# A Taxonomy of Machine Learning Clustering Algorithms, Challenges, and Future Realms
## 2 Taxonomy of Clustering Algorithms
### Hierarchical Clustering Algorithms
#### 2.1.2 Divisive Hierarchical Clustering  
The agglomerative clustering process breaks each cluster into smaller groups starting with each item in a single cluster and continuing until the necessary number of clusters is reached and it is reversed by the process known as \"divisive hierarchical clustering.\" The divisive approach, in contrast to the agglomerative clustering method, employs the top-down method, where the data objects are initially thought of as a fused cluster that gradually separates depending on when the cluster number is collected [42; 43; 44]. In order to divide a cluster into two subsets that each contain one or more components, the usual procedure takes into account all potential bipartitions. Even though it is common practice to examine all potential bipartitions in which each cluster is capable of being divided into two smaller clusters it is clear that the entire enumeration procedure provides a universal optimum but is quite costly in terms of computation cost.  
Diverse divisive clustering methods that do not take into account all bipartitions have been researched. For instance, [45] compared the conventional K-Means or agglomerative method, and a bisecting K-Means divisive clustering method was presented. Another study [46] combined it with the divisive clustering approach to investigate a unique clustering technique dubbed \"reference point-based dissimilarity measure\" (DIVFRP) for the aim of dataset division.  
The author in [47] proposed an improved particle optimizer (IDPSO) to identify the most convenient optimal partition hyperplane for dividing the chosen clusters into two parts. This dividing method is a practical and effective component of the divisive hierarchical approach. The authors in [48; 49] investigated the iterative division technique using the average dissimilarity between an object and a set of objects. A different strategy, however, focuses on optimization criteria that include partitioning or bi-partitioning and uses a dissimilarity matrix as input [50; 51]. There are two main categories of divisive clustering: monothetic and polythetic approaches. When a set of logical qualities are both required and sufficient for inclusion in a cluster, we refer to that cluster as monothetic [52].  
Monothetic divisive clusters are formed by dividing items based on a single variable in each breaking, such as whether or not they have a certain object value. The \"association analysis approach\" has a version called monothetic; the author of [53] developed it specifically for binary information. Several researchers have used monothetic clusters to solve problems. For instance, the authors of [54] provided an approach that gives an arrangement of things and a monothetic description of each cluster. Similarly, the author in [55] developed three monothetic techniques and principal component analysis (PCA) for inter-valued data. The initial PCA method utilized inter-valued data. The author's second approach relied on symbolic data, while their third and final algorithm was derived from the terminal values of intervals. In the end, the author tested their model using real-world data to ensure its accuracy.  
Contrarily, polythetic divisive clustering is a method that uses all parameters concurrently by calculating distances or resemblance values. Rather than relying on the relative positions of variables, it relies solely on distance values, which in turn indicate the dissimilarity between all of the variables simultaneously [56].