.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/manifold/plot_t_sne_perplexity.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_manifold_plot_t_sne_perplexity.py: ============================================================================= t-SNE: The effect of various perplexity values on the shape ============================================================================= An illustration of t-SNE on the two concentric circles and the S-curve datasets for different perplexity values. We observe a tendency towards clearer shapes as the perplexity value increases. The size, the distance and the shape of clusters may vary upon initialization, perplexity values and does not always convey a meaning. As shown below, t-SNE for higher perplexities finds meaningful topology of two concentric circles, however the size and the distance of the circles varies slightly from the original. Contrary to the two circles dataset, the shapes visually diverge from S-curve topology on the S-curve dataset even for larger perplexity values. For further details, "How to Use t-SNE Effectively" https://distill.pub/2016/misread-tsne/ provides a good discussion of the effects of various parameters, as well as interactive plots to explore those effects. .. GENERATED FROM PYTHON SOURCE LINES 26-147 .. image-sg:: /auto_examples/manifold/images/sphx_glr_plot_t_sne_perplexity_001.png :alt: Perplexity=5, Perplexity=30, Perplexity=50, Perplexity=100, Perplexity=5, Perplexity=30, Perplexity=50, Perplexity=100, Perplexity=5, Perplexity=30, Perplexity=50, Perplexity=100 :srcset: /auto_examples/manifold/images/sphx_glr_plot_t_sne_perplexity_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none circles, perplexity=5 in 0.13 sec circles, perplexity=30 in 0.21 sec circles, perplexity=50 in 0.23 sec circles, perplexity=100 in 0.24 sec S-curve, perplexity=5 in 0.14 sec S-curve, perplexity=30 in 0.19 sec S-curve, perplexity=50 in 0.23 sec S-curve, perplexity=100 in 0.23 sec uniform grid, perplexity=5 in 0.16 sec uniform grid, perplexity=30 in 0.24 sec uniform grid, perplexity=50 in 0.27 sec uniform grid, perplexity=100 in 0.27 sec | .. code-block:: Python # Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause from time import time import matplotlib.pyplot as plt import numpy as np from matplotlib.ticker import NullFormatter from sklearn import datasets, manifold n_samples = 150 n_components = 2 (fig, subplots) = plt.subplots(3, 5, figsize=(15, 8)) perplexities = [5, 30, 50, 100] X, y = datasets.make_circles( n_samples=n_samples, factor=0.5, noise=0.05, random_state=0 ) red = y == 0 green = y == 1 ax = subplots[0][0] ax.scatter(X[red, 0], X[red, 1], c="r") ax.scatter(X[green, 0], X[green, 1], c="g") ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) plt.axis("tight") for i, perplexity in enumerate(perplexities): ax = subplots[0][i + 1] t0 = time() tsne = manifold.TSNE( n_components=n_components, init="random", random_state=0, perplexity=perplexity, max_iter=300, ) Y = tsne.fit_transform(X) t1 = time() print("circles, perplexity=%d in %.2g sec" % (perplexity, t1 - t0)) ax.set_title("Perplexity=%d" % perplexity) ax.scatter(Y[red, 0], Y[red, 1], c="r") ax.scatter(Y[green, 0], Y[green, 1], c="g") ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) ax.axis("tight") # Another example using s-curve X, color = datasets.make_s_curve(n_samples, random_state=0) ax = subplots[1][0] ax.scatter(X[:, 0], X[:, 2], c=color) ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) for i, perplexity in enumerate(perplexities): ax = subplots[1][i + 1] t0 = time() tsne = manifold.TSNE( n_components=n_components, init="random", random_state=0, perplexity=perplexity, learning_rate="auto", max_iter=300, ) Y = tsne.fit_transform(X) t1 = time() print("S-curve, perplexity=%d in %.2g sec" % (perplexity, t1 - t0)) ax.set_title("Perplexity=%d" % perplexity) ax.scatter(Y[:, 0], Y[:, 1], c=color) ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) ax.axis("tight") # Another example using a 2D uniform grid x = np.linspace(0, 1, int(np.sqrt(n_samples))) xx, yy = np.meshgrid(x, x) X = np.hstack( [ xx.ravel().reshape(-1, 1), yy.ravel().reshape(-1, 1), ] ) color = xx.ravel() ax = subplots[2][0] ax.scatter(X[:, 0], X[:, 1], c=color) ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) for i, perplexity in enumerate(perplexities): ax = subplots[2][i + 1] t0 = time() tsne = manifold.TSNE( n_components=n_components, init="random", random_state=0, perplexity=perplexity, max_iter=400, ) Y = tsne.fit_transform(X) t1 = time() print("uniform grid, perplexity=%d in %.2g sec" % (perplexity, t1 - t0)) ax.set_title("Perplexity=%d" % perplexity) ax.scatter(Y[:, 0], Y[:, 1], c=color) ax.xaxis.set_major_formatter(NullFormatter()) ax.yaxis.set_major_formatter(NullFormatter()) ax.axis("tight") plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 3.068 seconds) .. _sphx_glr_download_auto_examples_manifold_plot_t_sne_perplexity.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/manifold/plot_t_sne_perplexity.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/index.html?path=auto_examples/manifold/plot_t_sne_perplexity.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_t_sne_perplexity.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_t_sne_perplexity.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_t_sne_perplexity.zip ` .. include:: plot_t_sne_perplexity.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_