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

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

.. _sphx_glr_auto_examples_sliced-wasserstein_plot_sliced_wasserstein_scaler.py:


============================================================
Sliced Wasserstein Distance with input scaling (DataScaler)
============================================================

.. note::
    Example added in release: 0.9.7.

This example illustrates why input scaling matters when computing the Sliced
Wasserstein Distance (SWD) between distributions whose features have very
different magnitudes. Without scaling, the SWD is dominated by high-magnitude
features and may miss meaningful differences in low-magnitude features.

The :class:`ot.utils.DataScaler` class fits normalization statistics once on a
representative sample and applies the same fixed transformation on every call.
This is preferred over re-normalizing inside each SWD call because the
transformation stays consistent across mini-batches during optimization.

.. GENERATED FROM PYTHON SOURCE LINES 21-31

.. code-block:: Python


    # Author: Harguna Sood <harguna.sood@gmail.com>
    #
    # License: MIT License

    import matplotlib.pylab as pl
    import numpy as np

    import ot








.. GENERATED FROM PYTHON SOURCE LINES 32-38

Generate two 2D distributions with mismatched feature scales
------------------------------------------------------------

Feature 1 is on the scale of 1000 with random noise.
Feature 2 is on the scale of 1 with a meaningful 5-sigma shift between
source and target distributions.

.. GENERATED FROM PYTHON SOURCE LINES 40-57

.. code-block:: Python


    rng = np.random.RandomState(0)
    n = 500

    X_s = np.column_stack(
        [
            rng.normal(1000, 100, n),  # feature 1: large scale, no real signal
            rng.normal(0, 1, n),  # feature 2: small scale, no shift
        ]
    )
    X_t = np.column_stack(
        [
            rng.normal(1000, 100, n),  # feature 1: same distribution as source
            rng.normal(5, 1, n),  # feature 2: shifted by 5 std
        ]
    )








.. GENERATED FROM PYTHON SOURCE LINES 58-64

SWD without scaling
-------------------

Because feature 1 has values ~1000x larger than feature 2, the random
projections used in SWD are dominated by feature 1. The meaningful shift
in feature 2 is buried.

.. GENERATED FROM PYTHON SOURCE LINES 66-70

.. code-block:: Python


    swd_raw = ot.sliced_wasserstein_distance(X_s, X_t, n_projections=200, seed=0)
    print("SWD without scaling: {:.4f}".format(swd_raw))





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

 .. code-block:: none

    SWD without scaling: 7.2575




.. GENERATED FROM PYTHON SOURCE LINES 71-77

SWD with DataScaler
-------------------

Fit a standard scaler jointly on both distributions, then pass it to SWD.
The same fixed statistics are reused on every call, giving a stable loss
across mini-batches.

.. GENERATED FROM PYTHON SOURCE LINES 79-86

.. code-block:: Python


    scaler = ot.utils.DataScaler(norm="standard").fit([X_s, X_t])
    swd_scaled = ot.sliced_wasserstein_distance(
        X_s, X_t, n_projections=200, seed=0, scaler=scaler
    )
    print("SWD with DataScaler: {:.4f}".format(swd_scaled))





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

 .. code-block:: none

    SWD with DataScaler: 1.2826




.. GENERATED FROM PYTHON SOURCE LINES 87-89

Visualize raw vs. scaled distributions
---------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 91-115

.. code-block:: Python


    X_s_n = scaler.transform(X_s)
    X_t_n = scaler.transform(X_t)

    pl.figure(1, figsize=(12, 5))

    pl.subplot(1, 2, 1)
    pl.scatter(X_s[:, 0], X_s[:, 1], alpha=0.5, label="$X_s$", s=10)
    pl.scatter(X_t[:, 0], X_t[:, 1], alpha=0.5, label="$X_t$", s=10)
    pl.title("Raw distributions\n(feature 2 signal hidden by feature 1 scale)")
    pl.xlabel("Feature 1 (large scale)")
    pl.ylabel("Feature 2 (small scale)")
    pl.legend()

    pl.subplot(1, 2, 2)
    pl.scatter(X_s_n[:, 0], X_s_n[:, 1], alpha=0.5, label="$X_s$ normalized", s=10)
    pl.scatter(X_t_n[:, 0], X_t_n[:, 1], alpha=0.5, label="$X_t$ normalized", s=10)
    pl.title("Normalized distributions\n(feature 2 shift clearly visible)")
    pl.xlabel("Feature 1 (normalized)")
    pl.ylabel("Feature 2 (normalized)")
    pl.legend()

    pl.tight_layout()
    pl.show()



.. image-sg:: /auto_examples/sliced-wasserstein/images/sphx_glr_plot_sliced_wasserstein_scaler_001.png
   :alt: Raw distributions (feature 2 signal hidden by feature 1 scale), Normalized distributions (feature 2 shift clearly visible)
   :srcset: /auto_examples/sliced-wasserstein/images/sphx_glr_plot_sliced_wasserstein_scaler_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.444 seconds)


.. _sphx_glr_download_auto_examples_sliced-wasserstein_plot_sliced_wasserstein_scaler.py:

.. only:: html

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

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

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

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

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

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

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


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