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

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.

Read more in the User Guide.


kernel : string or callable, default=”rbf”

Kernel map to be approximated. A callable should accept two arguments and the keyword arguments passed to this object as kernel_params, and should return a floating point number.

n_components : int

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

gamma : float, default=None

Gamma parameter for the RBF, laplacian, polynomial, exponential chi2 and sigmoid kernels. Interpretation of the default value is left to the kernel; see the documentation for sklearn.metrics.pairwise. Ignored by other kernels.

degree : float, default=3

Degree of the polynomial kernel. Ignored by other kernels.

coef0 : float, default=1

Zero coefficient for polynomial and sigmoid kernels. Ignored by other kernels.

kernel_params : mapping of string to any, optional

Additional parameters (keyword arguments) for kernel function passed as callable object.

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.


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_.

See also

An approximation to the RBF kernel using random Fourier features.
List of built-in kernels.


  • Williams, C.K.I. and Seeger, M. “Using the Nystroem 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


fit(X[, y]) Fit estimator to data.
fit_transform(X[, y]) Fit to data, then transform it.
get_params([deep]) Get parameters for this estimator.
set_params(**params) Set the parameters of this estimator.
transform(X) Apply feature map to X.
__init__(kernel='rbf', gamma=None, coef0=1, degree=3, kernel_params=None, n_components=100, random_state=None)[source]
fit(X, y=None)[source]

Fit estimator to data.

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


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

Training data.

fit_transform(X, y=None, **fit_params)[source]

Fit to data, then transform it.

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


X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.


X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.


Get parameters for this estimator.


deep : boolean, optional

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


params : mapping of string to any

Parameter names mapped to their values.


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 :

Apply feature map to X.

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


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

Data to transform.


X_transformed : array, shape=(n_samples, n_components)

Transformed data.

Examples using sklearn.kernel_approximation.Nystroem