Nystroem

classsklearn.kernel_approximation.Nystroem(kernel='rbf', *, gamma=None, coef0=None, degree=None, kernel_params=None, n_components=100, random_state=None, n_jobs=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.

Added in version 0.13.

Parameters:

kernelstr 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.

gammafloat, 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.

coef0float, default=None

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

degreefloat, default=None

Degree of the polynomial kernel. Ignored by other kernels.

kernel_paramsdict, default=None

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

n_componentsint, default=100

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

random_stateint, RandomState instance or None, default=None

Pseudo-random number generator to control the uniform sampling without replacement of n_components of the training data to construct the basis kernel. Pass an int for reproducible output across multiple function calls. See Glossary.

n_jobsint, default=None

The number of jobs to use for the computation. This works by breaking down the kernel matrix into n_jobs even slices and computing them in parallel.

None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Added in version 0.24.

Attributes:

components_ndarray of shape (n_components, n_features)

Subset of training points used to construct the feature map.

component_indices_ndarray of shape (n_components)

Indices of components_ in the training set.

normalization_ndarray of shape (n_components, n_components)

Normalization matrix needed for embedding. Square root of the kernel matrix on components_.

n_features_in_int

Number of features seen during fit.

Added in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

Added in version 1.0.

See also

AdditiveChi2Sampler

Approximate feature map for additive chi2 kernel.

PolynomialCountSketch

Polynomial kernel approximation via Tensor Sketch.

RBFSampler

Approximate a RBF kernel feature map using random Fourier features.

SkewedChi2Sampler

Approximate feature map for “skewed chi-squared” kernel.

sklearn.metrics.pairwise.kernel_metrics

List of built-in kernels.

References

• 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

Examples

>>> from sklearn import datasets, svm
>>> from sklearn.kernel_approximation import Nystroem
>>> X, y = datasets.load_digits(n_class=9, return_X_y=True)
>>> data = X / 16.
>>> clf = svm.LinearSVC()
>>> feature_map_nystroem = Nystroem(gamma=.2,
...                                 random_state=1,
...                                 n_components=300)
>>> data_transformed = feature_map_nystroem.fit_transform(data)
>>> clf.fit(data_transformed, y)
LinearSVC()
>>> clf.score(data_transformed, y)
0.9987...

fit(X, y=None)[source]

Fit estimator to data.

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

Parameters:

Xarray-like, shape (n_samples, n_features)

Training data, where n_samples is the number of samples and n_features is the number of features.

yarray-like, shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

Returns:

selfobject

Returns the instance itself.

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.

Parameters:

Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

Additional fit parameters.

Returns:

X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

get_feature_names_out(input_features=None)[source]

Get output feature names for transformation.

The feature names out will prefixed by the lowercased class name. For example, if the transformer outputs 3 features, then the feature names out are: ["class_name0", "class_name1", "class_name2"].

Parameters:

input_featuresarray-like of str or None, default=None

Only used to validate feature names with the names seen in fit.

Returns:

feature_names_outndarray of str objects

Transformed feature names.

get_metadata_routing()[source]

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)[source]

Get parameters for this estimator.

Parameters:

deepbool, default=True

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

Returns:

paramsdict

Parameter names mapped to their values.

set_output(*, transform=None)[source]

Set output container.

See Introducing the set_output API for an example on how to use the API.

Parameters:

transform{“default”, “pandas”, “polars”}, default=None

Configure output of transform and fit_transform.

• "default": Default output format of a transformer
• "pandas": DataFrame output
• "polars": Polars output
• None: Transform configuration is unchanged

Added in version 1.4: "polars" option was added.

Returns:

selfestimator instance

Estimator instance.

set_params(**params)[source]

Set the parameters of this estimator.

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

Parameters:

**paramsdict

Estimator parameters.

Returns:

selfestimator instance

Estimator instance.

transform(X)[source]

Apply feature map to X.

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

Parameters:

Xarray-like of shape (n_samples, n_features)

Data to transform.

Returns:

X_transformedndarray of shape (n_samples, n_components)

Transformed data.

Gallery examples

Time-related feature engineering

One-Class SVM versus One-Class SVM using Stochastic Gradient Descent

Comparing anomaly detection algorithms for outlier detection on toy datasets

Explicit feature map approximation for RBF kernels

Imputing missing values with variants of IterativeImputer