Cluster analysis hierarchical

In a typical appHcation of hierarchical cluster analysis, measurements are made on the samples and used to calculate interpoint distances using an appropriate distance metric. The general distance, is given by... 

Dubois M, Plaisance H, Thome JP, et al. 1996. Hierarchical cluster analysis of environmental pollutants through P450 induction in cultured hepatic cells. Ecotoxicol Environ Saf 34 205-215. 

Willett P, Winterman V, Bawden DJ. Implementation of non hierarchical cluster-analysis methods in chemical information-systems-selection of compounds for biological testing and clustering of substructure search output. Chem Inf Comp Sci 1986 26 109-18. 

I. Bondarenko, H. Van Malderen, B. Treiger, P. Van Espen and R. Van Grieken, Hierarchical cluster analysis with stopping rules built on Akaike s information criterion for aerosol particle classification based on electron probe X-ray microanalysis. Chemom. Intell. Lab. Syst., 22 (1994) 87-95. 

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. 

One of the most used techniques of non-hierarchical cluster analysis is the density method (potential method). The high density of objects in the m-dimension that characterizes clusters is estimated by means of a density function (potential function) P. For this, the objects are modelled by Gaus-... 

Figure 20.13 Unsupervised hierarchical cluster analysis of nine FFPE leiomyomas from 1990-2002 and one FFPE sarcoma from 1980. Reproduced with permission from Reference 22.

Unsupervised hierarchical cluster analysis showed clear separation between the sarcoma and the leiomyomas but did not reveal associations among the leiomyomas based on storage time, possibly indicating that individual differences exceeded any differences caused by storage (Fig. 20.13). 

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... 

FIGURE 3.24 Dendrogram of fatty acid concentration data from mummies and reference samples. Hierarchical cluster analysis (complete linkage) with Euclidean distances has been applied. 

FIGURE 3.28 Dendrogram resulting from hierarchical cluster analysis of the nri i... 

Hierarchical cluster analysis (Section 6.4)—with the result represented by a dendrogram—is a complementary, nonlinear, and widely used method for cluster analysis. The distance measure used was dTANi (Equation 6.5), and the cluster mode was average linkage. The dendrogram in Figure 6.6 (without the chemical structures) was obtained from the descriptor matrix X by... 

FIGURE 6.6 Dendrogram from hierarchical cluster analysis (average linkage) of n = 20 standard amino acids. Distance measure used was dTANi (Equation 6.5) calculated from eight binary substructure descriptors. Four structure pairs with identical descriptors merge at a distance of zero. Clustering widely corresponds to the chemist s point of view. 

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). 

Schuster et al. reported work on monitoring a complex ace-tone-butanol-ethanol (ABE) fermentation system.22 They looked at the qualitative nature of the biomass as well as the solvents present in the liquid phase. A hierarchical cluster analysis was performed on samples from various times of the fermentation. The clusters were then classified using classical markers and analyses. The resultant table, combining qualitative interpretation and quantitative results, shows an interesting mosaic of the system over time. Total solvents, optical density, and butyric acid are given as numeric values in either absorbance units of g/1. 

A number of chemometric tools have been employed for these classifications, including partial least squares - hierarchical cluster analysis (PLS-HCA) for Viagra tablets [98] and antimalarial artesunate tablets [99]. de Peinder et al. used partial least squares discriminant analysis (PLS-DA) models to distinguish genuine from counterfeit Lipitor tablets even when the real API was present [100]. The counterfeit samples also were found to have poorer API distribution than the genuine ones based on spectra collected in a cross pattern on the tablet. 

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.

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