Machine Learning Algorithms - Second Edition

Optimizing the inertia

The first method we are going to consider is based on the assumption that an appropriate number of clusters must produce a small inertia. However, this value reaches its minimum (0.0) when the number of clusters is equal to the number of samples. Therefore, we can't look for the minimum, but for a value that is a trade-off between the inertia and a reasonable number of clusters.

Let's suppose we have a dataset of 1,000 elements (such as the one employed in the previous example):

nb_samples = 1000X, _ = make_blobs(n_samples=nb_samples, n_features=2, centers=3, cluster_std=1.5, random_state=1000)

We can compute and collect the inertias (scikit-learn stores these values in the inertia_ instance variable) for a different ...