Hierarchical Cluster Analysis HCA

HCA is a powerful method for data sorting based on local decision criteria. These criteria are based on finding the smallest distances between items such as spectra, where the term distances may imply Euclidean or Mahalanobis distances [17], or correlahon coefficients. HCA is, per se, not an imaging method, but can be used to construct pseudocolor maps from hyperspectral data sets collected from cells or tissue sections [18]. 

In HCA, the spectral correlation matrix, C is calculated according to according to  

---

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) also provides a method of determining... 

Hierarchical Cluster Analysis (HCA) is a multivariate statistical method that can be used assign groundwater samples or monitoring sites to distinct categories (hydrochemical facies). HCA offers several advantages over other methods of... 

Another very useful exploration technique is cluster analyis, which quantifies similarities by calculating mathematic distances. The typical graphic output is a dendrogram. A common method of cluster analysis is Hierarchical cluster analysis (HCA). 

The bottleneck in utilizing Raman shifted rapidly from data acquisition to data interpretation. Visual differentiation works well when polymorph spectra are dramatically different or when reference samples are available for comparison, but is poorly suited for automation, for spectrally similar polymorphs, or when the form was previously unknown [231]. Spectral match techniques, such as are used in spectral libraries, help with automation, but can have trouble when the reference library is too small. Easily automated clustering techniques, such as hierarchical cluster analysis (HCA) or PCA, group similar spectra and provide information on the degree of similarity within each group [223,230]. The techniques operate best on large data sets. As an alternative, researchers at Pfizer tested several different analysis of variance (ANOVA) techniques, along with descriptive statistics, to identify different polymorphs from measurements of Raman... 

Figure 12.24 Dendrograms obtained from hierarchical cluster analysis (HCA) of the NIR. spectra of the poly(urethane) foam samples (shown in Figure 12.16), (A) using the first two PCA scores as input, (B) using the first five PCA scores as input. In both cases, the Mahalanobis distance measure and the nearest-neighbor linkage rule were used.

Hierarchical cluster analysis (HCA) is an unsupervised technique that examines the inteipoint distances between all of the samples and represents that information in the form of a twcKlimensional plot called a dendrogram. These dendrograms present the data from high-dimensional row spaces in a form that facilitates the use of human pattern-recognition abilities. 

Preliminary data analysis carried out for the spectral datasets were functional group mapping, and/or hierarchical cluster analysis (HCA). This latter method, which is well described in the literature,4,9 is an unsupervised approach that does not require any reference datasets. Like most of the multivariate methods, HCA is based on the correlation matrix Cut for all spectra in the dataset. This matrix, defined by Equation (9.1),... 

One of the emerging biological and biomedical application areas for vibrational spectroscopy and chemometrics is the characterization and discrimination of different types of microorganisms [74]. A recent review of various FTIR (Fourier transform infrared spectrometry) techniques describes such chemometrics methods as hierarchical cluster analysis (HCA), principal component analysis (PCA), and artificial neural networks (ANN) for use in taxonomical classification, discrimination according to susceptibility to antibiotic agents, etc. [74],... 

To investigate relationships between crustacean grazing rates on Phaeocystis and experimental conditions, a multiple correspondence analysis (MCA) followed by a hierarchical cluster analysis (HCA) was performed using SPAD 3.5 software (Lebart et al. 1988). The combination of MCA and cluster analysis is a common way to explore relationships among a large number of variables and to facilitate interpretation of the correspondence analysis results (Lebart et al. 2000). MCA uses a contingency table as data, which provides a simultaneous representation of the observations (rows) and variables (column) in a factorial space. This form of multivariate analysis describes the total inertia (or variability) of a multidimensional... 

Table 6 Sources of data used for the multiple correspondence analysis (MCA) and hierarchical cluster analysis (HCA) presented in Fig. 1, and quantitative summary in Fig. 2, respectively...

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... 

Figu re 5.9 (a) Brightfield image of a HeLa cell, attached to a Cap2 window, in buffer. Scale bar= 10 im (b) Raman spectral image, obtained via hierarchical cluster analysis (HCA) from a hyperspectral data cube collected atSOOnm spatial resolution (488 nm... 

Clustering methods such as hierarchical clustering analysis (HCA) are able to find clusters of similar molecules in a dataset (see Fig. 23a). The calculation is based on the descriptors, and thus no mapping errors occur [123, 124]. 

Fig. 23 Classification of the NSAID dataset based on three-dimensional autocorrelation descriptors, a) Hierarchical clustering analysis (HCA). The dark gray cluster includes the COX-2-selective drugs, b) Visualization of the minimal spanning tree (MST). The longest connections are drawn as dotted lines in order to derive classes of compounds.

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... 

Ratios are often shown on star or polar plots, but can be confusing when large numbers of samples are involved. Alternatively, hierarchical cluster analysis (HCA) can be used to group oils into families on the basis of their similarity to one another. The measure of similarity is based on the distance between samples, which is defined using the relationship shown below. 

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. 

The GPA allowed positioning the 12 perfumes within two main dimensions (representing 67% variance). A hierarchical clustering analysis (HCA) was also performed to obtain clusters based on the product similarity (Fig. 19.2). 

---