.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/ERP/plot_embedding_MEG.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_ERP_plot_embedding_MEG.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_ERP_plot_embedding_MEG.py:


============================================
Embedding ERP MEG data in 2D Euclidean space
============================================

Riemannian embeddings via Laplacian Eigenmaps (LE) and Locally Linear
Embedding (LLE) of a set of ERP data. Embedding via Laplacian Eigenmaps is
referred to as Spectral Embedding (SE).

Locally Linear Embedding (LLE) assumes that the local neighborhood of a
point on the manifold can be well approximated by  the affine subspace
spanned by the k-nearest neighbors of the point and finds a low-dimensional
embedding of the data based on these affine approximations.

Laplacian Eigenmaps (LE) are based on computing the low dimensional
representation that best preserves locality instead of local linearity in LLE
[1]_.

.. GENERATED FROM PYTHON SOURCE LINES 19-35

.. code-block:: Python

    # Authors:  Pedro Rodrigues <pedro.rodrigues01@gmail.com>,
    #           Gabriel Wagner vom Berg <gabriel@bccn-berlin.de>
    # License: BSD (3-clause)

    import matplotlib.pyplot as plt
    import mne
    from mne import io
    from mne.datasets import sample
    from sklearn.model_selection import train_test_split

    from pyriemann.estimation import XdawnCovariances
    from pyriemann.utils.viz import plot_embedding

    print(__doc__)









.. GENERATED FROM PYTHON SOURCE LINES 36-38

Set parameters and read data
----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 38-61

.. code-block:: Python


    data_path = str(sample.data_path())
    raw_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'
    event_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif'
    tmin, tmax = -0., 1
    event_id = dict(aud_l=1, aud_r=2, vis_l=3, vis_r=4)

    # Setup for reading the raw data
    raw = io.Raw(raw_fname, preload=True, verbose=False)
    raw.filter(2, None, method='iir')  # replace baselining with high-pass
    events = mne.read_events(event_fname)

    raw.info['bads'] = ['MEG 2443']  # set bad channels
    picks = mne.pick_types(raw.info, meg=True, eeg=False, stim=False, eog=False,
                           exclude='bads')

    # Read epochs
    epochs = mne.Epochs(raw, events, event_id, tmin, tmax, proj=False,
                        picks=picks, baseline=None, preload=True, verbose=False)

    X = epochs.get_data(copy=False)
    y = epochs.events[:, -1]





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

 .. code-block:: none

    Filtering raw data in 1 contiguous segment
    Setting up high-pass filter at 2 Hz

    IIR filter parameters
    ---------------------
    Butterworth highpass zero-phase (two-pass forward and reverse) non-causal filter:
    - Filter order 8 (effective, after forward-backward)
    - Cutoff at 2.00 Hz: -6.02 dB





.. GENERATED FROM PYTHON SOURCE LINES 62-64

Embedding of Xdawn covariance matrices
--------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 64-71

.. code-block:: Python


    nfilter = 4
    xdwn = XdawnCovariances(estimator='scm', nfilter=nfilter)
    split = train_test_split(X, y, train_size=0.25, random_state=42)
    Xtrain, Xtest, ytrain, ytest = split
    covs = xdwn.fit(Xtrain, ytrain).transform(Xtest)








.. GENERATED FROM PYTHON SOURCE LINES 72-74

Laplacian Eigenmaps (LE), also called Spectral Embedding (SE)
-------------------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 74-79

.. code-block:: Python


    plot_embedding(covs, ytest, metric='riemann', embd_type='Spectral',
                   normalize=True)
    plt.show()




.. image-sg:: /auto_examples/ERP/images/sphx_glr_plot_embedding_MEG_001.png
   :alt: Spectral Embedding of covariances
   :srcset: /auto_examples/ERP/images/sphx_glr_plot_embedding_MEG_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 80-82

Locally Linear Embedding (LLE)
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 82-88

.. code-block:: Python


    plot_embedding(covs, ytest, metric='riemann', embd_type='LocallyLinear',
                   normalize=False)
    plt.show()





.. image-sg:: /auto_examples/ERP/images/sphx_glr_plot_embedding_MEG_002.png
   :alt: LocallyLinear Embedding of covariances
   :srcset: /auto_examples/ERP/images/sphx_glr_plot_embedding_MEG_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 89-95

References
----------
.. [1] `Clustering and dimensionality reduction on Riemannian manifolds
   <https://ieeexplore.ieee.org/document/4587422>`_
   A. Goh and R Vidal, in 2008 IEEE Conference on Computer Vision and Pattern
   Recognition.


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

   **Total running time of the script:** (0 minutes 12.343 seconds)


.. _sphx_glr_download_auto_examples_ERP_plot_embedding_MEG.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_embedding_MEG.ipynb <plot_embedding_MEG.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_embedding_MEG.py <plot_embedding_MEG.py>`


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 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_