.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/cluster/plot_ward_structured_vs_unstructured.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_cluster_plot_ward_structured_vs_unstructured.py: =========================================================== Hierarchical clustering: structured vs unstructured ward =========================================================== Example builds a swiss roll dataset and runs hierarchical clustering on their position. For more information, see :ref:`hierarchical_clustering`. In a first step, the hierarchical clustering is performed without connectivity constraints on the structure and is solely based on distance, whereas in a second step the clustering is restricted to the k-Nearest Neighbors graph: it's a hierarchical clustering with structure prior. Some of the clusters learned without connectivity constraints do not respect the structure of the swiss roll and extend across different folds of the manifolds. On the opposite, when opposing connectivity constraints, the clusters form a nice parcellation of the swiss roll. .. GENERATED FROM PYTHON SOURCE LINES 22-38 .. code-block:: default # Authors : Vincent Michel, 2010 # Alexandre Gramfort, 2010 # Gael Varoquaux, 2010 # License: BSD 3 clause import time as time # The following import is required # for 3D projection to work with matplotlib < 3.2 import mpl_toolkits.mplot3d # noqa: F401 import numpy as np .. GENERATED FROM PYTHON SOURCE LINES 39-43 Generate data ------------- We start by generating the Swiss Roll dataset. .. GENERATED FROM PYTHON SOURCE LINES 43-52 .. code-block:: default from sklearn.datasets import make_swiss_roll n_samples = 1500 noise = 0.05 X, _ = make_swiss_roll(n_samples, noise=noise) # Make it thinner X[:, 1] *= 0.5 .. GENERATED FROM PYTHON SOURCE LINES 53-58 Compute clustering ------------------ We perform AgglomerativeClustering which comes under Hierarchical Clustering without any connectivity constraints. .. GENERATED FROM PYTHON SOURCE LINES 58-69 .. code-block:: default from sklearn.cluster import AgglomerativeClustering print("Compute unstructured hierarchical clustering...") st = time.time() ward = AgglomerativeClustering(n_clusters=6, linkage="ward").fit(X) elapsed_time = time.time() - st label = ward.labels_ print(f"Elapsed time: {elapsed_time:.2f}s") print(f"Number of points: {label.size}") .. rst-class:: sphx-glr-script-out .. code-block:: none Compute unstructured hierarchical clustering... Elapsed time: 0.04s Number of points: 1500 .. GENERATED FROM PYTHON SOURCE LINES 70-73 Plot result ----------- Plotting the unstructured hierarchical clusters. .. GENERATED FROM PYTHON SOURCE LINES 73-90 .. code-block:: default import matplotlib.pyplot as plt fig1 = plt.figure() ax1 = fig1.add_subplot(111, projection="3d", elev=7, azim=-80) ax1.set_position([0, 0, 0.95, 1]) for l in np.unique(label): ax1.scatter( X[label == l, 0], X[label == l, 1], X[label == l, 2], color=plt.cm.jet(float(l) / np.max(label + 1)), s=20, edgecolor="k", ) _ = fig1.suptitle(f"Without connectivity constraints (time {elapsed_time:.2f}s)") .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_ward_structured_vs_unstructured_001.png :alt: Without connectivity constraints (time 0.04s) :srcset: /auto_examples/cluster/images/sphx_glr_plot_ward_structured_vs_unstructured_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 91-93 We are defining k-Nearest Neighbors with 10 neighbors ----------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 93-98 .. code-block:: default from sklearn.neighbors import kneighbors_graph connectivity = kneighbors_graph(X, n_neighbors=10, include_self=False) .. GENERATED FROM PYTHON SOURCE LINES 99-103 Compute clustering ------------------ We perform AgglomerativeClustering again with connectivity constraints. .. GENERATED FROM PYTHON SOURCE LINES 103-114 .. code-block:: default print("Compute structured hierarchical clustering...") st = time.time() ward = AgglomerativeClustering( n_clusters=6, connectivity=connectivity, linkage="ward" ).fit(X) elapsed_time = time.time() - st label = ward.labels_ print(f"Elapsed time: {elapsed_time:.2f}s") print(f"Number of points: {label.size}") .. rst-class:: sphx-glr-script-out .. code-block:: none Compute structured hierarchical clustering... Elapsed time: 0.06s Number of points: 1500 .. GENERATED FROM PYTHON SOURCE LINES 115-119 Plot result ----------- Plotting the structured hierarchical clusters. .. GENERATED FROM PYTHON SOURCE LINES 119-135 .. code-block:: default fig2 = plt.figure() ax2 = fig2.add_subplot(121, projection="3d", elev=7, azim=-80) ax2.set_position([0, 0, 0.95, 1]) for l in np.unique(label): ax2.scatter( X[label == l, 0], X[label == l, 1], X[label == l, 2], color=plt.cm.jet(float(l) / np.max(label + 1)), s=20, edgecolor="k", ) fig2.suptitle(f"With connectivity constraints (time {elapsed_time:.2f}s)") plt.show() .. image-sg:: /auto_examples/cluster/images/sphx_glr_plot_ward_structured_vs_unstructured_002.png :alt: With connectivity constraints (time 0.06s) :srcset: /auto_examples/cluster/images/sphx_glr_plot_ward_structured_vs_unstructured_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 0.370 seconds) .. _sphx_glr_download_auto_examples_cluster_plot_ward_structured_vs_unstructured.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/1.2.X?urlpath=lab/tree/notebooks/auto_examples/cluster/plot_ward_structured_vs_unstructured.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_ward_structured_vs_unstructured.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_ward_structured_vs_unstructured.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_