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changes. Clearly this motivates many more avenues of research!
22.2 Bibliographic Note
K-Means Clustering is a well-known technique discussed in many machine learning textbooks. A
relatively straightforward introduction, without recourse to hard mathematics, is given in James
et al (2013)[59]. The basics of the algorithm are outlined as well as its pitfalls.
The graduate level books by Hastie et al (2009)[51] and Murphy (2012)[71] delve more deeply
into the "wider picture" of clustering algorithms, putting them into the probabalistic modelling
framework. They also place K-Means in context with other clustering algorithms such as Vector
Quantisation and Gaussian Mixture Models. Other books that discuss K-Means clustering
include Bishop (2007)[22] and Barber (2012)[20].
22.3 Full Code
# simulated_data.py
import itertools
import numpy as np
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
if __name__ == "__main__":
np.random.seed(1)
# Set the number of samples, the means and
# variances of each of the three simulated clusters
samples = 100
mu = [(7, 5), (8, 12), (1, 10)]
cov = [
[[0.5, 0], [0, 1.0]],
[[2.0, 0], [0, 3.5]],
[[3, 0], [0, 5]],
]
# Generate a list of the 2D cluster points
norm_dists = [
np.random.multivariate_normal(m, c, samples)
for m, c in zip(mu, cov)
]
X = np.array(list(itertools.chain(*norm_dists)))