Final answer:
Hierarchical clustering does not require the number of clusters to be specified in advance, offering flexibility in forming clusters. It can handle both numerical and qualitative data and is not limited to a single type of data. Examples include organizing biological taxa and geographical data points.
Step-by-step explanation:
Out of the given statements about hierarchical clustering, the true statement is that "Hierarchical clustering does not require the number of clusters to be specified in advance." Hierarchical clustering is a method of cluster analysis which seeks to build a hierarchy of clusters. In contrast to some other clustering methods like k-means, where the number of clusters needs to be specified before starting the algorithm, hierarchical clustering builds either a merger (agglomerative) or splitting (divisive) hierarchy that can be represented in a dendrogram. This technique is not limited to numerical data; it can also handle qualitative data and is flexible in accommodating various types of similarity measures.
Examples of Hierarchical Clustering
- In biological sciences, such as the taxonomic classification system, a hierarchical model is used to organize living organisms where each sublevel represents organisms with a higher degree of similarity.
- In geographical data, hierarchical clustering might help in identifying the clustering of points on a map, indicating the proximity of features to one another.
It is important to understand that hierarchical clustering is indeed a bottom-up approach if the agglomerative method is used. However, it can also be a top-down approach if using a divisive method, making statement 3 partially true, depending on the context.
Therefore, the most accurate answer to the student's question is that hierarchical clustering does not require the number of clusters to be specified in advance (statement 4).