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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_SSVEP_plot_classify_ssvep_pga.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_SSVEP_plot_classify_ssvep_pga.py:


===============================================================================
Visualization of SSVEP-based BCI Classification in Tangent Space
===============================================================================

Project extended covariance matrices of SSVEP-based BCI in the tangent space,
using principal geodesic analysis (PGA).

You should have a look to "Offline SSVEP-based BCI Multiclass Prediction"
before this example.

.. GENERATED FROM PYTHON SOURCE LINES 12-32

.. code-block:: default

    # Authors: Quentin Barthélemy, Emmanuel Kalunga and Sylvain Chevallier
    #
    # License: BSD (3-clause)

    import numpy as np
    import matplotlib.pyplot as plt
    from matplotlib.animation import FuncAnimation

    from mne import find_events, Epochs, make_fixed_length_epochs
    from mne.io import Raw
    from sklearn.pipeline import make_pipeline
    from sklearn.decomposition import PCA

    from pyriemann.estimation import BlockCovariances
    from pyriemann.classification import MDM
    from pyriemann.tangentspace import TangentSpace
    from pyriemann.utils.viz import _add_alpha
    from helpers.ssvep_helpers import download_data, extend_signal









.. GENERATED FROM PYTHON SOURCE LINES 33-51

.. code-block:: default


    clabel = ['resting-state', '13 Hz', '17 Hz', '21 Hz']
    clist = plt.cm.viridis(np.array([0, 1, 2, 3])/3)
    cmap = "viridis"


    def plot_pga(ax, data, labels, centers):
        sc = ax.scatter(data[:, 0], data[:, 1], c=labels, marker='P', cmap=cmap)
        ax.scatter(
            centers[:, 0], centers[:, 1], c=clist, marker='o', s=100, cmap=cmap
            )
        ax.set(xlabel='PGA, 1st axis', ylabel='PGA, 2nd axis')
        for i in range(len(clabel)):
            ax.scatter([], [], color=clist[i], marker='o', s=50, label=clabel[i])
        ax.legend(loc='upper right')
        return sc









.. GENERATED FROM PYTHON SOURCE LINES 52-54

Load EEG and extract covariance matrices for SSVEP
--------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 54-86

.. code-block:: default


    frequencies = [13, 17, 21]
    freq_band = 0.1
    events_id = {'13 Hz': 2, '17 Hz': 4, '21 Hz': 3, 'resting-state': 1}

    duration = 2.5    # duration of epochs
    interval = 0.25   # interval between successive epochs for online processing

    # Subject 12: first 4 sessions for training, last session for test

    # Training set
    raw = Raw(download_data(subject=12, session=1), preload=True, verbose=False)
    events = find_events(raw, shortest_event=0, verbose=False)
    raw = raw.pick_types(eeg=True)
    ch_count = len(raw.info['ch_names'])
    raw_ext = extend_signal(raw, frequencies, freq_band)
    epochs = Epochs(
        raw_ext, events, events_id, tmin=2, tmax=5, baseline=None, verbose=False)
    x_train = BlockCovariances(
        estimator='lwf', block_size=ch_count).transform(epochs.get_data())
    y_train = events[:, 2]

    # Testing set
    raw = Raw(download_data(subject=12, session=4), preload=True, verbose=False)
    raw = raw.pick_types(eeg=True)
    raw_ext = extend_signal(raw, frequencies, freq_band)
    epochs = make_fixed_length_epochs(
        raw_ext, duration=duration, overlap=duration - interval, verbose=False)
    x_test = BlockCovariances(
        estimator='lwf', block_size=ch_count).transform(epochs.get_data())






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

 .. code-block:: none

    Creating RawArray with float64 data, n_channels=24, n_times=92384
        Range : 0 ... 92383 =      0.000 ...   360.871 secs
    Ready.
    Using data from preloaded Raw for 32 events and 769 original time points ...
    0 bad epochs dropped

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    Creating RawArray with float64 data, n_channels=24, n_times=148544
        Range : 0 ... 148543 =      0.000 ...   580.246 secs
    Ready.
    Using data from preloaded Raw for 2312 events and 640 original time points ...
    0 bad epochs dropped




.. GENERATED FROM PYTHON SOURCE LINES 87-91

Classification with minimum distance to mean (MDM)
--------------------------------------------------

Classification for a 4-class SSVEP BCI, including resting-state class.

