# NMR in Metabolomics: From Conventional Statistics to Machine Learning and Neural Network Approaches
## 2 Conventional Approaches
### Unsupervised Methods
#### 2.1.2 Clustering  
Clustering is a data analysis technique used to regroup unlabeled data on the basis of their similarities or differences. Examples of clustering algorithms are essentially the following: exclusive, overlapping, hierarchical, and probabilistic clustering [40, 41]. Exclusive and overlapping clustering can be described together because they differ for the existence of one or multiple data points in one or more clustered sets. In fact, while exclusive clustering establishes that a data point can occur only in one cluster, overlapping clustering enables data points to be part of multiple clusters with different degrees of membership. Exclusive and overlapping clustering are hard or k-means clustering and soft or fuzzy k-means clustering, respectively [42, 43, 44]. In hard clustering, every element in a database might be a part of a single and precise cluster, whereas in soft clustering, there is a probability of having each data point into a different cluster [44]. Generally speaking, k-means clustering is a \"distance-based\" method in which each \"clustered set\" is linked with a centroid that is considered to minimize the sum of the distances between data points in the cluster.  
Hierarchical clustering analysis (HCA) is used to recognize non-linear evolution in the data--contrary to what was done by the PCA which shows a linear trend--by means of a regrouping of features sample by sample without having any previous information [45]. This clustering method could be divided in two groups: (i) agglomerative clustering, and (ii) divisive clustering [46, 47]. The first one allows to keep data points separate at first, unifying them iteratively later until it one cluster with a precise similarity between the data points is obtained. In the opposite way, divisive clustering creates a separation of data points in a data cluster on the basis of their differences. The clustering analysis leads to dendrograms that are diagrams in which the horizontal row represents the linked residues, whereas the vertical axis describes the correlation between a residue and previous groups. Figure 3 reports a dendrogram obtained by means of hierarchical cluster analysis performed on \({}^{1}\)H NMR data on the plasma metabolome of 50 patients with early breast cancer [48]. This kind of analysis allowed to discriminate among three different groups: LR-1 (red), LR-2 (blue) and LR-3 (green). They are characterized by significantly different levels of some metabolites, such as lactate, pyruvate and glutamin [48]. Furthermore, covariance analysis of NMR chemical shift changes allows defining functional clusters of coupled residues [49].  
Clustering has been largely applied for metabolomic studies covering fields from medicine to food science, as is reported in the Applications section (Section 4). Here, we anticipate that clustering is essentially adopted for samples' classification by grouping metabolites without any external bias. This allows entering into the details of the precise metabolic pathways that may provide a connection between metabolomics and molecular biology. In such a way, many biomedical applications, including diagnostics and drug synthesis, would reach important improvements.