Optimal Clustering with the Elbow Method

Introduction

Determining the right number of clusters is crucial in k-means clustering. The Elbow Method is a widely-used technique for this purpose.

The Elbow Method

This method involves calculating the inertia (sum of squared distances from each point to its cluster center) for various numbers of clusters and plotting these values. The point where the inertia starts to decrease more slowly (the “elbow”) indicates the optimal number of clusters.

Application on Police Shootings Data

We applied the Elbow Method to a dataset on police shootings, focusing on variables like age, race, and signs of mental illness. We ran k-means clustering for 1 to 10 clusters and recorded the inertia values:

Interpretation

Based on the inertia values, 3 or 4 clusters could be considered optimal, as the inertia starts to decrease more slowly after this point.

Conclusion

The Elbow Method provides a straightforward way to determine the optimal number of clusters, helping to reveal more nuanced insights in the data.