Chemometrics cluster analysis

Fig. 2 Generation of spectroscopic FTIR images, a Native sample, here a thin section of biological tissue, b FTIR spectra are collected at every pixel of the native sample. Bad spectra, e.g. from areas outside the sample, have already been removed, c Good spectra have been subject to a chemometric cluster analysis. Pixels are color-coded according to the cluster membership (spectral staining). Slightest chemical differences across the sample are now clearly revealed...

Calibration-check sample Chemometrics Cluster analysis Control chart Correlation coefficient Dependent variable Duplicates EDA... 

T. Fearn, Flat or natural A note on the choice of calibration samples, pp. 61-66 in Ref. [1]. T. Naes and T. Isaksson, Splitting of calibration data by cluster-analysis. J. Chemometr, 5 (1991)49-65. 

Multivariate chemometric techniques have subsequently broadened the arsenal of tools that can be applied in QSAR. These include, among others. Multivariate ANOVA [9], Simplex optimization (Section 26.2.2), cluster analysis (Chapter 30) and various factor analytic methods such as principal components analysis (Chapter 31), discriminant analysis (Section 33.2.2) and canonical correlation analysis (Section 35.3). An advantage of multivariate methods is that they can be applied in... 

Also, we do not cover several typical chemometrics types of analyses, such as cluster analysis, experimental design, pattern recognition, classification, neural networks, wavelet transforms, qualimetrics etc. This explains our decision not to include the word chemometrics in the title. 

The final methodological chapter (Chapter 6) is devoted to cluster analysis. Besides a general treatment of different clustering approaches, also more specific problems in chemometrics are included, like clustering binary vectors indicating presence or absence of certain substructures. 

Kowalski and Bender presented chemometrics (at this time called pattern recognition and roughly considered as a branch of artificial intelligence) in a broader scope as a general approach to interpret chemical data, especially by mapping multivariate data with the purposes of cluster analysis and classification (Kowalski and Bender 1972). 

A comprehensive two-volume Handbook of Chemometrics and Qualimetrics has been published by D. L. Massart et al. (1997) and B. G. M. Vandeginste et al. (1998) predecessors of this work and historically interesting are Chemometrics A Textbook (Massart et al. 1988), Evaluation and Optimization of Laboratory Methods and Analytical Procedures (Massart et al. 1978), and The Interpretation of Analytical Chemical Data by the Use of Cluster Analysis (Massart and Kaufmann 1983). A classical reference is still Multivariate Calibration (Martens and Naes 1989). A dictionary with extensive explanations containing about 1700 entries is The Data Analysis Handbook (Frank and Todeschini 1994). 

In most applications chemometric methods are applied to analytical data in an off-line mode that is, data has already been obtained by conventional techniques and is then applied to a particular chemometric method. Examples of this use are in cluster analysis and in pattern recognition. They are applied to spectroscopic, chromatographic, and other analytical data. 

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. 

Principal component analysis is a popular statistical method that tries to explain the covariance structure of data by means of a small number of components. These components are linear combinations of the original variables, and often allow for an interpretation and a better understanding of the different sources of variation. Because PCA is concerned with data reduction, it is widely used for the analysis of high-dimensional data, which are frequently encountered in chemometrics. PCA is then often the first step of the data analysis, followed by classification, cluster analysis, or other multivariate techniques [44], It is thus important to find those principal components that contain most of the information. 

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],... 

Chemometrics is a branch of science and technology dealing with the extraction of useful information from multidimensional measurement data using statistics and mathematics. It is applied in numerous scientific disciplines, including the analysis of food [313-315]. The most common techniques applied to multidimensional analysis include principal components analysis (PCA), factor analysis (FA), linear discriminant analysis (LDA), canonical discriminant function analysis (DA), cluster analysis (CA) and artificial neurone networks (ANN). 

Chemometric methods such as analysis of correlation coefficients, cluster analysis or neural network analysis are used, for example, in the classification of fragments of glass on the basis of their elemental composition or refractive index. Such methods allow the test material to be classified into the appropriate group of products on the basis of the measured parameter. 

T Naes and T Isaksson. Splitting of calibration data by cluster analysis. J. Chemometrics, 5 49-65, 1991. 

To establish a correlation between the concentrations of different kinds of nucleosides in a complex metabolic system and normal or abnormal states of human bodies, computer-aided pattern recognition methods are required (15, 16). Different kinds of pattern recognition methods based on multivariate data analysis such as principal component analysis (PCA) (8), partial least squares (16), stepwise discriminant analysis, and canonical discriminant analysis (10, 11) have been reported. Linear discriminant analysis (17, 18) and cluster analysis were also investigated (19,20). Artificial neural network (ANN) is a branch of chemometrics that resolves regression or classification problems. The applications of ANN in separation science and chemistry have been reported widely (21-23). For pattern recognition analysis in clinical study, ANN was also proven to be a promising method (8). 

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