Machine Learning Algorithms

Optimizing the inertia

The first method 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 which is a trade-off between the inertia and the number of clusters.

Let's suppose we have a dataset of 1,000 elements. We can compute and collect the inertias (scikit-learn stores these values in the instance variable inertia_) for a different number of clusters:

>>> nb_clusters = [2, 3, 5, 6, 7, 8, 9, 10]>>> inertias = []>>> for n in nb_clusters:>>>    km = KMeans(n_clusters=n)>>>    km.fit(X)>>>    inertias.append(km.inertia_)

Plotting the values, ...