What is true about running the hierarchical clustering algorithm multiple times?

Running the hierarchical clustering algorithm multiple times can yield different cluster assignments due to the nature of the algorithm and how it constructs the clusters. Hierarchical clustering does not require a predetermined number of clusters and builds a hierarchy of clusters based on the data’s structure. The results can depend on the linkage method used (e.g., single, complete, average) and the distance metric chosen (e.g., Euclidean, Manhattan).

Each time you run the algorithm, variation in these parameters or even minute changes in the data (like noise or small sampling variations) can lead to different outcomes. Additionally, since hierarchical clustering builds a dendrogram, the way the clusters are formed at each level can lead to varied interpretations of the data depending on where the “cut” is made to define clusters, which can also affect the final cluster assignments.

This characteristic of hierarchical clustering is important to recognize, as it emphasizes the potential for non-deterministic behavior in its outputs, aligning with the idea that repeated runs can lead to different clustering results.