:orphan:

========
Examples
========



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    <div class="sphx-glr-thumbcontainer" tooltip="In classical signal processing, a filter can be translated in the vertex domain. We cannot do that on graphs. Instead, we can localize a filter kernel. Note how on classic structures (like the ring), the localized kernel is the same everywhere, while it changes when localized on irregular graphs.">

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  .. image:: /examples/images/thumb/sphx_glr_kernel_localization_thumb.png
    :alt:

  :ref:`sphx_glr_examples_kernel_localization.py`

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      <div class="sphx-glr-thumbnail-title">Kernel localization</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The eigenvectors of the graph Laplacian form the Fourier basis. The eigenvalues are a measure of variation of their corresponding eigenvector. The lower the eigenvalue, the smoother the eigenvector. They are hence a measure of &quot;frequency&quot;.">

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  .. image:: /examples/images/thumb/sphx_glr_fourier_basis_thumb.png
    :alt:

  :ref:`sphx_glr_examples_fourier_basis.py`

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      <div class="sphx-glr-thumbnail-title">Fourier basis</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The eigenvalues of the graph Laplacian concentrates to the same value as the graph becomes full.">

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  .. image:: /examples/images/thumb/sphx_glr_eigenvalue_concentration_thumb.png
    :alt:

  :ref:`sphx_glr_examples_eigenvalue_concentration.py`

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      <div class="sphx-glr-thumbnail-title">Concentration of the eigenvalues</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The graph Fourier transform pygsp.graphs.Graph.gft transforms a signal from the vertex domain to the spectral domain. The smoother the signal (see pygsp.graphs.Graph.dirichlet_energy), the lower in the frequencies its energy is concentrated.">

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  .. image:: /examples/images/thumb/sphx_glr_fourier_transform_thumb.png
    :alt:

  :ref:`sphx_glr_examples_fourier_transform.py`

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      <div class="sphx-glr-thumbnail-title">Fourier transform</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Solve the heat equation by filtering the initial conditions with the heat kernel pygsp.filters.Heat.">

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  .. image:: /examples/images/thumb/sphx_glr_heat_diffusion_thumb.png
    :alt:

  :ref:`sphx_glr_examples_heat_diffusion.py`

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      <div class="sphx-glr-thumbnail-title">Heat diffusion</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Solve the wave equation by filtering the initial conditions with the wave kernel pygsp.filters.Wave.">

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  .. image:: /examples/images/thumb/sphx_glr_wave_propagation_thumb.png
    :alt:

  :ref:`sphx_glr_examples_wave_propagation.py`

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      <div class="sphx-glr-thumbnail-title">Wave propagation</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="The Fourier modes (the eigenvectors of the graph Laplacian) can be localized in the spacial domain. As a consequence, graph signals can be localized in both space and frequency (which is impossible for Euclidean domains or manifolds, by the Heisenberg&#x27;s uncertainty principle).">

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  .. image:: /examples/images/thumb/sphx_glr_eigenvector_localization_thumb.png
    :alt:

  :ref:`sphx_glr_examples_eigenvector_localization.py`

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      <div class="sphx-glr-thumbnail-title">Localization of Fourier modes</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A graph signal is filtered by transforming it to the spectral domain (via the Fourier transform), performing a point-wise multiplication (motivated by the convolution theorem), and transforming it back to the vertex domain (via the inverse graph Fourier transform).">

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  .. image:: /examples/images/thumb/sphx_glr_filtering_thumb.png
    :alt:

  :ref:`sphx_glr_examples_filtering.py`

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      <div class="sphx-glr-thumbnail-title">Filtering a signal</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Probability of a random walker to be on any given vertex after a given number of steps starting from a given distribution.">

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  .. image:: /examples/images/thumb/sphx_glr_random_walk_thumb.png
    :alt:

  :ref:`sphx_glr_examples_random_walk.py`

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      <div class="sphx-glr-thumbnail-title">Random walks</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /examples/kernel_localization
   /examples/fourier_basis
   /examples/eigenvalue_concentration
   /examples/fourier_transform
   /examples/heat_diffusion
   /examples/wave_propagation
   /examples/eigenvector_localization
   /examples/filtering
   /examples/random_walk


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

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

      :download:`Download all examples in Python source code: examples_python.zip </examples/examples_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: examples_jupyter.zip </examples/examples_jupyter.zip>`


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

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