Chemometrics, definition

An Introduction to Chemometrics Definitions, can be found at http / /ourworld.compuserve.com/ homepages/Catbar/cheni def.htm 1997 ... 

Many people use the term PRESS to refer to the result of leave-one-out cross-validation. This usage is especially common among the community of statisticians. For this reason, the terms PRESS and cross-validation are sometimes used interchangeably. However, there is nothing inate in the definition of PRESS that need restrict it to a particular set of predictions. As a result, many in the chemometrics community use the term PRESS more generally, applying it to predictions other than just those produced during cross-validation. 

Every scientist has designed experiments. So what is there left for us to say about that topic that chemometrics/statistics can shed some light on Well, quite a bit actually, since not all experiments are designed equally, but some are definitely more equal than others (to steal a paraphrase). Another way to say it is that every experiment is a designed experiment, but some designs are better than others. 

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 . 

This definition is convenient because it allows us to then jump directly to what is arguably the simplest Chemometric technique in use, and consider that as the prototype for all chemometric methods that technique is multiple regression analysis. Written out in matrix notation, multiple regression analysis takes the form of a relatively simple matrix equation ... 

Advanced mathematical and statistical techniques used in analytical chemistry are often referred to under the umbrella term of chemometrics. This is a loose definition, and chemometrics are not readily distinguished from the more rudimentary techniques discussed in the earlier parts of this chapter, except in terms of sophistication. The techniques are applied to the development and assessment of analytical methods as well as to the assessment and interpretation of results. Once the province of the mathematician, the computational powers of the personal computer now make such techniques routinely accessible to analysts. Hence, although it would be inappropriate to consider the detail of the methods in a book at this level, it is nevertheless important to introduce some of the salient features to give an indication of their value. Two important applications in analytical chemistry are in method optimization and pattern recognition of results. 

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). 

All regression methods aim at the minimization of residuals, for instance minimization of the sum of the squared residuals. It is essential to focus on minimal prediction errors for new cases—the test set—but not (only) for the calibration set from which the model has been created. It is relatively easy to create a model— especially with many variables and eventually nonlinear features—that very well fits the calibration data however, it may be useless for new cases. This effect of overfitting is a crucial topic in model creation. Definition of appropriate criteria for the performance of regression models is not trivial. About a dozen different criteria— sometimes under different names—are used in chemometrics, and some others are waiting in the statistical literature for being detected by chemometricians a basic treatment of the criteria and the methods how to estimate them is given in Section 4.2. 

EXMAT - A Linked Network of Expert Systems for Materials Analysis. Seven individual expert systems comprise EXMAT (1) problem definition and analytical strategy (2) instrumental configuration and conditions (3) data generation (4) chemometric/search algorithms (5) results (6) interpretation (7) analytical goals. Dynamic headspace (DHS)/GC and pyrolysis GC (PGC)/concentrators... 

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. 

There are probably as many definitions of chemometrics as there are those who claim to practice it. However, there appear to be three elements that are consistently used in historical applications of... 

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]. 

Before describing the six habits, it is important to define what is meant by the term chemometrics. A general definition is the use of statistical and mathematical techniques to analyze chemical data. In this book, we prefer the broader definition of chemometrics as the entire process whereby data (e.g., numbers in a table) are transformed into information used for decision making. ... 

In 1997, D.L. Massart suggested the following definition "Chemometrics is a chemical discipline that uses mathematics, statistics and formal logic (a) to design or select optimal experimental procedures (b) to provide maximum relevant chemical information by analyzing chemical data and (c) to obtain knowledge about chemical systems" (Massart et ah, 1997). 

As the definition says, a model is a description of a real phenomenon performed by means of mathematical relationships (Box and Draper, 1987). It follows that a model is not the reality itself it is just a simplified representation of reality. Chemometric models, different from the models developed within other chemical disciplines (such as theoretical chemistry and, more generally, physical chemistry), are characterized by an elevated simplicity grade and, for this reason, their validity is often limited to restricted ranges of the whole experimental domain. 

Key words in the definition are optimal and material systems . These express the fact that chemical analysis is related to a problem and not to a sample and that economical aspects of chemical analysis prevail. The result of chemometric research is chemometric software, which enable a large scale implementation and application of chemometric tools in practical chemical analysis. 

The present state of chemometrics and the differing points of view are illustrated by the definition of DANZER [1990] Chemometrics is the linking element between chemistry (not only analytical chemistry), mathematics, and hard- and software . 

Using a definition similar to that of the International Chemometrics Society, chemometrics can therefore be summarized as follows ... 

One possibility is to classify the methods used in the various steps of the analytical process (see also Section 1.5). Note that the analytical process usually starts with the definition or selection of the matter to be investigated. Here it is very important to realize that every sample or object of investigation has a history. Because this history may cause severe systematic errors, THIERS [1957] explains Unless the complete history of any sample is known with certainty, the analyst is well advised not to spend his time in analyzing it. Clearly, in such circumstances one should be extremely cautious about drawing conclusions from chemometric interpretations even where data are available. 

According to its already classical definition, chemometrics is a branch of modem analytical chemistry that involves the application of mathematical, statistical, and other methods employing formal logic... 

Ecotoxicological considerations and the effort to achieve an increasingly accurate description of the state of the environment challenge analytical chemists who need to determine increasingly lower concentrations of various analytes in samples that have complex and even non-homogenous matrices. The newly coined expression "analytics" emphasizes the interdisciplinary nature of available methods for obtaining information about material systems, with many methods that exceed the strict definition of analytical chemistry. Drawing on the disciplines of chemistry, physics, computer science, electronics, material science, and chemometrics, this book provides in depth information on the most important problems in analytics of samples from aquatic ecosystems. 

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