# 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
Without providing any background information about the datasets, automatic clustering algorithms yield identical results to the conventional clustering technique [7; 20; 22; 69]. Automatic labeling of unlabeled data points in real-world datasets has also been found to be feasible using this method, which is obviously difficult and extremely difficult to accomplish traditionally. Automatic clustering algorithms are more likely to find an optimum ideal solution than local searching algorithms, which are affected by early originating regions. A generalized optimization problem requires a linear and convex solution [7]. Additionally, nature-inspired clustering algorithms are more adaptable to addressing clustering challenges across sectors than traditional clustering approaches, which are generally a concern and lack continuity [22]. The main goal of automatic clustering algorithms is to produce clusters with lowered based on inter-distance and enhanced inter-cluster distance [7]. * Square error clustering:  
Using a sum of the square error criterion functions, data points are clustered into a set number of categories with the square error clustering technique. Differentiated by the number of standard deviations, each data point from the stated group mean is included in the information shown here. When the sum of the squared errors for the data points in a cluster is zero, we may say that the points in the cluster are statistically very near to one another (very close). K-means clustering; the K-means clustering algorithm is often used to fix clustering issues. This is an instance of unsupervised learning. Some benefits it offers are as follows: it outperforms hierarchical clustering in terms of computing efficiency for very large variables. If you choose a globular cluster with a small value for k, you will obtain denser clusters than you would with hierarchical clustering. This algorithm's main advantage is how simple it is to use and understand the clustering results. The algorithm's complexity is O(K*n*d), making it very efficient from a computing standpoint [70]. Using this number, we may join the data point to the nearest cluster. When a new data point is added to a cluster, a new mean is calculated using the items already distributed among clusters, which raises the level of intra-cluster similarity. The data items are then reassigned using the new mean. Repeat this process multiple times until stability is attained. The goal of the K-Means method is to reduce the total squared error threshold [22; 71; 72]. The problem of the basic formulation of the number of clusters at the computation inception is one of the key concerns with K-Means clustering algorithms. There is not a reliable, all-encompassing strategy for determining how many clusters and how many partitions to start with. According to reports, the K-means algorithm is particularly sensitive to the initial centroid selection, which might lead to the production of a less-than-ideal solution [34]. * Miscellaneous clustering techniques:  
Miscellaneous clustering technique includes time series mode seeking and streaming clustering techniques. Time series clustering: time series clustering, similar to stable data clustering, needs a clustering method or technique to build clusters given a set of unordered items, and the selection of the clustering algorithm relies on both kind of information provided and the specific goal and purpose. Discrete-valued and real-valued data, uniform and non-uniform sampling, univariate and multivariate data, and data series of equal and unequal length are all various types of time series data. Before performing clustering procedures, non-uniformly sampled data must be transformed into uniform data. This may be accomplished in several ways, from straightforward down sampling based on the roughest sampling interval to a complex modeling and estimate strategy [73]. Streaming clustering: a data stream is a vast, continually arriving series of multidimensional objects that is unlimited and quickly changing over time [74].