.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/neighbors/plot_nca_illustration.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via JupyterLite or Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_neighbors_plot_nca_illustration.py: ============================================= Neighborhood Components Analysis Illustration ============================================= This example illustrates a learned distance metric that maximizes the nearest neighbors classification accuracy. It provides a visual representation of this metric compared to the original point space. Please refer to the :ref:`User Guide ` for more information. .. GENERATED FROM PYTHON SOURCE LINES 12-24 .. code-block:: Python # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause import matplotlib.pyplot as plt import numpy as np from matplotlib import cm from scipy.special import logsumexp from sklearn.datasets import make_classification from sklearn.neighbors import NeighborhoodComponentsAnalysis .. GENERATED FROM PYTHON SOURCE LINES 25-31 Original points --------------- First we create a data set of 9 samples from 3 classes, and plot the points in the original space. For this example, we focus on the classification of point no. 3. The thickness of a link between point no. 3 and another point is proportional to their distance. .. GENERATED FROM PYTHON SOURCE LINES 31-79 .. code-block:: Python X, y = make_classification( n_samples=9, n_features=2, n_informative=2, n_redundant=0, n_classes=3, n_clusters_per_class=1, class_sep=1.0, random_state=0, ) plt.figure(1) ax = plt.gca() for i in range(X.shape[0]): ax.text(X[i, 0], X[i, 1], str(i), va="center", ha="center") ax.scatter(X[i, 0], X[i, 1], s=300, c=cm.Set1(y[[i]]), alpha=0.4) ax.set_title("Original points") ax.axes.get_xaxis().set_visible(False) ax.axes.get_yaxis().set_visible(False) ax.axis("equal") # so that boundaries are displayed correctly as circles def link_thickness_i(X, i): diff_embedded = X[i] - X dist_embedded = np.einsum("ij,ij->i", diff_embedded, diff_embedded) dist_embedded[i] = np.inf # compute exponentiated distances (use the log-sum-exp trick to # avoid numerical instabilities exp_dist_embedded = np.exp(-dist_embedded - logsumexp(-dist_embedded)) return exp_dist_embedded def relate_point(X, i, ax): pt_i = X[i] for j, pt_j in enumerate(X): thickness = link_thickness_i(X, i) if i != j: line = ([pt_i[0], pt_j[0]], [pt_i[1], pt_j[1]]) ax.plot(*line, c=cm.Set1(y[j]), linewidth=5 * thickness[j]) i = 3 relate_point(X, i, ax) plt.show() .. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_nca_illustration_001.png :alt: Original points :srcset: /auto_examples/neighbors/images/sphx_glr_plot_nca_illustration_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 80-85 Learning an embedding --------------------- We use :class:`~sklearn.neighbors.NeighborhoodComponentsAnalysis` to learn an embedding and plot the points after the transformation. We then take the embedding and find the nearest neighbors. .. GENERATED FROM PYTHON SOURCE LINES 85-103 .. code-block:: Python nca = NeighborhoodComponentsAnalysis(max_iter=30, random_state=0) nca = nca.fit(X, y) plt.figure(2) ax2 = plt.gca() X_embedded = nca.transform(X) relate_point(X_embedded, i, ax2) for i in range(len(X)): ax2.text(X_embedded[i, 0], X_embedded[i, 1], str(i), va="center", ha="center") ax2.scatter(X_embedded[i, 0], X_embedded[i, 1], s=300, c=cm.Set1(y[[i]]), alpha=0.4) ax2.set_title("NCA embedding") ax2.axes.get_xaxis().set_visible(False) ax2.axes.get_yaxis().set_visible(False) ax2.axis("equal") plt.show() .. image-sg:: /auto_examples/neighbors/images/sphx_glr_plot_nca_illustration_002.png :alt: NCA embedding :srcset: /auto_examples/neighbors/images/sphx_glr_plot_nca_illustration_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.162 seconds) .. _sphx_glr_download_auto_examples_neighbors_plot_nca_illustration.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/1.6.X?urlpath=lab/tree/notebooks/auto_examples/neighbors/plot_nca_illustration.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/index.html?path=auto_examples/neighbors/plot_nca_illustration.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_nca_illustration.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_nca_illustration.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_nca_illustration.zip ` .. include:: plot_nca_illustration.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_