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# `sklearn.kernel_approximation`.Nystroem

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

  Read more in the User Guide.

  New in version 0.13.

  Parameters:
    kernel str 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.

    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.

    coef0 float, default=None

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

    degree float, default=None

      Degree of the polynomial kernel. Ignored by other kernels.

    kernel_params dict, default=None

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

    n_components int, default=100

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

    random_state int, 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_jobs int, 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.

      New 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.

      New 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.

      New 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(dual="auto")
      >>> 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(dual='auto')
      >>> clf.score(data_transformed, y)
      0.9987...

  Methods

  `fit`(X[, y]) | Fit estimator to data.
  `fit_transform`(X[, y]) | Fit to data, then transform it.
  `get_feature_names_out`([input_features]) | Get output feature names for transformation.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `set_output`(*[, transform]) | Set output container.
  `set_params`(**params) | Set the parameters of this estimator.
  `transform`(X) | Apply feature map to X.

  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_features)

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

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

        Target values (None for unsupervised transformations).

    Returns:
      self object

        Returns the instance itself.

  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 array-like of shape (n_samples, n_features)

        Input samples.

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

        Target values (None for unsupervised transformations).

      **fit_params dict

        Additional fit parameters.

    Returns:
      X_new ndarray array of shape (n_samples, n_features_new)

        Transformed array.

  get_feature_names_out(input_features=None)

    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_features array-like of str or None, default=None

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

    Returns:
      feature_names_out ndarray of str objects

        Transformed feature names.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  get_params(deep=True)

    Get parameters for this estimator.

    Parameters:
      deep bool, default=True

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

    Returns:
      params dict

        Parameter names mapped to their values.

  set_output(*, transform=None)

    Set output container.

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

    Parameters:
      transform{“default”, “pandas”}, default=None

        Configure output of `transform` and `fit_transform`.

        - `"default"`: Default output format of a transformer

        - `"pandas"`: DataFrame output

        - `None`: Transform configuration is unchanged

    Returns:
      self estimator instance

        Estimator instance.

  set_params(**params)

    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:
      **params dict

        Estimator parameters.

    Returns:
      self estimator instance

        Estimator instance.

  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 of shape (n_samples, n_features)

        Data to transform.

    Returns:
      X_transformed ndarray of shape (n_samples, n_components)

        Transformed data.

## Examples using `sklearn.kernel_approximation.Nystroem`

Time-related feature engineering

Time-related feature engineering

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

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

Comparing anomaly detection algorithms for outlier detection on toy datasets

Comparing anomaly detection algorithms for outlier detection on toy datasets

Explicit feature map approximation for RBF kernels

Explicit feature map approximation for RBF kernels

Imputing missing values with variants of IterativeImputer

Imputing missing values with variants of IterativeImputer