# Bootstrap-CURE: A Novel Clustering Approach for Sensor Data--An Application to 3D Printing Industry
## 3 State-of-the-Art
### Clustering Strategies
#### 3.2.3 Detection of the Number of Clusters
The _CSP_ is used as a substitute for the _Calinski-Harabasz_ index, and it functions in a similar relationship between intracluster homogeneity and intercluster separability. However, part of the CSP is focused on building a minimum spanning tree, and the proposal is of \(O(n^{3})\), which is prohibitive in large dataset contexts. The _Calinski-Harabasz_ index [76] is often regarded as the most suitable criterion to determine the number of clusters in hierarchical clustering. [PERSON] in [77] conducted an extensive experiment on 30 different CVIs and concluded the _Calinski-Harabsz_ index to be the most consistent one. In the recent work by [PERSON] et al. [78], the authors performed empirical analysis on several real-life datasets and presented an improved CVI, called \(\Delta_{K_{cont}}\), that maximizes the difference of successive _Calinski-Harabasz_ indices over a range of \(K\) clusters (\(k=1,2,\ldots K\)) and suggests the conditional criterion to select between 2 and the next best clustering solution. However, several instances were found where the number of clusters by the proposed \(\Delta_{K_{cont}}\) criterion did not match correctly against the expert's judgment based on the dendrogram. Additionally, several unique solutions to correctly determine the number of clusters are mentioned in the literature. In [79], [PERSON] et al. proposed the genetic-algorithm-based method, _COWCLUS_, which optimizes a fitness function defined in terms of _within-cluster cohesion_ and _between-cluster isolation_ which itself is a _Calinski-Harabasz_ criterion. However, such a method does not appear to be scalable for large datasets and, hence, not very suitable for real-life applications. Similarly, in [80,81], [PERSON] et al. proposed a permutation test-based approach to determine the optimal number of clusters in hierarchical clustering. This too appears to be complex to execute for large-scale datasets in real time. In [82], the reachability plot (derived from the density-based clustering methods) is used as preprocessing to identify the number of clusters of the hierarchical tree. The process of the heights of tree nodes is complex and iterative in this technique. In [83], a single-height similarity threshold is applied, using a dynamic slider to identify the main clusters. Continuing this, in [84], [PERSON] et al. used the height of the nodes to identify interesting branches of the tree. However, the concept of using non-horizontal cuts of the trees violates the ultra-metric properties of the dendrogram itself and is thus not very aligned with the objective of this current research work by the authors. To the extent of interpreting cluster patterns, several works are studied. In [85], the authors presented an approach to interpret cluster patterns in real datasets. [PERSON] et al. [86] presented the _KLASS_ clustering system to measure similarity in ill-structured domains. In [5], using mixed metrics was proposed while clustering complex messy datasets. [PERSON] et al. in [87] introduced the concept of semantic variables and generalized _[PERSON]'s_ mixed metrics for clustering heterogeneous data matrices. Another related work can be seen in [4], where the authors presented a real-life application from a wastewater treatment plant, using a clustering-based approach. In the recent study by [PERSON] et al. [88], a new cluster-validity-criteria was proposed that operates directly on the linkage matrix of the hierarchical clustering to detect the suitable number of clusters similar to how human experts perceive clusters visually in a dendrogram.