# 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  
In a hard or crisp clustering procedure, each data point refers to an exactly particular cluster. Miscellaneous clustering, density-based clustering, graph-theoretic clustering, model-based clustering and subspace clustering are some of the clustering techniques included in this category. * Graph-theoretic clustering:  
A data structure known as a \"graph\" is composed of nodes and the edges that connect them. When conducting data analysis, a graph can be used to list significant, pertinent features and model relationships between features of data items. Graphs are used to represent clusters in graph-theoretic clustering [15]. The representation of the data objects consists of nodes connected by edges. The edges show how close together pairs of data points are [10]. Separating cells into distinct clusters reduces the number of edges among groups while increasing the number of edges inside them [15]. Consistent edges are those whose clustering length (weight) is significantly greater than the average of the nearby edges. Points are classified into groups based on the graph structure, which results in result clusters with strong intra-connectivity/homogeneity and minimal inter-connectivity/homogeneity among the produced clusters. Although useful, representing clusters on graphs is not robust enough to handle outliers. Using particular graph topological characteristics, this clustering method produces bunches from a collection of data items. Similar to the search for the most connected graph subgraphs, the problem of single linkage hierarchical clustering is a graph-based one. Comparable to total-linkage, hierarchical clustering is the search for the most comprehensive subgraphs in a given network [20]. * Subspace clustering:  
Subspace clustering aims to discover a low-dimensional subspace that best fits each cluster of points in the data while clustering the data into numerous subspaces at the same time [60]. Instead of explaining a big dimensional dataset as a whole, it is frequently preferable to do so using the subspaces in which it exists [61]. In such a large dimensional dataset, the subspace clustering method enables the discovery of hidden knowledge. Subspace clustering makes it simple to spot clusters that exist in several overlapping subspaces. Utilizing feature selection, subspace clustering eliminates unnecessary and redundant dimensions, leaving only the pertinent dimension for the clustering algorithm to employ when locating clusters in the dataset. Using the top-down and bottom-up clustering algorithm search techniques, the subspace clustering algorithm is divided into two subcategories. The bottom-up subspace method makes use of the downward closure property of density to minimize search space using an APRORI-style methodology. Top-down subspace clustering starts by finding an estimation of the clusters throughout the full-length feature set, where each dimension is entitled to equal weight. * Density-based clustering:In pattern space, clusters are regarded as dense regions that are divided by less dense parts. When compared to the items in the sparse regions dividing the clusters, which are referred to as noise and outliers, the high-density regions, or modes, are connected with a cluster core [62]. The closest center clusters are then created using the data points. To determine the pattern space modes, the pattern space is divided into non-overlapping sections and a histogram is created. The valleys of the histogram's structure serve as the boundaries between the clusters, while the regions with high-frequency counts represent potential modes. The main problem with a histogram is that it requires too large of a pattern space to distinguish the portions required for determining the density function [20]. Furthermore, because they cannot be accurately described, small clusters are typically exceedingly noisy. The diverse qualities of the member patterns, however, prevent huge clusters from accurately defining the cluster properties.