.. _sphx_glr_auto_examples_simulated:

Simulated data
---------------

Examples using datasets sampled from known probability distributions.



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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Spectral embedding of samples from the Riemannian Gaussian distribution with different centerings and dispersions.">

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  .. image:: /auto_examples/simulated/images/thumb/sphx_glr_plot_riemannian_gaussian_thumb.png
    :alt:

  :doc:`/auto_examples/simulated/plot_riemannian_gaussian`

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      <div class="sphx-glr-thumbnail-title">Sample from the Riemannian Gaussian distribution in the SPD manifold</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Generate several datasets containing data points from two-classes. Each class is generated with a Riemannian Gaussian distribution centered at the class mean and with the same dispersion sigma. The distance between the class means is parametrized by Delta, which we make vary between zero and 5*sigma. We illustrate how the accuracy of the MDM classifier and the value of the class distinctiveness [1]_ vary when Delta increases.">

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  .. image:: /auto_examples/simulated/images/thumb/sphx_glr_plot_toy_classification_thumb.png
    :alt:

  :doc:`/auto_examples/simulated/plot_toy_classification`

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      <div class="sphx-glr-thumbnail-title">Classification accuracy vs class distinctiveness vs class separability</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A comparison between Euclidean and Riemannian means [1]_, and Euclidean and Riemannian geometric medians [2]_, on low-dimensional synthetic datasets.">

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  .. image:: /auto_examples/simulated/images/thumb/sphx_glr_plot_mean_median_comparison_thumb.png
    :alt:

  :doc:`/auto_examples/simulated/plot_mean_median_comparison`

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      <div class="sphx-glr-thumbnail-title">Mean and median comparison</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A comparison of several clustering algorithms on low-dimensional synthetic datasets, adapted to SPD matrices from [1]_. The point of this example is to illustrate the nature of clustering of different algorithms, used with different metrics [2]_. This should be taken with a grain of salt, as the intuition conveyed by these examples does not necessarily carry over to real datasets.">

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  .. image:: /auto_examples/simulated/images/thumb/sphx_glr_plot_clusterer_comparison_thumb.png
    :alt:

  :doc:`/auto_examples/simulated/plot_clusterer_comparison`

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      <div class="sphx-glr-thumbnail-title">Clustering algorithm comparison</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Estimate the mean of SPD matrices corrupted by NaN values [1]_.">

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  .. image:: /auto_examples/simulated/images/thumb/sphx_glr_plot_nanmean_thumb.png
    :alt:

  :doc:`/auto_examples/simulated/plot_nanmean`

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      <div class="sphx-glr-thumbnail-title">Mean of SPD matrices with NaN values</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A comparison of several classifiers on low-dimensional synthetic datasets, adapted to SPD matrices from [1]_. The point of this example is to illustrate the nature of decision boundaries of different classifiers, used with different metrics [2]_. This should be taken with a grain of salt, as the intuition conveyed by these examples does not necessarily carry over to real datasets.">

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  .. image:: /auto_examples/simulated/images/thumb/sphx_glr_plot_classifier_comparison_thumb.png
    :alt:

  :doc:`/auto_examples/simulated/plot_classifier_comparison`

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      <div class="sphx-glr-thumbnail-title">Classifier comparison</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /auto_examples/simulated/plot_riemannian_gaussian
   /auto_examples/simulated/plot_toy_classification
   /auto_examples/simulated/plot_mean_median_comparison
   /auto_examples/simulated/plot_clusterer_comparison
   /auto_examples/simulated/plot_nanmean
   /auto_examples/simulated/plot_classifier_comparison