Multivariate data definitions

Despite the broad definition of chemometrics, the most important part of it is the application of multivariate data analysis to chemistry-relevant data. Chemistry deals with compounds, their properties, and their transformations into other compounds. Major tasks of chemists are the analysis of complex mixtures, the synthesis of compounds with desired properties, and the construction and operation of chemical technological plants. However, chemical/physical systems of practical interest are often very complicated and cannot be described sufficiently by theory. Actually, a typical chemometrics approach is not based on first principles—that means scientific laws and mles of nature—but is data driven. Multivariate statistical data analysis is a powerful tool for analyzing and structuring data sets that have been obtained from such systems, and for making empirical mathematical models that are for instance capable to predict the values of important properties not directly measurable (Figure 1.1). 

A fundamental idea in multivariate data analysis is to regard the distance between objects in the variable space as a measure of the similarity of the objects. Distance and similarity are inverse a large distance means a low similarity. Two objects are considered to belong to the same category or to have similar properties if their distance is small. The distance between objects depends on the selected distance definition, the used variables, and on the scaling of the variables. Distance measurements in high-dimensional space are extensions of distance measures in two dimensions (Table 2.3). 

The simplest multivariate data set is a data set consisting of measurements (or calculated properties) of J variables on I objects. Such a data set can be arranged in an / x. / matrix X. This matrix X contains variation which is supposed to be relevant for the (chemical) problem at hand. Several types of methods are available to investigate this variation depending on the purpose of the research and the problem definition. 

Figure 13. Multivariate data processing techniques employed by electronic noses. See reference [2] for definition of acronyms.

Process analyzer measurements, e.g., spectra or chemical images, typically require a mathematical transformation, e.g., multivariate data analysis, to correlate the process analytical data to a more relevant critical product attribute for design space definition. For brevity, throughout this section the measurement system that yields process analytical data is noted as a PAT method and the subsequent mathematical transformation is described as a model. To forego a debate regarding what constitutes a process analyzer, i.e., temperature sensor versus a Raman fiber optic probe, herein focuses on process analyzers that yield multivariate data. 

The acronym NIRA, or near-infrared analysis, is a term that implies the use of computer algorithms and multivariate data-handling techniques to provide either qualitative or quantitative analysis of a sample (or samples). NIRS includes a single spectral measurement and as such is a more generic definition. For example, an optical engineer involved in the design of a MR instrument would be involved with NIRS but not necessarily NIRA. 

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 . 

Data quality is a broad, often loosely defined term. There are many problem- and discipline-related definitions to be found in the literature. This section shall not try to define data quality in any comprehensive, far less complete sense - suffice to denounce any definition that does not include the specific aspect of sample representativity however. Data is often equated with information, but this can only be in a hidden, potential form. Only data analysis together with interpretation may reveal information - which will always be in a particular problem-specific context only. Such issues are not usually seen as problematic in chemometrics and in PAT, where the pre-history of a data table ( data ) in general receives but scant attention. One relevant, major exception is Martens and Martens (2001) [26] who focus comprehensively on Multivariate Analysis of Quality . But even here there is a narrow focus on quality of information only, defined as ... dependent on reliability and relevance , without further clarifying the definition of these open-ended adjectives. 

With this in mind, I ask the reader to accept my humble definition of chemometrics the application of multivariate, empirical modeling methods to chemical data [2]. 

In addition to the discrepancies generated as a result of study definition (univariate discrepancies), discrepancies may also arise when a batch validation detects data inconsistencies (univariate and multivariate discrepancies). Discrepancies are also identified by a visual review of the data, e.g., monitoring lists, SDV review. Discrepancies may also be created by people responsible for data analysis (e.g., statisticians, pharmacoeconomists, clinical pharmacologists). All discrepancies and data fields requiring verification or clarification are tracked using the clinical database. 

The most useful result of multivariate analysis procedures is the reduction in apparent dimensionality of the data. From an initial collection of several hundred mass peaks, the data are reduced to only a few factors, each of which is by definition a linear combination of the original mass peak intensities. By plotting these linear combinations in the form of spectra, significant information about the chemical components underlying the factors can be obtained. Often this requires rotation of the factors in order to optimize the chemical component patterns. 

Figure 6.6 Schematic procedure of a multivariate calibration. Data are taken from the NIR spectroscopic monitoring of the nitration of toluene conducted in microreactors using pure nitric acid as nitrating agent [10]. Note that model optimization is an iterative approach that requires the multiple application of steps (c) and (d). (a) Definition of an experimental design within the investigated parameter space. Here, a central composite plan is presented, (b) Experiments in accordance with the design spectrum generation in a flow-through cell and...

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