A Silhouette score is a metric used to evaluate the clustering of a data set. It measures how distinct each cluster is from the others and how well-defined the clusters are. The score ranges from -1 to 1, with higher values indicating a better clustering.
The Silhouette score is calculated by taking the average Silhouette coefficient of each sample in the data set. The Silhouette coefficient for each sample is calculated by measuring its similarity to other samples in the same cluster, as well as its dissimilarity to samples in other clusters.
To calculate the Silhouette coefficient for a given sample, we first compute its average intra-cluster distance (the average distance between all samples in that cluster) and its average nearest-cluster distance (the average distance between that sample and all samples in the closest neighboring cluster). We then calculate a ratio of these two distances, where higher values indicate better separation between clusters.
The Silhouette score takes into account both within-cluster similarity and between-cluster separation, so it provides an objective measure of clustering quality. It can be used to compare different clustering algorithms and determine which one is best for a particular application.
In addition to providing an overall evaluation of clustering quality, the Silhouette score can also be used to identify individual outliers or misclassified points. A point with a low Silhouette coefficient may indicate that it does not belong in its assigned cluster or that it should be assigned to a different one.
Overall, the Silhouette score provides an objective measure of clustering quality that takes into account both within-cluster similarity and between-cluster separation. By considering both factors, it can help identify good clusters as well as individual outliers or misclassified points.
In short: What’s a good Silhouette Score? A good Silhouette Score is one that has a high value (>0), indicating good separation between clusters and inter-cluster similarity.
Conclusion:
A good Silhouette Score is one that has a high value (>0), indicating good separation between clusters and inter-cluster similarity.