/usr/lib/python3/dist-packages/sklearn/decomposition/kernel_pca.py is in python3-sklearn 0.17.0-4.
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# Author: Mathieu Blondel <mathieu@mblondel.org>
# License: BSD 3 clause
import numpy as np
from scipy import linalg
from ..utils.arpack import eigsh
from ..utils.validation import check_is_fitted, NotFittedError
from ..base import BaseEstimator, TransformerMixin
from ..preprocessing import KernelCenterer
from ..metrics.pairwise import pairwise_kernels
class KernelPCA(BaseEstimator, TransformerMixin):
"""Kernel Principal component analysis (KPCA)
Non-linear dimensionality reduction through the use of kernels (see
:ref:`metrics`).
Read more in the :ref:`User Guide <kernel_PCA>`.
Parameters
----------
n_components: int or None
Number of components. If None, all non-zero components are kept.
kernel: "linear" | "poly" | "rbf" | "sigmoid" | "cosine" | "precomputed"
Kernel.
Default: "linear"
degree : int, default=3
Degree for poly kernels. Ignored by other kernels.
gamma : float, optional
Kernel coefficient for rbf and poly kernels. Default: 1/n_features.
Ignored by other kernels.
coef0 : float, optional
Independent term in poly and sigmoid kernels.
Ignored by other kernels.
kernel_params : mapping of string to any, optional
Parameters (keyword arguments) and values for kernel passed as
callable object. Ignored by other kernels.
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 for non-precomputed kernels.
(i.e. learn to find the pre-image of a point)
Default: False
eigen_solver: string ['auto'|'dense'|'arpack']
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
convergence tolerance for arpack.
Default: 0 (optimal value will be chosen by arpack)
max_iter : int
maximum number of iterations for arpack
Default: None (optimal value will be chosen by arpack)
remove_zero_eig : boolean, default=True
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.
Attributes
----------
lambdas_ :
Eigenvalues of the centered kernel matrix
alphas_ :
Eigenvectors of the centered kernel matrix
dual_coef_ :
Inverse transform matrix
X_transformed_fit_ :
Projection of the fitted data on the kernel principal components
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.
"""
def __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):
if fit_inverse_transform and kernel == 'precomputed':
raise ValueError(
"Cannot fit_inverse_transform with a precomputed kernel.")
self.n_components = n_components
self.kernel = kernel
self.kernel_params = kernel_params
self.gamma = gamma
self.degree = degree
self.coef0 = coef0
self.alpha = alpha
self.fit_inverse_transform = fit_inverse_transform
self.eigen_solver = eigen_solver
self.remove_zero_eig = remove_zero_eig
self.tol = tol
self.max_iter = max_iter
self._centerer = KernelCenterer()
@property
def _pairwise(self):
return self.kernel == "precomputed"
def _get_kernel(self, X, Y=None):
if callable(self.kernel):
params = self.kernel_params or {}
else:
params = {"gamma": self.gamma,
"degree": self.degree,
"coef0": self.coef0}
return pairwise_kernels(X, Y, metric=self.kernel,
filter_params=True, **params)
def _fit_transform(self, K):
""" Fit's using kernel K"""
# center kernel
K = self._centerer.fit_transform(K)
if self.n_components is None:
n_components = K.shape[0]
else:
n_components = min(K.shape[0], self.n_components)
# compute eigenvectors
if self.eigen_solver == 'auto':
if K.shape[0] > 200 and n_components < 10:
eigen_solver = 'arpack'
else:
eigen_solver = 'dense'
else:
eigen_solver = self.eigen_solver
if eigen_solver == 'dense':
self.lambdas_, self.alphas_ = linalg.eigh(
K, eigvals=(K.shape[0] - n_components, K.shape[0] - 1))
elif eigen_solver == 'arpack':
self.lambdas_, self.alphas_ = eigsh(K, n_components,
which="LA",
tol=self.tol,
maxiter=self.max_iter)
# sort eigenvectors in descending order
indices = self.lambdas_.argsort()[::-1]
self.lambdas_ = self.lambdas_[indices]
self.alphas_ = self.alphas_[:, indices]
# remove eigenvectors with a zero eigenvalue
if self.remove_zero_eig or self.n_components is None:
self.alphas_ = self.alphas_[:, self.lambdas_ > 0]
self.lambdas_ = self.lambdas_[self.lambdas_ > 0]
return K
def _fit_inverse_transform(self, X_transformed, X):
if hasattr(X, "tocsr"):
raise NotImplementedError("Inverse transform not implemented for "
"sparse matrices!")
n_samples = X_transformed.shape[0]
K = self._get_kernel(X_transformed)
K.flat[::n_samples + 1] += self.alpha
self.dual_coef_ = linalg.solve(K, X, sym_pos=True, overwrite_a=True)
self.X_transformed_fit_ = X_transformed
def fit(self, 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.
"""
K = self._get_kernel(X)
self._fit_transform(K)
if self.fit_inverse_transform:
sqrt_lambdas = np.diag(np.sqrt(self.lambdas_))
X_transformed = np.dot(self.alphas_, sqrt_lambdas)
self._fit_inverse_transform(X_transformed, X)
self.X_fit_ = X
return self
def fit_transform(self, 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)
"""
self.fit(X, **params)
X_transformed = self.alphas_ * np.sqrt(self.lambdas_)
if self.fit_inverse_transform:
self._fit_inverse_transform(X_transformed, X)
return X_transformed
def transform(self, X):
"""Transform X.
Parameters
----------
X: array-like, shape (n_samples, n_features)
Returns
-------
X_new: array-like, shape (n_samples, n_components)
"""
check_is_fitted(self, 'X_fit_')
K = self._centerer.transform(self._get_kernel(X, self.X_fit_))
return np.dot(K, self.alphas_ / np.sqrt(self.lambdas_))
def inverse_transform(self, 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.
"""
if not self.fit_inverse_transform:
raise NotFittedError("The fit_inverse_transform parameter was not"
" set to True when instantiating and hence "
"the inverse transform is not available.")
K = self._get_kernel(X, self.X_transformed_fit_)
return np.dot(K, self.dual_coef_)
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