What are some alternative metrics to evaluate K-means clustering besides the sum of squared errors?

1 Silhouette score

The silhouette score is a metric that measures how cohesive and separated the clusters are. It ranges from -1 to 1, where a higher value indicates that the points are well matched to their own cluster and poorly matched to the neighboring clusters. The silhouette score is calculated by taking the average of the silhouette coefficients for each point, which are defined as the difference between the average distance to the points in the same cluster and the average distance to the points in the nearest cluster, divided by the maximum of these two distances. The silhouette score can help you choose the optimal number of clusters, by comparing the scores for different values of K.

2 Calinski-Harabasz index

The Calinski-Harabasz index is another metric that measures how well the clusters are separated and compact. It is based on the ratio of the between-cluster variance and the within-cluster variance, multiplied by a factor that depends on the number of clusters and the number of points. The higher the Calinski-Harabasz index, the better the clustering. Unlike the silhouette score, the Calinski-Harabasz index does not require computing the distances between all the points, which can be computationally expensive for large datasets. However, it assumes that the clusters are convex and isotropic, which may not be true for some data.

3 Davies-Bouldin index

The Davies-Bouldin index is a metric that measures how similar the clusters are in terms of size, shape, and density. It is based on the average of the similarity measures between each cluster and its most similar cluster, where the similarity measure is defined as the sum of the average distances from the points to the cluster centers, divided by the distance between the cluster centers. The lower the Davies-Bouldin index, the better the clustering. The Davies-Bouldin index can handle clusters of different shapes and sizes, but it is sensitive to outliers and noise.

4 Gap statistic

The gap statistic is a metric that compares the clustering results with a null reference distribution, which is generated by sampling uniformly from the data range. It is based on the difference between the observed within-cluster dispersion and the expected within-cluster dispersion under the null reference distribution, normalized by a standard deviation term. The larger the gap statistic, the better the clustering. The gap statistic can help you determine the optimal number of clusters, by finding the smallest value of K that maximizes the gap statistic.

5 Mutual information

The mutual information is a metric that measures how much information is shared between the clustering labels and some external labels, such as class labels or ground truth labels. It is based on the entropy of the clustering labels, the entropy of the external labels, and the joint entropy of both labels. The higher the mutual information, the more agreement between the clustering labels and the external labels. The mutual information can help you evaluate how well the clustering captures the underlying structure or patterns of the data.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?