.. GENERATED FROM PYTHON SOURCE LINES 91-98

.. code-block:: default


    print("Number of training trials: {}".format(len(x_train)))

    mdm = MDM(metric=dict(mean='riemann', distance='riemann'))
    mdm.fit(x_train, y_train)






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

 .. code-block:: none

    Number of training trials: 32

    MDM(metric={'distance': 'riemann', 'mean': 'riemann'})



.. GENERATED FROM PYTHON SOURCE LINES 99-105

Projection in tangent space with principal geodesic analysis (PGA)
------------------------------------------------------------------

Project covariance matrices from the Riemannian manifold into the Euclidean
tangent space at the grand average, and apply a principal component analysis
(PCA) to obtain an unsupervised dimension reduction [1]_.

.. GENERATED FROM PYTHON SOURCE LINES 105-115

.. code-block:: default


    pga = make_pipeline(
        TangentSpace(metric="riemann", tsupdate=False),
        PCA(n_components=2)
    )

    ts_train = pga.fit_transform(x_train)
    ts_means = pga.transform(np.array(mdm.covmeans_))









.. GENERATED FROM PYTHON SOURCE LINES 116-125

Offline training of MDM visualized by PGA
-----------------------------------------

These figures show the trajectory on the tangent space taken by covariance
matrices during a 4-class SSVEP experiment, and how they are classified epoch
by epoch.

This figure reproduces Fig 3(c) of reference [2]_, showing training trials of
best subject.

.. GENERATED FROM PYTHON SOURCE LINES 125-132

.. code-block:: default


    fig, ax = plt.subplots(figsize=(8, 8))
    fig.suptitle('PGA of training set', fontsize=16)
    plot_pga(ax, ts_train, y_train, ts_means)
    plt.show()





.. image-sg:: /auto_examples/SSVEP/images/sphx_glr_plot_classify_ssvep_pga_001.png
   :alt: PGA of training set
   :srcset: /auto_examples/SSVEP/images/sphx_glr_plot_classify_ssvep_pga_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 133-141

Online classification by MDM visualized by PGA
----------------------------------------------

This figure reproduces Fig 6 of reference [2]_, with an animation to imitate
an online acquisition, processing and classification of EEG time-series.

Warning: [2]_ uses a curved based online classification, while a single trial
classification is used here.

.. GENERATED FROM PYTHON SOURCE LINES 141-154

.. code-block:: default


    # Prepare data for online classification
    test_visu = 50     # nb of matrices to display simultaneously
    colors, ts_visu = [], np.empty([0, 2])
    alphas = np.linspace(0, 1, test_visu)

    fig, ax = plt.subplots(figsize=(8, 8))
    fig.suptitle('PGA of testing set', fontsize=16)
    pl = plot_pga(ax, ts_visu, colors, ts_means)
    pl.axes.set_xlim(-5, 6)
    pl.axes.set_ylim(-5, 5)





.. image-sg:: /auto_examples/SSVEP/images/sphx_glr_plot_classify_ssvep_pga_002.png
   :alt: PGA of testing set
   :srcset: /auto_examples/SSVEP/images/sphx_glr_plot_classify_ssvep_pga_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    (-5.0, 5.0)



.. GENERATED FROM PYTHON SOURCE LINES 155-186

.. code-block:: default


    # Prepare animation for online classification
    def online_classify(t):
        global colors, ts_visu

        # Online classification
        y = mdm.predict(x_test[np.newaxis, t])
        color = clist[int(y[0] - 1)]
        ts_test = pga.transform(x_test[np.newaxis, t])

        # Update data
        colors.append(color)
        ts_visu = np.vstack((ts_visu, ts_test))
        if len(ts_visu) > test_visu:
            colors.pop(0)
            ts_visu = ts_visu[1:]
        colors = _add_alpha(colors, alphas)

        # Update plot
        pl.set_offsets(np.c_[ts_visu[:, 0], ts_visu[:, 1]])
        pl.set_color(colors)
        return pl


    interval_display = 1.0  # can be changed for a slower display

    visu = FuncAnimation(fig, online_classify,
                         frames=range(0, len(x_test)),
                         interval=interval_display, blit=False, repeat=False)









.. GENERATED FROM PYTHON SOURCE LINES 187-203

.. code-block:: default


    # Plot online classification

    # Plot complete visu: a dynamic display is required
    plt.show()

    # Plot only 10s, for animated documentation
    try:
        from IPython.display import HTML
    except ImportError:
        raise ImportError("Install IPython to plot animation in documentation")

    plt.rcParams["animation.embed_limit"] = 10
    HTML(visu.to_jshtml(fps=5, default_mode='loop'))






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

 .. code-block:: none

    Animation size has reached 10525072 bytes, exceeding the limit of 10485760.0. If you're sure you want a larger animation embedded, set the animation.embed_limit rc parameter to a larger value (in MB). This and further frames will be dropped.


