.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/biosignal-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_biosignal-erp_plot_embedding_MEG.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_biosignal-erp_plot_embedding_MEG.py:


===============================================
Comparison of embeddings of covariance matrices
===============================================

Comparison of several embeddings of a set of ERP covariance matrices extracted
on MEG data: SE, LLE and t-SNE

Spectral Embedding (SE) is based on computing the low-dimensional
representation that best preserves locality instead of local linearity in LLE
[1]_.

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

t-SNE reduces SPD matrices into lower dimensional SPD matrices by computing
conditional probabilities that represent similarities [2]_. This fully
Riemannian algorithm helps preserve the non-Euclidean structure of the data.

.. GENERATED FROM PYTHON SOURCE LINES 22-39

.. code-block:: Python

    # Authors:  Pedro Rodrigues <pedro.rodrigues01@gmail.com>,
    #           Gabriel Wagner vom Berg <gabriel@bccn-berlin.de>
    #           Thibault de Surrel <thibault.de-surrel@lamsade.dauphine.fr>
    #
    # 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 40-42

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

.. GENERATED FROM PYTHON SOURCE LINES 42-64

.. 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

    Using default location ~/mne_data for sample...

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    Download complete in 52s (1576.2 MB)
    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 65-67

Extract Xdawn covariance matrices
---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 67-74

.. 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 75-77

Spectral Embedding (SE)
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 77-83

.. code-block:: Python


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





.. image-sg:: /auto_examples/biosignal-erp/images/sphx_glr_plot_embedding_MEG_001.png
   :alt: Spectral Embedding of SPD matrices
   :srcset: /auto_examples/biosignal-erp/images/sphx_glr_plot_embedding_MEG_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 84-86

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

.. GENERATED FROM PYTHON SOURCE LINES 86-92

.. code-block:: Python


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





.. image-sg:: /auto_examples/biosignal-erp/images/sphx_glr_plot_embedding_MEG_002.png
   :alt: LocallyLinear Embedding of SPD matrices
   :srcset: /auto_examples/biosignal-erp/images/sphx_glr_plot_embedding_MEG_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 93-95

TNSE
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 95-100

.. code-block:: Python


    plot_embedding(covs, ytest, metric="riemann", embd_type="TSNE",
                   normalize=False, max_iter=50)
    plt.show()




.. image-sg:: /auto_examples/biosignal-erp/images/sphx_glr_plot_embedding_MEG_003.png
   :alt: TSNE Embedding of SPD matrices
   :srcset: /auto_examples/biosignal-erp/images/sphx_glr_plot_embedding_MEG_003.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    /home/docs/checkouts/readthedocs.org/user_builds/pyriemann/checkouts/v0.10/pyriemann/optimization/positive_definite.py:284: UserWarning: Convergence not reached. Try increasing max_iter.
      warnings.warn("Convergence not reached. Try increasing max_iter.")




.. GENERATED FROM PYTHON SOURCE LINES 101-112

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.
.. [2] `Geometry-Aware visualization of high dimensional Symmetric
    Positive Definite matrices
    <https://openreview.net/pdf?id=DYCSRf3vby>`_
    T. de Surrel, S. Chevallier, F. Lotte and F. Yger.
    Transactions on Machine Learning Research, 2025


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

   **Total running time of the script:** (1 minutes 0.360 seconds)


.. _sphx_glr_download_auto_examples_biosignal-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>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_embedding_MEG.zip <plot_embedding_MEG.zip>`


.. only:: html

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

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