# A Taxonomy of Machine Learning Clustering Algorithms, Challenges, and Future Realms
## 2 Taxonomy of Clustering Algorithms
### Partitional Clustering Algorithm
#### 2.2.2 Hard/Crisp Clustering
Finding the exact values for the histogram's peak and the valley is another challenge [20]. Engineering has made substantial use of this clustering technique, primarily in remote sensing applications [63]. In some other instances, clusters are created depending on the number of data points present in a certain area. Data points are added to the cluster up until a predetermined threshold is reached for the neighborhood's density. In this scenario, a cluster within a specific radius must have a certain minimum number of objects that fall inside the provided criterion. Building of the cluster this makes it possible to create clusters with any shape. Naturally, noisy or outlier data points are removed. For example, density-based spatial clustering of applications with noise (DBSCAN) and optimal points for identifying cluster structure (OPTICS) are two methods for determining a clustering's organizational framework (DENCLUE) DBSCAN's cluster model is well-defined and just somewhat complicated [62]. OPTICS fixed the problem with DBSCAN's range parameter selection, producing a hierarchical outcome similar to linkage clustering [62]. Moreover, the HDBSCAN clustering algorithm is a successor of the DBSCAN algorithm; it shares all the advantages of the DBSCAN algorithm and eliminates the problem of clusters of varying densities, which is often referred as a strength of the algorithm. However, it still needs to select a minimum cluster size which is said to be its weakness [64]. According to reports, the model's complexity increased from \(O(n^{2})\) to \(O(n\ log\ n)\) when the spatial index was used to define a data point's neighborhood [18]. Model-based clustering:  
Model-based clustering is a method for maximizing the usefulness of a selected model with the information at hand. Since clusters are formed according to the data set provided, the total nodes may be estimated rapidly, facilitating the discovery of outliers. Clustering using models utilizes a hybrid model to depict the data, with the model's components standing in for the various clusters. Cluster composition models can be generated in one of two ways, e.g., methods such as the mixing likelihood and the categorization probable. Parameter estimates for a model are often determined using the Maximum Likelihood Estimation (MLE) criteria [65], or with the Bayesian Information Criterion (BIC) [66]. The BIC may also use distance to decide which of two clusters to place a data point in [65]. Search-based clustering:  
Automatic data clustering techniques, or search-based clustering algorithms, are metaheuristic methods inspired by nature. The architecture and quantity of clusters in such a dataset are determined without prior knowledge of the characteristics or elements in the array [7]. They appear as a response to the requirement to supply the conventional clustering algorithms, a priori data [67]. Based on the quantity of clusters produced. The necessity of providing this crucial data typically results in some additional computing demands or loads on the pertinent conventional clustering techniques [7; 8]. A fundamental issue in cluster analysis known as the \"automated clustering problem\" is finding the best estimate of the number of clusters [68]. Legitimate data clustering analysis using high-density and dimensional datasets exacerbates this difficulty. It is tough to pick sufficient cluster numbers when there is a lack of previous domain knowledge, particularly in datasetswith several dimensions and a broad range of cluster size, shape, density, and occasionally overlap. This was before the number of clusters needed for a data clustering technique is not straightforward since figuring out the appropriate number of clusters needed for such huge datasets is a very tricky subject. For real-world data sets with high density and dimensionality, automatic clustering algorithms are developed, where such a prerequisite is not necessary, and become a superior choice.