.. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. 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 preplexity 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" http://distill.pub/2016/misread-tsne/ provides a good discussion of the effects of various parameters, as well as interactive plots to explore those effects. .. image:: /auto_examples/manifold/images/sphx_glr_plot_t_sne_perplexity_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out Out: .. code-block:: none circles, perplexity=5 in 0.98 sec circles, perplexity=30 in 1.3 sec circles, perplexity=50 in 1.6 sec circles, perplexity=100 in 1.8 sec S-curve, perplexity=5 in 1.1 sec S-curve, perplexity=30 in 1.3 sec S-curve, perplexity=50 in 1.8 sec S-curve, perplexity=100 in 2.1 sec uniform grid, perplexity=5 in 0.91 sec uniform grid, perplexity=30 in 1.3 sec uniform grid, perplexity=50 in 1.3 sec uniform grid, perplexity=100 in 2.1 sec | .. code-block:: default # Author: Narine Kokhlikyan # License: BSD print(__doc__) import numpy as np import matplotlib.pyplot as plt from matplotlib.ticker import NullFormatter from sklearn import manifold, datasets from time import time n_samples = 300 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=.5, noise=.05) 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) 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.samples_generator.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) 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) 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 18.346 seconds) .. _sphx_glr_download_auto_examples_manifold_plot_t_sne_perplexity.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: sphx-glr-download :download:`Download Python source code: plot_t_sne_perplexity.py ` .. container:: sphx-glr-download :download:`Download Jupyter notebook: plot_t_sne_perplexity.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_