What is the Difference Between Hierarchical and Partitional Clustering?

The main differences between hierarchical and partitional clustering lie in their structure, computational complexity, and the way they partition the data. Here are the key differences:

1. Structure: Hierarchical clustering organizes patterns into a hierarchical structure, consisting of a sequence of nested data partitions. In contrast, partitional clustering organizes patterns into a small number of clusters, usually assuming the a priori specification of the number of clusters or the definition of cluster validity criteria.
2. Computational Complexity: Hierarchical clustering involves the pre-computation of a similarity matrix between all sample pairs, which can lead to higher computational complexity compared to partitional clustering. Partitional clustering is typically faster than hierarchical clustering.
3. Data Partitioning: In hierarchical clustering, each item within a dataset starts as an individual cluster, and the algorithm computes the proximity among each cluster. It then proceeds to merge each pair of closest clusters and computes the new proximity among them. This process is repeated until there is one cluster left, represented using a dendrogram. In partitional clustering, the data is divided into mutually disjoint partitions, typically by selecting the number of K clusters to be used as initial centroids.
4. Optimality: Solutions found in hierarchical clustering are dependent on the value of a design parameter, th, and the order of patterns' presentation, which may lead to performance degradation. Unlike the hierarchical approach, clustering results in partitional clustering are independent of the order of patterns' presentation, overcoming potential performance degradation.

In summary, hierarchical clustering creates a hierarchical structure among the data points, while partitional clustering divides the data into a small number of disjoint clusters. Hierarchical clustering is more computationally complex, while partitional clustering is generally faster and less reliant on the order of patterns' presentation.

Comparative Table: Hierarchical vs Partitional Clustering

Hierarchical and Partitional Clustering are two different techniques used in data analysis and organization. Here is a table comparing the differences between the two:

In summary, Hierarchical Clustering creates a multilevel hierarchy of clusters, allowing for the exploration of different levels of clustering, while Partitional Clustering divides data into non-overlapping clusters based on a specific criterion. Hierarchical Clustering is more suitable for discovering natural groupings in the data, while Partitional Clustering is more suitable for grouping data according to predefined criteria.