What is a fundamental feature of hierarchical clustering?

Hierarchical clustering is a method that builds a hierarchy of clusters, allowing for a visual representation of data relationships through a dendrogram. One of its fundamental features is that it can be sensitive to outliers, which can significantly impact the results of the clustering process. Outliers can skew the distances between data points, leading to incorrect grouping or misrepresentation of natural clusters within the data.

The presence of outliers might cause the algorithm to either isolate them into their own clusters or influence the formation of nearby clusters, thereby affecting the overall structure and interpretation of the dendrogram. This sensitivity highlights the importance of pre-processing data to mitigate the effects of outliers when using hierarchical clustering techniques.

In contrast, the other options address misconceptions about how hierarchical clustering operates. It does not require pre-specification of the number of clusters, allows for varying numbers of clusters to be visualized in the dendrogram, and is, in fact, susceptible to changes in data, especially when those changes involve outliers. Understanding this sensitivity to outliers is crucial for effective implementation and interpretation of hierarchical clustering methods.