.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">

    <link rel="stylesheet"
    href="https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css">
    <script language="javascript">
      function isInternetExplorer() {
        ua = navigator.userAgent;
        /* MSIE used to detect old browsers and Trident used to newer ones*/
        return ua.indexOf("MSIE ") > -1 || ua.indexOf("Trident/") > -1;
      }

      /* Define the Animation class */
      function Animation(frames, img_id, slider_id, interval, loop_select_id){
        this.img_id = img_id;
        this.slider_id = slider_id;
        this.loop_select_id = loop_select_id;
        this.interval = interval;
        this.current_frame = 0;
        this.direction = 0;
        this.timer = null;
        this.frames = new Array(frames.length);

        for (var i=0; i<frames.length; i++)
        {
         this.frames[i] = new Image();
         this.frames[i].src = frames[i];
        }
        var slider = document.getElementById(this.slider_id);
        slider.max = this.frames.length - 1;
        if (isInternetExplorer()) {
            // switch from oninput to onchange because IE <= 11 does not conform
            // with W3C specification. It ignores oninput and onchange behaves
            // like oninput. In contrast, Microsoft Edge behaves correctly.
            slider.setAttribute('onchange', slider.getAttribute('oninput'));
            slider.setAttribute('oninput', null);
        }
        this.set_frame(this.current_frame);
      }

      Animation.prototype.get_loop_state = function(){
        var button_group = document[this.loop_select_id].state;
        for (var i = 0; i < button_group.length; i++) {
            var button = button_group[i];
            if (button.checked) {
                return button.value;
            }
        }
        return undefined;
      }

      Animation.prototype.set_frame = function(frame){
        this.current_frame = frame;
        document.getElementById(this.img_id).src =
                this.frames[this.current_frame].src;
        document.getElementById(this.slider_id).value = this.current_frame;
      }

      Animation.prototype.next_frame = function()
      {
        this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));
      }

      Animation.prototype.previous_frame = function()
      {
        this.set_frame(Math.max(0, this.current_frame - 1));
      }

      Animation.prototype.first_frame = function()
      {
        this.set_frame(0);
      }

      Animation.prototype.last_frame = function()
      {
        this.set_frame(this.frames.length - 1);
      }

      Animation.prototype.slower = function()
      {
        this.interval /= 0.7;
        if(this.direction > 0){this.play_animation();}
        else if(this.direction < 0){this.reverse_animation();}
      }

      Animation.prototype.faster = function()
      {
        this.interval *= 0.7;
        if(this.direction > 0){this.play_animation();}
        else if(this.direction < 0){this.reverse_animation();}
      }

      Animation.prototype.anim_step_forward = function()
      {
        this.current_frame += 1;
        if(this.current_frame < this.frames.length){
          this.set_frame(this.current_frame);
        }else{
          var loop_state = this.get_loop_state();
          if(loop_state == "loop"){
            this.first_frame();
          }else if(loop_state == "reflect"){
            this.last_frame();
            this.reverse_animation();
          }else{
            this.pause_animation();
            this.last_frame();
          }
        }
      }

      Animation.prototype.anim_step_reverse = function()
      {
        this.current_frame -= 1;
        if(this.current_frame >= 0){
          this.set_frame(this.current_frame);
        }else{
          var loop_state = this.get_loop_state();
          if(loop_state == "loop"){
            this.last_frame();
          }else if(loop_state == "reflect"){
            this.first_frame();
            this.play_animation();
          }else{
            this.pause_animation();
            this.first_frame();
          }
        }
      }

      Animation.prototype.pause_animation = function()
      {
        this.direction = 0;
        if (this.timer){
          clearInterval(this.timer);
          this.timer = null;
        }
      }

      Animation.prototype.play_animation = function()
      {
        this.pause_animation();
        this.direction = 1;
        var t = this;
        if (!this.timer) this.timer = setInterval(function() {
            t.anim_step_forward();
        }, this.interval);
      }

      Animation.prototype.reverse_animation = function()
      {
        this.pause_animation();
        this.direction = -1;
        var t = this;
        if (!this.timer) this.timer = setInterval(function() {
            t.anim_step_reverse();
        }, this.interval);
      }
    </script>

