Average Silhouette width is a technique used to assess the relative homogeneity of a cluster or set of data points. It is often used as a metric of cluster “goodness” in unsupervised learning, or as part of validation criteria when clustering data. As its name implies, average Silhouette width measures the “width” of the average Silhouette of all clusters in a dataset.
The intuition behind this metric is that if all the data points in a given cluster are very similar, then all their Silhouettes should be narrow, since they will be close to each other.
Similarly, if there is high variability within the data set, then each Silhouette should be wider as points further away from the center will have more variance from the center point.
The average Silhouette width for a given set of clusters is calculated by first determining the Silhouette width for each individual point in the dataset. For each point, its Silhouette width is calculated by subtracting its distance from all other points in its own cluster, from its distance from all points in all other clusters. The average Silhouette width for a given data set is then computed by taking an average of these individual values.
To calculate Average Silhouette Width (ASW):
- Calculate intra-cluster distances
- Calculate inter-cluster distances
- For each data point, subtract intra-cluster distances from inter-cluster distances
- Compute an average value across all these differences
The higher this value is, the better it indicates that the clustering algorithm has been able to identify meaningful groups in the dataset.
It should also be noted that different types of clustering algorithms can lead to different values for ASW and thus can provide insight into which algorithm works best for your particular dataset.
Conclusion:
In conclusion, Average Silhouette Width (ASW) is an important technique used to assess relative homogeneity amongst clusters or sets of data points and can help determine which clustering algorithm works best for your particular dataset.