KernelPCA

class ibex.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=1)

Bases: sklearn.decomposition.kernel_pca.KernelPCA, ibex._base.FrameMixin

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Note

The documentation following is of the original class wrapped by this class. This class wraps the attribute components_.

Example:

>>> import pandas as pd
>>> import numpy as np
>>> from ibex.sklearn import datasets
>>> from ibex.sklearn.decomposition import PCA as PdPCA

>>> iris = datasets.load_iris()
>>> features = iris['feature_names']
>>> iris = pd.DataFrame(
...     np.c_[iris['data'], iris['target']],
...     columns=features+['class'])

>>> iris[features]
sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)
0                5.1               3.5                1.4               0.2
1                4.9               3.0                1.4               0.2
2                4.7               3.2                1.3               0.2
3                4.6               3.1                1.5               0.2
4                5.0               3.6                1.4               0.2
...

>>> PdPCA(n_components=2).fit(iris[features], iris['class']).transform(iris[features])
    comp_0    comp_1
0   -2.684207 ...0.326607
1   -2.715391 ...0.169557
2   -2.889820 ...0.137346
3   -2.746437 ...0.311124
4   -2.728593 ...0.333925
...

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.

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, default=1

The number of parallel jobs to run. If -1, then the number of jobs is set to the number of CPU cores.

New in version 0.18.

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. Set if fit_inverse_transform is True.
X_transformed_fit_ : array, (n_samples, n_components)
Projection of the fitted data on the kernel principal components.
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.
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.
fit(X, y=None)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Fit the model from data in X.

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.
self : object
Returns the instance itself.
fit_transform(X, y=None, **params)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Fit the model from data in X and transform X.

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.

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

inverse_transform(X)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Transform X back to original space.

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

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

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

transform(X)[source]

Note

The documentation following is of the class wrapped by this class. There are some changes, in particular:

Transform X.

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

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