Show illustration of StandardScaler() in lecture notebook

[ArturoAmorQ]

Using the notebook introduced in #432, we find that Q4 and Q5 from M1.2 have scores under 0.65. Both questions ask for the effect of StandardScaler() on data but one is visual (Q4) and the other one (Q5) is not.

To address this issue while improving the intuition of scaling, I would suggest showing in this notebook an illustration similar to this one:

Or even adding the piece of code I used for creating that image, so that people can play on their own (the disadvantage would be making this particular notebook too heavy...)

import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
plt.rcParams["figure.figsize"] = (10,7)
plt.rcParams.update({'font.size': 16}) 

centers = [[0, 2], [3, 0.5]]
X, _ = make_blobs(n_samples=100, n_features=2, centers=centers, 
                 cluster_std=0.5, center_box=(1, 10.0), 
                 shuffle=True, random_state=0)
 
# plot the training points
fig, ax = plt.subplots()
plt.scatter(X[:, 0], X[:, 1])
ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['bottom'].set_position('zero')
ax.spines['top'].set_color('none')
plt.show()

from sklearn.preprocessing import StandardScaler

scaler = StandardScaler()
scaler.fit(X)
X_scaled = scaler.transform(X)

fig, ax = plt.subplots()
plt.scatter(X_scaled[:, 0], X_scaled[:, 1])
ax.spines['left'].set_position('zero')
ax.spines['right'].set_color('none')
ax.spines['bottom'].set_position('zero')
ax.spines['top'].set_color('none')
plt.show()

What do you think?