%matplotlib inline

Another tutorial

This is also a Jupyter notebook. This time, let’s do some Machine Learning™, based on this (BSD-3 licensed) tutorial by Phil Roth from scikit-learn.

Simulated data

First we simulate some data:

import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs

n_samples = 1500
random_state = 170
X, y = make_blobs(n_samples=n_samples, random_state=random_state)

plt.scatter(X[:, 0], X[:, 1], c="k")
plt.xlabel("x1")
plt.ylabel("x2");

Text(0, 0.5, 'x2')

Clustering

Now let’s cluster using K-means with several different assumptions about the parameters:

import numpy as np
from sklearn.cluster import KMeans

plt.figure(figsize=(12, 12))

# Incorrect number of clusters
y_pred = KMeans(n_clusters=2, random_state=random_state).fit_predict(X)

plt.subplot(221)
plt.scatter(X[:, 0], X[:, 1], c=y_pred)
plt.title("Incorrect Number of Blobs")

# Anisotropicly distributed data
transformation = [[0.60834549, -0.63667341], [-0.40887718, 0.85253229]]
X_aniso = np.dot(X, transformation)
y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_aniso)

plt.subplot(222)
plt.scatter(X_aniso[:, 0], X_aniso[:, 1], c=y_pred)
plt.title("Anisotropicly Distributed Blobs")

# Different variance
X_varied, y_varied = make_blobs(n_samples=n_samples,
                                cluster_std=[1.0, 2.5, 0.5],
                                random_state=random_state)
y_pred = KMeans(n_clusters=3, random_state=random_state).fit_predict(X_varied)

plt.subplot(223)
plt.scatter(X_varied[:, 0], X_varied[:, 1], c=y_pred)
plt.title("Unequal Variance")

# Unevenly sized blobs
X_filtered = np.vstack((X[y == 0][:500], X[y == 1][:100], X[y == 2][:10]))
y_pred = KMeans(n_clusters=3,
                random_state=random_state).fit_predict(X_filtered)

plt.subplot(224)
plt.scatter(X_filtered[:, 0], X_filtered[:, 1], c=y_pred)
plt.title("Unevenly Sized Blobs");

Text(0.5, 1.0, 'Unevenly Sized Blobs')

Conclusion

Your choices matter when teaching the machines.