Added seaborn.

Author: rossant

main.md

@@ -45,7 +45,7 @@ Some imports.
 <pre data-code-language="python"
      data-executable="true"
      data-type="programlisting">
-# That's an impressive list of imports!
+# That's an impressive list of imports.
 import numpy as np
 from numpy import linalg
 from numpy.linalg import norm
@@ -63,18 +63,20 @@ from sklearn.manifold.t_sne import (_joint_probabilities,
                                     _kl_divergence)
 from sklearn.utils.extmath import _ravel
 
-# matplotlib for graphics
+# matplotlib for graphics.
 import matplotlib.pyplot as plt
 import matplotlib.patheffects as PathEffects
 import matplotlib
+%matplotlib inline
+
+# We import seaborn for improve aesthetics.
+import seaborn as sns
+sns.set_style('darkgrid')
+sns.set_context("notebook", font_scale=1.5, rc={"lines.linewidth": 2.5})
 
-# We'll generate an animation with matplotlib and moviepy
+# We'll generate an animation with matplotlib and moviepy.
 from moviepy.video.io.bindings import mplfig_to_npimage
 import moviepy.editor as mpy
-
-# Some matplotlib params.
-%matplotlib inline
-matplotlib.rcParams.update({'font.size': 22})
 </pre>
 
 Illustration on digit dataset.
@@ -290,37 +292,41 @@ animation.write_gif("anim2.gif", fps=20)
 
 <img src="anim2.gif" />
 
-<pre data-code-language="python"
-     data-executable="true"
-     data-type="programlisting">
-def simpleaxis(ax):
-    ax.spines['top'].set_visible(False)
-    ax.spines['left'].set_visible(False)
-    ax.set_yticks([]);
-    ax.get_xaxis().tick_bottom()
-    ax.set_xticks([0., .5, 1.]);
-</pre>
-
 <pre data-code-language="python"
      data-executable="true"
      data-type="programlisting">
 npoints = 1000
-plt.figure(figsize=(14, 3))
+plt.figure(figsize=(15, 4))
 for i, D in enumerate((2, 5, 10)):
+    # Normally distributed points.
     u = np.random.randn(npoints, D)
+    # Now on the sphere.
     u /= norm(u, axis=1)[:, None]
+    # Uniform radius.
     r = np.random.rand(npoints, 1)
+    # Uniformly within the ball.
     points = u * r**(1./D)
+    # Plot.
     ax = plt.subplot(1, 3, i+1)
     ax.set_xlabel('Ball radius')
     if i == 0:
-        ax.set_ylabel('Distance from\norigin')
-    simpleaxis(ax)
+        ax.set_ylabel('Distance from origin')
     ax.hist(norm(points, axis=1), 
             bins=np.linspace(0., 1., 50))
     ax.set_title('D=%d' % D, loc='left')
 </pre>
 
+<pre data-code-language="python"
+     data-executable="true"
+     data-type="programlisting">
+z = np.linspace(0., 5., 1000)
+gauss = np.exp(-z**2)
+cauchy = 1/(1+z**2)
+plt.plot(z, gauss, label='Gaussian distribution');
+plt.plot(z, cauchy, label='Cauchy distribution');
+plt.legend();
+</pre>
+
 Equations:
 
 <span class="math-tex" data-type="tex">\\(p_{j|i} = \frac{\exp(-\lVert\mathbf{x}_i - \mathbf{x}_j\rVert^2 / 2\sigma_i^2)}{\sum_{k \neq i} \exp(-\lVert\mathbf{x}_i - \mathbf{x}_k\rVert^2 / 2\sigma_i^2)}\\)</span>