Principal components analysis hierarchical

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. 

Cluster analysis is far from an automatic technique each stage of the process requires many decisions and therefore close supervision by the analyst. It is imperative that the procedure be as interactive as possible. Therefore, for this study, a menu-driven interactive statistical package was written for PDP-11 and VAX (VMS and UNIX) series computers, which includes adequate computer graphics capabilities. The graphical output includes a variety of histograms and scatter plots based on the raw data or on the results of principal-components analysis or canonical-variates analysis (14). Hierarchical cluster trees are also available. All of the methods mentioned in this study were included as an integral part of the package. 

The compositional data was analyzed by multivariate statistics using 24 well-acquired elements (i.e., measured in all samples), free of contamination and dilution effects. These included Al, Ti, V, Cr, Mn, Fe, Co, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf and Ta. The log-transformed data with various treatments of the raw data, was analyzed by hierarchical cluster analysis, discriminant analysis and principal component analysis. 

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],... 

With a different meaning, the term hierarchical QSAR was also used to denote the application of Partial Least Squares (PLS) and Principal Component Analysis (PGA) to different logical blocks of molecular descriptors to summarize descriptors of each block into a few latent variables or components, which were called supervariables [Eriksson, Johansson et al, 2002]. 

Suzuki, T, Ide, K., Ishida, M. and Shapiro, S. (2001) Classification of environmental estrogens by physico-chemical properties using principal component analysis and hierarchical cluster analysis. /. Chem. Inf. Comput. Sci., 41, 718-726. 

Jun, B.S., Ghosh, T.K., and Loyalka, S.K. (2000) Determination of CHF pattern using principal component analysis and the hierarchical clustering method (critical heat flux in reactors). Proceedings of the American Nuclear Society 2000 Summer Meeting, June 4-8, San Diego, CA. In Trans Am Nucl Soc, 82,250-251 (2000). 

A whole spectrum of statistical techniques have been applied to the analysis of DNA microarray data [26-28]. These include clustering analysis (hierarchical, K-means, self-organizing maps), dimension reduction (singular value decomposition, principal component analysis, multidimensional scaling, or correspondence analysis), and supervised classification (support vector machines, artificial neural networks, discriminant methods, or between-group analysis) methods. More recently, a number of Bayesian and other probabilistic approaches have been employed in the analysis of DNA microarray data [11], Generally, the first phase of microarray data analysis is exploratory data analysis. 

It is also worthwhile using additional exploratory analysis methods. An ordination method such as principal component analysis (PCA) is a complement to hierarchical clustering. 

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