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Examples
========

Explore example workflows for **HDMRLib**, including basic decompositions,
structured workflows, and research-oriented examples.


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General Examples
================

Basic examples for getting started with HDMRLib.


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    <div class="sphx-glr-thumbcontainer" tooltip="Run HDMR on a small 2D tensor, reconstruct the approximation, and compare the reconstructed tensor with the original input.">

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  .. image:: /auto_examples/general_examples/images/thumb/sphx_glr_plot_01_hdmr_2d_thumb.png
    :alt:

  :doc:`/auto_examples/general_examples/plot_01_hdmr_2d`

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      <div class="sphx-glr-thumbnail-title">HDMR on a 2D Tensor</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Run HDMR on a structured 2D tensor and inspect the resulting additive and interaction terms.">

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  .. image:: /auto_examples/general_examples/images/thumb/sphx_glr_plot_02_hdmr_2d_distinct_comp_thumb.png
    :alt:

  :doc:`/auto_examples/general_examples/plot_02_hdmr_2d_distinct_comp`

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      <div class="sphx-glr-thumbnail-title">HDMR on a 2D Tensor with Interaction Terms</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Run EMPR and HDMR on the same 2D tensor, compare the reconstructions, and visualize the remaining approximation errors.">

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  .. image:: /auto_examples/general_examples/images/thumb/sphx_glr_plot_03_empr_hdmr_2d_thumb.png
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  :doc:`/auto_examples/general_examples/plot_03_empr_hdmr_2d`

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      <div class="sphx-glr-thumbnail-title">EMPR vs HDMR on a 2D Tensor</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Load an RGB image as a 3D tensor, run EMPR, reconstruct the tensor, and compare the reconstruction with the original image.">

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  .. image:: /auto_examples/general_examples/images/thumb/sphx_glr_plot_04_empr_3d_thumb.png
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  :doc:`/auto_examples/general_examples/plot_04_empr_3d`

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      <div class="sphx-glr-thumbnail-title">EMPR on an 3D Tensor</div>
    </div>


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Decomposition Workflows
=======================

Examples for comparing decomposition settings and structured workflows.


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    <div class="sphx-glr-thumbcontainer" tooltip="Compare reconstruction quality across retained decomposition orders on the same tensor.">

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  .. image:: /auto_examples/decomposition_workflows/images/thumb/sphx_glr_plot_compare_orders_thumb.png
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  :doc:`/auto_examples/decomposition_workflows/plot_compare_orders`

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      <div class="sphx-glr-thumbnail-title">Compare Decomposition Orders</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Run EMPR with user-defined support vectors and inspect how the chosen supports affect the reconstruction.">

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  .. image:: /auto_examples/decomposition_workflows/images/thumb/sphx_glr_plot_empr_custom_supports_thumb.png
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  :doc:`/auto_examples/decomposition_workflows/plot_empr_custom_supports`

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      <div class="sphx-glr-thumbnail-title">EMPR with Custom Supports</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Run HDMR with user-defined weight vectors and inspect how the chosen weights affect the reconstruction.">

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  .. image:: /auto_examples/decomposition_workflows/images/thumb/sphx_glr_plot_hdmr_custom_weights_thumb.png
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  :doc:`/auto_examples/decomposition_workflows/plot_hdmr_custom_weights`

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      <div class="sphx-glr-thumbnail-title">HDMR with Custom Weights</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Inspect the available component keys and visualize the magnitude of each component term.">

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  .. image:: /auto_examples/decomposition_workflows/images/thumb/sphx_glr_plot_inspect_components_thumb.png
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  :doc:`/auto_examples/decomposition_workflows/plot_inspect_components`

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      <div class="sphx-glr-thumbnail-title">Inspect Component Terms</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Compare full and lower-order reconstructions and relate the approximation quality to the retained component terms.">

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  .. image:: /auto_examples/decomposition_workflows/images/thumb/sphx_glr_plot_lower_order_reconstruction_thumb.png
    :alt:

  :doc:`/auto_examples/decomposition_workflows/plot_lower_order_reconstruction`

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      <div class="sphx-glr-thumbnail-title">Lower-Order Reconstruction</div>
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Research Examples
=================

Examples connected to papers, comparisons, and research-oriented use cases.


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    <div class="sphx-glr-thumbcontainer" tooltip="This example demonstrates how to use HDMRLib to extract representative spectral signatures from hyperspectral datasets like Indian Pines. We utilize Enhanced Multivariance Products Representation (EMPR) to decompose the 3D tensor into lower-dimensional components that represent the core spectral characteristics of the data. By isolating the behavior of the third dimension (spectral bands), we reach an average spectral signature that captures the essential information of the scene.">

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  .. image:: /auto_examples/research_examples/images/thumb/sphx_glr_hyperspectral_signature_thumb.png
    :alt:

  :doc:`/auto_examples/research_examples/hyperspectral_signature`

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      <div class="sphx-glr-thumbnail-title">Hyperspectral Data Analysis using EMPR Spectral Signatures</div>
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.. toctree::
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   /auto_examples/general_examples/index.rst
   /auto_examples/decomposition_workflows/index.rst
   /auto_examples/research_examples/index.rst


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

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

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


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