What is the final resultant cluster size in Divisive algorithm, which is one of the hierarchical clustering approaches?Review LaterZeroThreeTwosingleton

The divisive clustering algorithm is a type of hierarchical clustering that works by starting with a single cluster containing all data points and recursively splitting it into smaller clusters until certain stopping criteria are met. Here’s how the final resultant cluster size can be analyzed:

1. Understanding Divisive Clustering: In the divisive algorithm, the process begins with one large cluster containing all the points. It successively divides this cluster into smaller sub-clusters. This continues until each cluster reaches a predefined size, until no further divisions are possible, or until a certain number of clusters is reached.

2. Final Cluster Size: The final resultant cluster size depends on two main factors:

   • Stopping Criterion: Whether the algorithm stops after a predetermined number of clusters or when clusters are no longer distinct.
   • Data Distribution: The inherent structure or distribution of the data can lead to different final cluster sizes.

3. Example Scenario: If the stopping criterion is to reach a final number of clusters $k$, then the final resultant cluster size could be represented as $n/k$, where $n$ is the total number of data points.

In conclusion, the final resultant cluster size in a divisive algorithm is variable and is determined by the stopping criteria set by the user as well as the nature of the dataset being analyzed. Typically, it could result in any number of clusters ranging from a minimum of 1 (all points in one cluster) to $n$ (each point as its own cluster).