Society of Actuaries (SOA) PA Practice Exam

What distinguishes agglomerative clustering from divisive clustering?

1. Agglomerative clustering splits clusters while divisive combines them

2. Agglomerative is a top-down approach while divisive is bottom-up

3. Agglomerative starts with individual clusters while divisive starts with one cluster

4. Agglomerative requires prior knowledge of cluster number while divisive does not

The correct answer is: Agglomerative starts with individual clusters while divisive starts with one cluster

Agglomerative clustering and divisive clustering represent two different approaches to hierarchical clustering, which is a method used to group similar data points into clusters. In agglomerative clustering, the process begins by considering each data point as its own individual cluster. As the algorithm progresses, it iteratively merges the closest pairs of clusters until a specified condition is met, such as reaching a desired number of clusters or merging all clusters into one. This bottom-up approach effectively combines the data points, gradually forming larger clusters from smaller ones. In contrast, divisive clustering starts with a single, comprehensive cluster that contains all data points. The algorithm then systematically splits this large cluster into smaller clusters, working downwards through the levels of hierarchy until it reaches the desired granularity of the data. This approach is top-down, beginning with one cluster and dividing it into smaller segments instead of merging smaller ones. Understanding these core differences is key: agglomerative clustering focuses on merging clusters from the smallest elements, while divisive clustering is about splitting a large cluster into smaller, more refined groups. Thus, identifying agglomerative clustering as starting with individual clusters is what makes this statement accurate.