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# `sklearn.manifold`.Isomap

class sklearn.manifold.Isomap(*, n_neighbors=5, radius=None, n_components=2, eigen_solver='auto', tol=0, max_iter=None, path_method='auto', neighbors_algorithm='auto', n_jobs=None, metric='minkowski', p=2, metric_params=None)

  Isomap Embedding.

  Non-linear dimensionality reduction through Isometric Mapping

  Read more in the User Guide.

  Parameters:
    n_neighbors int or None, default=5

      Number of neighbors to consider for each point. If `n_neighbors` is an int, then `radius` must be `None`.

    radius float or None, default=None

      Limiting distance of neighbors to return. If `radius` is a float, then `n_neighbors` must be set to `None`.

      New in version 1.1.

    n_components int, default=2

      Number of coordinates for the manifold.

    eigen_solver{‘auto’, ‘arpack’, ‘dense’}, default=’auto’

      ‘auto’ : Attempt to choose the most efficient solver for the given problem.

      ‘arpack’ : Use Arnoldi decomposition to find the eigenvalues and eigenvectors.

      ‘dense’ : Use a direct solver (i.e. LAPACK) for the eigenvalue decomposition.

    tol float, default=0

      Convergence tolerance passed to arpack or lobpcg. not used if eigen_solver == ‘dense’.

    max_iter int, default=None

      Maximum number of iterations for the arpack solver. not used if eigen_solver == ‘dense’.

    path_method{‘auto’, ‘FW’, ‘D’}, default=’auto’

      Method to use in finding shortest path.

      ‘auto’ : attempt to choose the best algorithm automatically.

      ‘FW’ : Floyd-Warshall algorithm.

      ‘D’ : Dijkstra’s algorithm.

    neighbors_algorithm{‘auto’, ‘brute’, ‘kd_tree’, ‘ball_tree’}, default=’auto’

      Algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance.

    n_jobs int or None, default=None

      The number of parallel jobs to run. `None` means 1 unless in a `joblib.parallel_backend` context. `-1` means using all processors. See Glossary for more details.

    metric str, or callable, default=”minkowski”

      The metric to use when calculating distance between instances in a feature array. If metric is a string or callable, it must be one of the options allowed by `sklearn.metrics.pairwise_distances` for its metric parameter. If metric is “precomputed”, X is assumed to be a distance matrix and must be square. X may be a Glossary.

      New in version 0.22.

    p float, default=2

      Parameter for the Minkowski metric from sklearn.metrics.pairwise.pairwise_distances. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.

      New in version 0.22.

    metric_params dict, default=None

      Additional keyword arguments for the metric function.

      New in version 0.22.

  Attributes:
    embedding_array-like, shape (n_samples, n_components)

      Stores the embedding vectors.

    kernel_pca_object

      `KernelPCA` object used to implement the embedding.

    nbrs_sklearn.neighbors.NearestNeighbors instance

      Stores nearest neighbors instance, including BallTree or KDtree if applicable.

    dist_matrix_array-like, shape (n_samples, n_samples)

      Stores the geodesic distance matrix of training data.

    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

  `sklearn.decomposition.PCA`

    Principal component analysis that is a linear dimensionality reduction method.

  `sklearn.decomposition.KernelPCA`

    Non-linear dimensionality reduction using kernels and PCA.

  `MDS`

    Manifold learning using multidimensional scaling.

  `TSNE`

    T-distributed Stochastic Neighbor Embedding.

  `LocallyLinearEmbedding`

    Manifold learning using Locally Linear Embedding.

  `SpectralEmbedding`

    Spectral embedding for non-linear dimensionality.

  References

  [1]

  Tenenbaum, J.B.; De Silva, V.; & Langford, J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (5500)

  Examples

      >>> from sklearn.datasets import load_digits
      >>> from sklearn.manifold import Isomap
      >>> X, _ = load_digits(return_X_y=True)
      >>> X.shape
      (1797, 64)
      >>> embedding = Isomap(n_components=2)
      >>> X_transformed = embedding.fit_transform(X[:100])
      >>> X_transformed.shape
      (100, 2)

  Methods

  `fit`(X[, y]) | Compute the embedding vectors for data X.
  `fit_transform`(X[, y]) | Fit the model from data in X and transform X.
  `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.
  `reconstruction_error`() | Compute the reconstruction error for the embedding.
  `set_output`(*[, transform]) | Set output container.
  `set_params`(**params) | Set the parameters of this estimator.
  `transform`(X) | Transform X.

  fit(X, y=None)

    Compute the embedding vectors for data X.

    Parameters:
      X{array-like, sparse matrix, BallTree, KDTree, NearestNeighbors}

        Sample data, shape = (n_samples, n_features), in the form of a numpy array, sparse matrix, precomputed tree, or NearestNeighbors object.

      y Ignored

        Not used, present for API consistency by convention.

    Returns:
      self object

        Returns a fitted instance of self.

  fit_transform(X, y=None)

    Fit the model from data in X and transform X.

    Parameters:
      X{array-like, sparse matrix, BallTree, KDTree}

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

      y Ignored

        Not used, present for API consistency by convention.

    Returns:
      X_new array-like, shape (n_samples, n_components)

        X transformed in the new space.

  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.

  reconstruction_error()

    Compute the reconstruction error for the embedding.

    Returns:
      reconstruction_error float

        Reconstruction error.

    Notes

    The cost function of an isomap embedding is

    `E = frobenius_norm[K(D) - K(D_fit)] / n_samples`

    Where D is the matrix of distances for the input data X, D_fit is the matrix of distances for the output embedding X_fit, and K is the isomap kernel:

    `K(D) = -0.5 * (I - 1/n_samples) * D^2 * (I - 1/n_samples)`

  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)

    Transform X.

    This is implemented by linking the points X into the graph of geodesic distances of the training data. First the `n_neighbors` nearest neighbors of X are found in the training data, and from these the shortest geodesic distances from each point in X to each point in the training data are computed in order to construct the kernel. The embedding of X is the projection of this kernel onto the embedding vectors of the training set.

    Parameters:
      X{array-like, sparse matrix}, shape (n_queries, n_features)

        If neighbors_algorithm=’precomputed’, X is assumed to be a distance matrix or a sparse graph of shape (n_queries, n_samples_fit).

    Returns:
      X_new array-like, shape (n_queries, n_components)

        X transformed in the new space.

## Examples using `sklearn.manifold.Isomap`

Release Highlights for scikit-learn 0.22

Release Highlights for scikit-learn 0.22

Comparison of Manifold Learning methods

Comparison of Manifold Learning methods

Manifold Learning methods on a severed sphere

Manifold Learning methods on a severed sphere

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

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