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# `sklearn.neighbors`.NeighborhoodComponentsAnalysis

class sklearn.neighbors.NeighborhoodComponentsAnalysis(n_components=None, *, init='auto', warm_start=False, max_iter=50, tol=1e-05, callback=None, verbose=0, random_state=None)

  Neighborhood Components Analysis.

  Neighborhood Component Analysis (NCA) is a machine learning algorithm for metric learning. It learns a linear transformation in a supervised fashion to improve the classification accuracy of a stochastic nearest neighbors rule in the transformed space.

  Read more in the User Guide.

  Parameters:
    n_components int, default=None

      Preferred dimensionality of the projected space. If None it will be set to `n_features`.

    init{‘auto’, ‘pca’, ‘lda’, ‘identity’, ‘random’} or ndarray of shape (n_features_a, n_features_b), default=’auto’

      Initialization of the linear transformation. Possible options are `'auto'`, `'pca'`, `'lda'`, `'identity'`, `'random'`, and a numpy array of shape `(n_features_a, n_features_b)`.

      - `'auto'`

          Depending on `n_components`, the most reasonable initialization will be chosen. If `n_components <= n_classes` we use `'lda'`, as it uses labels information. If not, but `n_components < min(n_features, n_samples)`, we use `'pca'`, as it projects data in meaningful directions (those of higher variance). Otherwise, we just use `'identity'`.

      - `'pca'`

          `n_components` principal components of the inputs passed to `fit` will be used to initialize the transformation. (See `PCA`)

      - `'lda'`

          `min(n_components, n_classes)` most discriminative components of the inputs passed to `fit` will be used to initialize the transformation. (If `n_components > n_classes`, the rest of the components will be zero.) (See `LinearDiscriminantAnalysis`)

      - `'identity'`

          If `n_components` is strictly smaller than the dimensionality of the inputs passed to `fit`, the identity matrix will be truncated to the first `n_components` rows.

      - `'random'`

          The initial transformation will be a random array of shape `(n_components, n_features)`. Each value is sampled from the standard normal distribution.

      - numpy array

          `n_features_b` must match the dimensionality of the inputs passed to `fit` and n_features_a must be less than or equal to that. If `n_components` is not `None`, `n_features_a` must match it.

    warm_start bool, default=False

      If `True` and `fit` has been called before, the solution of the previous call to `fit` is used as the initial linear transformation (`n_components` and `init` will be ignored).

    max_iter int, default=50

      Maximum number of iterations in the optimization.

    tol float, default=1e-5

      Convergence tolerance for the optimization.

    callback callable, default=None

      If not `None`, this function is called after every iteration of the optimizer, taking as arguments the current solution (flattened transformation matrix) and the number of iterations. This might be useful in case one wants to examine or store the transformation found after each iteration.

    verbose int, default=0

      If 0, no progress messages will be printed. If 1, progress messages will be printed to stdout. If > 1, progress messages will be printed and the `disp` parameter of `scipy.optimize.minimize` will be set to `verbose - 2`.

    random_state int or numpy.RandomState, default=None

      A pseudo random number generator object or a seed for it if int. If `init='random'`, `random_state` is used to initialize the random transformation. If `init='pca'`, `random_state` is passed as an argument to PCA when initializing the transformation. Pass an int for reproducible results across multiple function calls. See Glossary.

  Attributes:
    components_ndarray of shape (n_components, n_features)

      The linear transformation learned during fitting.

    n_features_in_int

      Number of features seen during fit.

      New in version 0.24.

    n_iter_int

      Counts the number of iterations performed by the optimizer.

    random_state_numpy.RandomState

      Pseudo random number generator object used during initialization.

    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

  `sklearn.discriminant_analysis.LinearDiscriminantAnalysis`

    Linear Discriminant Analysis.

  `sklearn.decomposition.PCA`

    Principal component analysis (PCA).

  References

  [1]

  J. Goldberger, G. Hinton, S. Roweis, R. Salakhutdinov. “Neighbourhood Components Analysis”. Advances in Neural Information Processing Systems. 17, 513-520, 2005. http://www.cs.nyu.edu/~roweis/papers/ncanips.pdf

  [2]

  Wikipedia entry on Neighborhood Components Analysis https://en.wikipedia.org/wiki/Neighbourhood_components_analysis

  Examples

      >>> from sklearn.neighbors import NeighborhoodComponentsAnalysis
      >>> from sklearn.neighbors import KNeighborsClassifier
      >>> from sklearn.datasets import load_iris
      >>> from sklearn.model_selection import train_test_split
      >>> X, y = load_iris(return_X_y=True)
      >>> X_train, X_test, y_train, y_test = train_test_split(X, y,
      ... stratify=y, test_size=0.7, random_state=42)
      >>> nca = NeighborhoodComponentsAnalysis(random_state=42)
      >>> nca.fit(X_train, y_train)
      NeighborhoodComponentsAnalysis(...)
      >>> knn = KNeighborsClassifier(n_neighbors=3)
      >>> knn.fit(X_train, y_train)
      KNeighborsClassifier(...)
      >>> print(knn.score(X_test, y_test))
      0.933333...
      >>> knn.fit(nca.transform(X_train), y_train)
      KNeighborsClassifier(...)
      >>> print(knn.score(nca.transform(X_test), y_test))
      0.961904...

  Methods

  `fit`(X, y) | Fit the model according to the given training 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 the learned transformation to the given data.

  fit(X, y)

    Fit the model according to the given training data.

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

        The training samples.

      y array-like of shape (n_samples,)

        The corresponding training labels.

    Returns:
      self object

        Fitted estimator.

  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 the learned transformation to the given data.

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

        Data samples.

    Returns:
      X_embedded: ndarray of shape (n_samples, n_components)

        The data samples transformed.

    Raises:
      NotFittedError

        If `fit` has not been called before.

## Examples using `sklearn.neighbors.NeighborhoodComponentsAnalysis`

Manifold learning on handwritten digits: Locally Linear Embedding, Isomap…

Manifold learning on handwritten digits: Locally Linear Embedding, Isomap...

Comparing Nearest Neighbors with and without Neighborhood Components Analysis

Comparing Nearest Neighbors with and without Neighborhood Components Analysis

Dimensionality Reduction with Neighborhood Components Analysis

Dimensionality Reduction with Neighborhood Components Analysis

Neighborhood Components Analysis Illustration

Neighborhood Components Analysis Illustration