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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
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.. _sphx_glr_auto_examples_manifold_plot_lle_digits.py:


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

We illustrate various embedding techniques on the digits dataset.

.. GENERATED FROM PYTHON SOURCE LINES 9-18

.. code-block:: default


    # Authors: Fabian Pedregosa <fabian.pedregosa@inria.fr>
    #          Olivier Grisel <olivier.grisel@ensta.org>
    #          Mathieu Blondel <mathieu@mblondel.org>
    #          Gael Varoquaux
    #          Guillaume Lemaitre <g.lemaitre58@gmail.com>
    # License: BSD 3 clause (C) INRIA 2011









.. GENERATED FROM PYTHON SOURCE LINES 19-22

Load digits dataset
-------------------
We will load the digits dataset and only use six first of the ten available classes.

.. GENERATED FROM PYTHON SOURCE LINES 22-29

.. code-block:: default

    from sklearn.datasets import load_digits

    digits = load_digits(n_class=6)
    X, y = digits.data, digits.target
    n_samples, n_features = X.shape
    n_neighbors = 30








.. GENERATED FROM PYTHON SOURCE LINES 30-31

We can plot the first hundred digits from this data set.

.. GENERATED FROM PYTHON SOURCE LINES 31-39

.. code-block:: default

    import matplotlib.pyplot as plt

    fig, axs = plt.subplots(nrows=10, ncols=10, figsize=(6, 6))
    for idx, ax in enumerate(axs.ravel()):
        ax.imshow(X[idx].reshape((8, 8)), cmap=plt.cm.binary)
        ax.axis("off")
    _ = fig.suptitle("A selection from the 64-dimensional digits dataset", fontsize=16)




.. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_001.png
   :alt: A selection from the 64-dimensional digits dataset
   :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 40-46

Helper function to plot embedding
---------------------------------
Below, we will use different techniques to embed the digits dataset. We will plot
the projection of the original data onto each embedding. It will allow us to
check whether or digits are grouped together in the embedding space, or
scattered across it.

.. GENERATED FROM PYTHON SOURCE LINES 46-84

.. code-block:: default

    import numpy as np
    from matplotlib import offsetbox

    from sklearn.preprocessing import MinMaxScaler


    def plot_embedding(X, title):
        _, ax = plt.subplots()
        X = MinMaxScaler().fit_transform(X)

        for digit in digits.target_names:
            ax.scatter(
                *X[y == digit].T,
                marker=f"${digit}$",
                s=60,
                color=plt.cm.Dark2(digit),
                alpha=0.425,
                zorder=2,
            )
        shown_images = np.array([[1.0, 1.0]])  # just something big
        for i in range(X.shape[0]):
            # plot every digit on the embedding
            # show an annotation box for a group of digits
            dist = np.sum((X[i] - shown_images) ** 2, 1)
            if np.min(dist) < 4e-3:
                # don't show points that are too close
                continue
            shown_images = np.concatenate([shown_images, [X[i]]], axis=0)
            imagebox = offsetbox.AnnotationBbox(
                offsetbox.OffsetImage(digits.images[i], cmap=plt.cm.gray_r), X[i]
            )
            imagebox.set(zorder=1)
            ax.add_artist(imagebox)

        ax.set_title(title)
        ax.axis("off")









.. GENERATED FROM PYTHON SOURCE LINES 85-103

Embedding techniques comparison
-------------------------------

Below, we compare different techniques. However, there are a couple of things
to note:

* the :class:`~sklearn.ensemble.RandomTreesEmbedding` is not
  technically a manifold embedding method, as it learn a high-dimensional
  representation on which we apply a dimensionality reduction method.
  However, it is often useful to cast a dataset into a representation in
  which the classes are linearly-separable.
* the :class:`~sklearn.discriminant_analysis.LinearDiscriminantAnalysis` and
  the :class:`~sklearn.neighbors.NeighborhoodComponentsAnalysis`, are supervised
  dimensionality reduction method, i.e. they make use of the provided labels,
  contrary to other methods.
* the :class:`~sklearn.manifold.TSNE` is initialized with the embedding that is
  generated by PCA in this example. It ensures global stability  of the embedding,
  i.e., the embedding does not depend on random initialization.