    <style>
    .animation {
        display: inline-block;
        text-align: center;
    }
    input[type=range].anim-slider {
        width: 374px;
        margin-left: auto;
        margin-right: auto;
    }
    .anim-buttons {
        margin: 8px 0px;
    }
    .anim-buttons button {
        padding: 0;
        width: 36px;
    }
    .anim-state label {
        margin-right: 8px;
    }
    .anim-state input {
        margin: 0;
        vertical-align: middle;
    }
    </style>

    <div class="animation">
      <img id="_anim_img86edcf6f8fdd4a24a7937896143f61a7">
      <div class="anim-controls">
        <input id="_anim_slider86edcf6f8fdd4a24a7937896143f61a7" type="range" class="anim-slider"
               name="points" min="0" max="1" step="1" value="0"
               oninput="anim86edcf6f8fdd4a24a7937896143f61a7.set_frame(parseInt(this.value));">
        <div class="anim-buttons">
          <button title="Decrease speed" aria-label="Decrease speed" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.slower()">
              <i class="fa fa-minus"></i></button>
          <button title="First frame" aria-label="First frame" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.first_frame()">
            <i class="fa fa-fast-backward"></i></button>
          <button title="Previous frame" aria-label="Previous frame" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.previous_frame()">
              <i class="fa fa-step-backward"></i></button>
          <button title="Play backwards" aria-label="Play backwards" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.reverse_animation()">
              <i class="fa fa-play fa-flip-horizontal"></i></button>
          <button title="Pause" aria-label="Pause" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.pause_animation()">
              <i class="fa fa-pause"></i></button>
          <button title="Play" aria-label="Play" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.play_animation()">
              <i class="fa fa-play"></i></button>
          <button title="Next frame" aria-label="Next frame" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.next_frame()">
              <i class="fa fa-step-forward"></i></button>
          <button title="Last frame" aria-label="Last frame" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.last_frame()">
              <i class="fa fa-fast-forward"></i></button>
          <button title="Increase speed" aria-label="Increase speed" onclick="anim86edcf6f8fdd4a24a7937896143f61a7.faster()">
              <i class="fa fa-plus"></i></button>
        </div>
        <form title="Repetition mode" aria-label="Repetition mode" action="#n" name="_anim_loop_select86edcf6f8fdd4a24a7937896143f61a7"
              class="anim-state">
          <input type="radio" name="state" value="once" id="_anim_radio1_86edcf6f8fdd4a24a7937896143f61a7"
                 >
          <label for="_anim_radio1_86edcf6f8fdd4a24a7937896143f61a7">Once</label>
          <input type="radio" name="state" value="loop" id="_anim_radio2_86edcf6f8fdd4a24a7937896143f61a7"
                 checked>
          <label for="_anim_radio2_86edcf6f8fdd4a24a7937896143f61a7">Loop</label>
          <input type="radio" name="state" value="reflect" id="_anim_radio3_86edcf6f8fdd4a24a7937896143f61a7"
                 >
          <label for="_anim_radio3_86edcf6f8fdd4a24a7937896143f61a7">Reflect</label>
        </form>
      </div>
    </div>


    <script language="javascript">
      /* Instantiate the Animation class. */
      /* The IDs given should match those used in the template above. */
      (function() {
        var img_id = "_anim_img86edcf6f8fdd4a24a7937896143f61a7";
        var slider_id = "_anim_slider86edcf6f8fdd4a24a7937896143f61a7";
        var loop_select_id = "_anim_loop_select86edcf6f8fdd4a24a7937896143f61a7";
        var frames = new Array(258);
    
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        /* set a timeout to make sure all the above elements are created before
           the object is initialized. */
        setTimeout(function() {
            anim86edcf6f8fdd4a24a7937896143f61a7 = new Animation(frames, img_id, slider_id, 200,
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    </script>

    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 204-215

References
----------
.. [1] `Principal geodesic analysis for the study of nonlinear statistics of
   shape
   <https://ieeexplore.ieee.org/document/1318725>`_
   P.T. Fletcher, C. Lu, S. M. Pizer, S. Joshi. IEEE Transactions on Medical
   Imaging (Volume: 23, Issue: 8, August 2004).
.. [2] `Online SSVEP-based BCI using Riemannian geometry
   <https://hal.archives-ouvertes.fr/hal-01351623>`_
   E. K. Kalunga, S. Chevallier, Q. Barthélemy, K. Djouani, E. Monacelli,
   Y. Hamam. Neurocomputing, Elsevier, 2016, 191, pp.55-68.


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

   **Total running time of the script:** ( 4 minutes  10.612 seconds)


.. _sphx_glr_download_auto_examples_SSVEP_plot_classify_ssvep_pga.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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