Hierarchical cluster analysis example

Two examples of unsupervised classical pattern recognition methods are hierarchical cluster analysis (HCA) and principal components analysis (PCA). Unsupervised methods attempt to discover natural clusters within data sets. Both HCA and PCA cluster data. 

Hierarchical cluster analysis (HCA) and the closely related tree cluster analysis (TCA) provide a simple view of distances between samples, often viewed in a tree-like structure called a dendrogram (see Fig. 6a as an example). These types of analyses methods allow for the development of quick and simple classification schemes. Distances are calculated between all samples within the data set where the data parameters are the coordinates in a multidimensional variable parameter space (of dimension Mvar)- The general distance... 

An in-depth review of statistical methods for metabonomic data analysis is beyond the scope of this chapter. Briefly, there are a few main approaches to data analysis. Examples of multivariate data analyses include the so-called unsupervised analyses such as PCA, independent component analysis (ICA), and hierarchical clustering analysis (HCA), while partial least square differential analysis (PLS-DA) is... 

Figure 11 Example dendrogram of hierarchical cluster analysis of conformations. Individual conformers are along on the bottom and progressively merge into broader and broader families toward the top.

These various chemometrics methods are used in those works, according to the aim of the studies. Generally speaking, the chemometrics methods can be divided into two types unsupervised and supervised methods(Mariey et al., 2001). The objective of unsupervised methods is to extrapolate the odor fingerprinting data without a prior knowledge about the bacteria studied. Principal component analysis (PCA) and Hierarchical cluster analysis (HCA) are major examples of unsupervised methods. Supervised methods, on the other hand, require prior knowledge of the sample identity. With a set of well-characterized samples, a model can be trained so that it can predict the identity of unknown samples. Discriminant analysis (DA) and artificial neural network (ANN) analysis are major examples of supervised methods. 

It is this diversity of metabolites that presents the most difficult challenge. There are not only a variety of metabolites but they are also dynamic spatially and temporally. To master a universal "omics" approach, one has to have several measurement strategies. For example, a suite of quantitative methods analyzing key metabolites from different biochemical pathways and metabolic "fingerprinting" that compares patterns like multidimensional hierarchical clustering or principal cluster analysis.9... 

The manner in which sample-to-sample resemblance is defined is a key difference between the various hierarchical clustering techniques. Sample analyses may be similar to one another in a variety of ways and reflect interest in drawing attention to different underlying processes or properties. The selection of an appropriate measure of similarity is dependent, therefore, on the objectives of the research as set forth in the problem definition. Examples of different similarity measures or coefficients that have been used in compositional studies are average Euclidean distance, correlation, and cosine. Many others that could be applied are discussed in the literature dealing with cluster analysis (15, 18, 19, 36, 37). 

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