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)

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_components : int, default=None

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

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

Kernel. Default=”linear”.

gamma : float, default=1/n_features

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

degree : int, default=3

Degree for poly kernels. Ignored by other kernels.

coef0 : float, default=1

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

kernel_params : mapping of string to any, default=None

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

alpha : int, default=1.0

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

fit_inverse_transform : bool, default=False

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

eigen_solver : string [‘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.

tol : float, default=0

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

max_iter : int, default=None

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

remove_zero_eig : boolean, 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_state : int, 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_X : boolean, 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_jobs : int 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(X[, y])	Fit the model from data in X.
fit_transform(X[, y])	Fit the model from data in X and transform X.
get_params([deep])	Get parameters for this estimator.
inverse_transform(X)	Transform X back to original space.
set_params(**params)	Set the parameters of this estimator.
transform(X)	Transform X.

__init__(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)

fit(X, y=None)

Fit the model from data in X.

Parameters:

X : array-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:

self : object

Returns the instance itself.

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

Fit the model from data in X and transform X.

Parameters:

X : array-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_new : array-like, shape (n_samples, n_components)

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deep : boolean, optional

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

Returns:

params : mapping of string to any

Parameter names mapped to their values.

inverse_transform(X)

Transform X back to original space.

Parameters:

X : array-like, shape (n_samples, n_components)

Returns:

X_new : array-like, shape (n_samples, n_features)

References

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

set_params(**params)

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(X)

Transform X.

Parameters:

X : array-like, shape (n_samples, n_features)

Returns:

X_new : array-like, shape (n_samples, n_components)

Examples using sklearn.decomposition.KernelPCA

Kernel PCA