8.14.2. sklearn.kernel_approximation.Nystroem

class sklearn.kernel_approximation.Nystroem(kernel='rbf', gamma=None, coef0=1, degree=3, n_components=100, random_state=None)

Approximate a kernel map using a subset of the training data.

Constructs an approximate feature map for an arbitrary kernel using a subset of the data as basis.

Parameters:

kernel : string or callable, default=”rbf”

Kernel map to be approximated.

n_components : int

Number of features to construct. How many data points will be used to construct the mapping.

gamma : float, default=1/n_features.

Parameter for the RBF kernel.

random_state : {int, RandomState}, optional

If int, random_state is the seed used by the random number generator; if RandomState instance, random_state is the random number generator.

See also

RBFSampler

An approximation to the RBF kernel using random Fourier features.

sklearn.metric.pairwise.kernel_metrics

List of build-in kernels.

References

• Williams, C.K.I. and Seeger, M. “Using the Nystrom method to speed up kernel machines”, Advances in neural information processing systems 2001
• T. Yang, Y. Li, M. Mahdavi, R. Jin and Z. Zhou “Nystroem Method vs Random Fourier Features: A Theoretical and Empirical Comparison”, Advances in Neural Information Processing Systems 2012

Attributes

components_	array, shape (n_components, n_features)	Subset of training points used to construct the feature map.
component_indices_	array, shape (n_components)	Indices of components_ in the training set.
normalization_	array, shape (n_components, n_components)	Normalization matrix needed for embedding. Square root of the kernel matrix on components_.

Methods

fit(X[, y])	Fit estimator to data.
fit_transform(X[, y])	Fit to data, then transform it
get_params([deep])	Get parameters for the estimator
set_params(**params)	Set the parameters of the estimator.
transform(X)	Apply feature map to X.

__init__(kernel='rbf', gamma=None, coef0=1, degree=3, n_components=100, random_state=None)

fit(X, y=None)

Fit estimator to data.

Samples a subset of training points, computes kernel on these and computes normalization matrix.

Parameters:

X : array-like, shape=(n_samples, n_feature)

Training data.

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

Fit to data, then transform it

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns:

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

get_params(deep=True)

Get parameters for the estimator

Parameters:

deep: boolean, optional :

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

set_params(**params)

Set the parameters of the estimator.

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

Returns:self :

transform(X)

Apply feature map to X.

Computes an approximate feature map using the kernel between some training points and X.

Parameters:

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

Data to transform.

Returns:

X_transformed : array, shape=(n_samples, n_components)

Transformed data.