scikits.learn.decomposition.KernelPCA

class scikits.learn.decomposition.KernelPCA(n_components=None, kernel='linear', sigma=1.0, degree=3, alpha=1.0, fit_inverse_transform=False)

Kernel Principal component analysis (KPCA)

Non-linear dimensionality reduction through the use of kernels.

Parameters :

n_components: int or None :

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

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

kernel Default: “linear”

sigma: float :

width of the rbf kernel Default: 1.0

degree: int :

degree of the polynomial kernel Default: 3

alpha: int :

hyperparameter of the ridge regression that learns the inverse transform (when fit_inverse_transform=True) Default: 1.0

fit_inverse_transform: bool :

learn the inverse transform (i.e. learn to find the pre-image of a point) Default: False

Attributes

lambdas_, alphas_:	Eigenvalues and eigenvectors of the centered kernel matrix
dual_coef_:	Inverse transform matrix
X_transformed_fit_:	Projection of the fitted data on the kernel principal components

Methods

__init__(n_components=None, kernel='linear', sigma=1.0, degree=3, alpha=1.0, fit_inverse_transform=False)

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

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) :

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) :

transform(X)

Transform X.

Parameters :X: array-like, shape (n_samples, n_features) : Returns :X_new: array-like, shape (n_samples, n_components) :