are removed regardless.

random_stateint, RandomState instance or None, optional (default=None)

If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when eigen_solver == ‘arpack’.

New in version 0.18.

copy_Xboolean, default=True

If True, input X is copied and stored by the model in the X_fit_ attribute. If no further changes will be done to X, setting copy_X=False saves memory by storing a reference.

New in version 0.18.

n_jobsint or None, optional (default=None)

The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

New in version 0.18.

Attributes
lambdas_array, (n_components,)

Eigenvalues of the centered kernel matrix in decreasing order. If n_components and remove_zero_eig are not set, then all values are stored.

alphas_array, (n_samples, n_components)

Eigenvectors of the centered kernel matrix. If n_components and remove_zero_eig are not set, then all components are stored.

dual_coef_array, (n_samples, n_features)

Inverse transform matrix. Only available when fit_inverse_transform is True.

X_transformed_fit_array, (n_samples, n_components)

Projection of the fitted data on the kernel principal components. Only available when fit_inverse_transform is True.

X_fit_(n_samples, n_features)

The data used to fit the model. If copy_X=False, then X_fit_ is a reference. This attribute is used for the calls to transform.

References

Kernel PCA was introduced in:

Bernhard Schoelkopf, Alexander J. Smola, and Klaus-Robert Mueller. 1999. Kernel principal component analysis. In Advances in kernel methods, MIT Press, Cambridge, MA, USA 327-352.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.decomposition import KernelPCA
>>> X, _ = load_digits(return_X_y=True)
>>> transformer = KernelPCA(n_components=7, kernel='linear')
>>> X_transformed = transformer.fit_transform(X)
>>> X_transformed.shape
(1797, 7)

Methods

fit(self, X[, y])

Fit the model from data in X.

fit_transform(self, X[, y])

Fit the model from data in X and transform X.

get_params(self[, deep])

Get parameters for this estimator.

inverse_transform(self, X)

Transform X back to original space.

set_params(self, \*\*params)

Set the parameters of this estimator.

transform(self, X)

Transform X.

__init__(self, n_components=None, kernel='linear', gamma=None, degree=3, coef0=1, kernel_params=None, alpha=1.0, fit_inverse_transform=False, eigen_solver='auto', tol=0, max_iter=None, remove_zero_eig=False, random_state=None, copy_X=True, n_jobs=None)[source]

Initialize self. See help(type(self)) for accurate signature.

fit(self, X, y=None)[source]

Fit the model from data in X.

Parameters
Xarray-like, shape (n_samples, n_features)

Training vector, where n_samples in the number of samples and n_features is the number of features.

Returns
selfobject

Returns the instance itself.

fit_transform(self, X, y=None, **params)[source]

Fit the model from data in X and transform X.

Parameters
Xarray-like, shape (n_samples, n_features)

Training vector, where n_samples in the number of samples and n_features is the number of features.

Returns
X_newarray-like, shape (n_samples, n_components)
get_params(self, deep=True)[source]

Get parameters for this estimator.

Parameters
deepboolean, optional

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

Returns
paramsmapping of string to any

Parameter names mapped to their values.

inverse_transform(self, X)[source]

Transform X back to original space.

Parameters
Xarray-like, shape (n_samples, n_components)
Returns
X_newarray-like, shape (n_samples, n_features)

References

“Learning to Find Pre-Images”, G BakIr et al, 2004.

set_params(self, **params)[source]

Set the parameters of this estimator.

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

Returns
self
transform(self, X)[source]

Transform X.

Parameters
Xarray-like, shape (n_samples, n_features)
Returns
X_newarray-like, shape (n_samples, n_components)

Examples using sklearn.decomposition.KernelPCA