# A Taxonomy of Machine Learning Clustering Algorithms, Challenges, and Future Realms
## 2 Taxonomy of Clustering Algorithms
### Hierarchical Clustering Algorithms
#### 2.1.1 Agglomerative Clustering  
In unsupervised machine learning, hierarchical, agglomerative clustering is a significant and well-established approach. Agglomerative clustering methods begin by dividing the data set into singleton nodes and gradually combining the two currently closest nodes  
Figure 1: Taxonomy for various clustering techniques.  
into a single node until only one node is left, which contains the whole data set. This process serves as a common description for several clustering systems, but they vary in how the measure of inter-cluster dissimilarity is updated after each step [32]. The objective function's optimal value serves as the criterion for selecting the pair of clusters to merge at each phase. Instead of binary data, this clustering algorithm is best suited for quantitative variables. The research of [33] devised a non-parametric hierarchy, with a conventional closest neighbor approach, an agglomerative clustering method determines a sample point's mutual neighborhood value (MNV) and mutual nearest neighbors (MNN). Agglomerative hierarchical clustering is further subdivided into the following categories.  
* Single-linkage clustering: this type of clustering is also known as the minimal, connectedness, or nearest-neighbor approach. The closest distance between any two cluster members of any cluster is measured. By calculating the closest distance between a single element pair, it calculates the similarity between two clusters. The chaining effect of the single linkage clustering has the propensity to produce extended clusters [34].
* Average linkage clustering: the minimum-variance linkage is another name for average linkage clustering [15; 20]. It determines the average or median distance between each cluster of data points [34].
* Complete linkage: the complete linkage, often referred to as the maximum, diameter, or farthest neighbor method, measures the longest distance between any member of one cluster and any member of the other cluster in order to calculate the distance between two clusters. Compared to single-linkage clustering, the complete-linkage algorithm clusters are smaller and more closely linked [20]. The three-proximity metrics that were described earlier take into account all the points in a pair of clusters when calculating the inter-cluster distances. They are thought of as graph techniques [10; 35].  
SLINK is an implementation of the single linkage hierarchical clustering technique [36]; the authors of [37; 38] developed CLINK, which is an implementation of the complete linkage clustering algorithm and are examples of the average link clustering algorithm. Other geometrical techniques were created using the center point as a proximity measure based on the same concept. These comprised the minimum variance linkage metrics, centroid linkage, and median linkage metrics [39; 40; 41]. While similarity metrics capture intra-cluster connectedness, a distance-based proximity measure captures inter-cluster closeness. The adjustable amount of granularity and any similarity metric can be handled by the hierarchical clustering techniques [34].