What type of clustering allows for different numbers of clusters derived from a dendrogram?

Hierarchical clustering is the method that allows for different numbers of clusters to be derived from a dendrogram. A dendrogram is a tree-like diagram that illustrates the arrangement of the clusters produced by hierarchical clustering. The key feature of hierarchical clustering is its ability to create a hierarchy of clusters, which can be defined at various levels of granularity.

In a dendrogram, the vertical lines represent the distance or dissimilarity between clusters, and the points where these lines merge indicate where clusters combine. By cutting the dendrogram at different heights, a user can obtain varying numbers of clusters. This flexibility makes hierarchical clustering particularly useful for exploratory data analysis, as it gives insights into the data structure at multiple cluster resolutions.

While other clustering methods like K-means and partitional clustering focus on a pre-specified number of clusters and do not inherently provide a visualization like a dendrogram, hierarchical clustering emphasizes the relationship among the data points and allows for dynamic determination of cluster quantity based on the analysis requirements.