.. GENERATED FROM PYTHON SOURCE LINES 103-160

.. code-block:: default

    from sklearn.decomposition import TruncatedSVD
    from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
    from sklearn.ensemble import RandomTreesEmbedding
    from sklearn.manifold import (
        MDS,
        TSNE,
        Isomap,
        LocallyLinearEmbedding,
        SpectralEmbedding,
    )
    from sklearn.neighbors import NeighborhoodComponentsAnalysis
    from sklearn.pipeline import make_pipeline
    from sklearn.random_projection import SparseRandomProjection

    embeddings = {
        "Random projection embedding": SparseRandomProjection(
            n_components=2, random_state=42
        ),
        "Truncated SVD embedding": TruncatedSVD(n_components=2),
        "Linear Discriminant Analysis embedding": LinearDiscriminantAnalysis(
            n_components=2
        ),
        "Isomap embedding": Isomap(n_neighbors=n_neighbors, n_components=2),
        "Standard LLE embedding": LocallyLinearEmbedding(
            n_neighbors=n_neighbors, n_components=2, method="standard"
        ),
        "Modified LLE embedding": LocallyLinearEmbedding(
            n_neighbors=n_neighbors, n_components=2, method="modified"
        ),
        "Hessian LLE embedding": LocallyLinearEmbedding(
            n_neighbors=n_neighbors, n_components=2, method="hessian"
        ),
        "LTSA LLE embedding": LocallyLinearEmbedding(
            n_neighbors=n_neighbors, n_components=2, method="ltsa"
        ),
        "MDS embedding": MDS(
            n_components=2, n_init=1, max_iter=120, n_jobs=2, normalized_stress="auto"
        ),
        "Random Trees embedding": make_pipeline(
            RandomTreesEmbedding(n_estimators=200, max_depth=5, random_state=0),
            TruncatedSVD(n_components=2),
        ),
        "Spectral embedding": SpectralEmbedding(
            n_components=2, random_state=0, eigen_solver="arpack"
        ),
        "t-SNE embeedding": TSNE(
            n_components=2,
            n_iter=500,
            n_iter_without_progress=150,
            n_jobs=2,
            random_state=0,
        ),
        "NCA embedding": NeighborhoodComponentsAnalysis(
            n_components=2, init="pca", random_state=0
        ),
    }








.. GENERATED FROM PYTHON SOURCE LINES 161-164

Once we declared all the methodes of interest, we can run and perform the projection
of the original data. We will store the projected data as well as the computational
time needed to perform each projection.

.. GENERATED FROM PYTHON SOURCE LINES 164-179

.. code-block:: default

    from time import time

    projections, timing = {}, {}
    for name, transformer in embeddings.items():
        if name.startswith("Linear Discriminant Analysis"):
            data = X.copy()
            data.flat[:: X.shape[1] + 1] += 0.01  # Make X invertible
        else:
            data = X

        print(f"Computing {name}...")
        start_time = time()
        projections[name] = transformer.fit_transform(data, y)
        timing[name] = time() - start_time





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Computing Random projection embedding...
    Computing Truncated SVD embedding...
    Computing Linear Discriminant Analysis embedding...
    Computing Isomap embedding...
    Computing Standard LLE embedding...
    Computing Modified LLE embedding...
    Computing Hessian LLE embedding...
    Computing LTSA LLE embedding...
    Computing MDS embedding...
    Computing Random Trees embedding...
    Computing Spectral embedding...
    Computing t-SNE embeedding...
    Computing NCA embedding...




.. GENERATED FROM PYTHON SOURCE LINES 180-181

Finally, we can plot the resulting projection given by each method.

.. GENERATED FROM PYTHON SOURCE LINES 181-186

.. code-block:: default

    for name in timing:
        title = f"{name} (time {timing[name]:.3f}s)"
        plot_embedding(projections[name], title)

    plt.show()



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_002.png
         :alt: Random projection embedding (time 0.001s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_003.png
         :alt: Truncated SVD embedding (time 0.010s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_004.png
         :alt: Linear Discriminant Analysis embedding (time 0.010s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_005.png
         :alt: Isomap embedding (time 0.674s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_006.png
         :alt: Standard LLE embedding (time 0.225s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_006.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_007.png
         :alt: Modified LLE embedding (time 0.436s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_007.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_008.png
         :alt: Hessian LLE embedding (time 0.485s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_008.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_009.png
         :alt: LTSA LLE embedding (time 0.370s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_009.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_010.png
         :alt: MDS embedding (time 1.623s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_010.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_011.png
         :alt: Random Trees embedding (time 0.152s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_011.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_012.png
         :alt: Spectral embedding (time 0.271s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_012.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_013.png
         :alt: t-SNE embeedding (time 0.784s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_013.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_014.png
         :alt: NCA embedding (time 2.363s)
         :srcset: /auto_examples/manifold/images/sphx_glr_plot_lle_digits_014.png
         :class: sphx-glr-multi-img






.. rst-class:: sphx-glr-timing

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