Multivariate data analysis purposes

Exploratory data analysis has the aim to learn about the data distribution (clusters, groups of similar objects). In multivariate data analysis, an X-matrix (objects/samples characterized by a set of variables/measurements) is considered. Most used method for this purpose is PCA, which uses latent variables with maximum variance of the scores (Chapter 3). Another approach is cluster analysis (Chapter 6). 

There are many possibilities for pretreatment of the data before the multivariate data analysis, depending on the nature of the data and the purpose of the analysis. 

Generally, two types of questions are asked when applying multivariate data analysis techniques one question aims to explore the gathered data without ary preconceived assumptions or notions, while the second question relates to sample classification and finding valid and powerful models for prediction purposes. 

It is not the purpose of this chapter to provide a detailed explanation and considered comparative argument for the many pre-processing and multivariate data analysis procedures that are used, later chapters in this book and references cited therein provide useful sources to such information the purpose of this section in this chapter was to provide a very brief insight into the uses of the procedures for those unfamiliar with the manner in which mid-IR spectra are used to assign a state of cancer aggressiveness to such as a biopsy or cell sample. 

PCA is by far the most important method in multivariate data analysis and has two main applications (a) visualization of multivariate data by scatter plots as described above (b) data reduction and transformation, especially if features are highly correlating or noise has to be removed. For this purpose instead of the original p variables X a subset of uncorrelated principal component scores U can be used. The number of principal components considered is often determined by applying a threshold for the score variance. For instance, only principal components with a variance greater than 1% of the total variance may be selected, while the others are considered as noise. The number of principal components with a non-negligible variance is a measure for the intrinsic dimensionality of the data. As an example consider a data set with three features. If all object points are situated exactly on a plane, then the intrinsic dimensionality is two. The third principal component in this example has a variance of zero. Therefore two variables (the scores of PCI and PC2) are sufficient for a complete description of the data structure. 

A definition of Chemometrics is a little trickier of come by. The term was originally coined by Kowalski, but nowadays many Chemometricians use the definition by Massart [4], On the other hand, one compilation presents nine different definitions for Chemometrics [5, 6] (including What Chemometricians do , a definition that apparently was suggested only HALF humorously ). But our goal here is not to get into the argument over the definition of the term, so for our current purposes, it is convenient to consider a perhaps somewhat simplified definition of Chemometrics as meaning multivariate methods of data analysis applied to data of chemical interest . 

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). 

Data have been collected since 1970 on the prevalence and levels of various chemicals in human adipose (fat) tissue. These data are stored on a mainframe computer and have undergone routine quality assurance/quality control checks using univariate statistical methods. Upon completion of the development of a new analysis file, multivariate statistical techniques are applied to the data. The purpose of this analysis is to determine the utility of pattern recognition techniques in assessing the quality of the data and its ability to assist in their interpretation. 

Multivariate methods of data analysis were first applied in chromatography for retention prediction purposes [7. More recently, principal component analysis (PCA), correspondence factor analysis (CFA) and spectral mapping analysis (SMA) have been employed to objectively cla.ssify. stationary phase materials according to the retention... 

A data matrix produced by compositional analysis commonly contains 10 or more metric variables (elemental concentrations) determined for an even greater number of observations. The bridge between this multidimensional data matrix and the desired archaeological interpretation is multivariate analysis. The purposes of multivariate analysis are data exploration, hypothesis generation, hypothesis testing, and data reduction. Application of multivariate techniques to data for these purposes entails an assumption that some form of structure exists within the data matrix. The notion of structure is therefore fundamental to compositional investigations. 

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