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Objects xi X Data structures for modelling: a relationship between two variables x and y for a set of objects, i. Techniques that allow us to work with such data structures are extremely important topics in chemometrics.
However, we do not share the tendency of some chemometricians to consider this as the only topic of importance.
The modelling element can be important without being explicit. This is the case with the neural networks of Chapter One of its main uses is to model complex phenomena. Very good results can be obtained, but the model as such is usually not derived. Modelling and hypothesis testing are related. In many cases they are either alternatives or complementary. When such a technique is applied, the question will be: how does the result or response depend on pH?
When simplifying both questions, one eventually is led to ask: does the pH influence the result or response? It is, therefore, not surprising that the same question can be treated both with hypothesis tests and modelling approaches, as will be the case in Chapters 13 on method validation and Chapter 22 on two-level factorial designs. The data structures are shown in Figs. Chapters 30 and 33 are devoted entirely to this aspect and it is an important topic in Chapter Basically, there are three types of question: - Can the objects be classified into certain classes see also Fig.
The classes are not known a priori. This is called unsupervised pattern recognition or learning or also clustering; it is discussed in Chapter The Kohonen and fuzzy adaptive resonance theory networks of Chapter 43 have the same purpose. This is called supervised pattern recognition or discriminant analysis and is described in Chapter Most of the neural networks described in Chapter 44 can be applied for the same purpose and so can the inductive expert systems of Chapter Data structures for classification: a classification of a set of objects, characterized by several variables, classes not known a priori; b classification of a new object into one of a number of given classes, each class being described by a set of objects for which several variables were measured; c does a new object belong to a given class, described by a set of objects for which several variables were measured?
Additional aspects are discussed in Chapter 16 quality of attributes in relation to classification in one of a few classes and Chapter 19 fuzzy search. We should stress here again the relationship between classification on the one hand and modelling or hypothesis testing on the other. For instance, supervised pattern recognition methods can, in certain cases, be replaced by modelling meth- ods such as PLS see Chapter 33 when the y-variables are class indicator variables e.
This reasoning capacity is gener- ally associated with the concept of intelligence. With the development of numeri- cal methods and computer technology it became possible to extract chemical information from data in a way that had not previously been possible.
Chemomet- ric methods were developed that incorporated and adapted these numerical tech- niques to solve chemical problems. It became clear, however, that numerical chemometric techniques did not replace deductive reasoning, but rather were complementary. Problems that can be solved by numerical techniques, e. However, selection of the best chemical analysis conditions, for example, is a deductive reasoning process and cannot be solved in a straightforward way by mathematical methods.
To increase further the efficiency and power of chemometric methods the deductive reasoning process must be incorporated. This has resulted in the devel- opment of the so-called "expert systems" Chapter These are computer programs which incorporate a small part of the formalized reasoning process of an expert. In the s they were very popular but their performance to solve difficult problems was clearly overestimated.
In the early s there was a dip in their application and development and the phrase "expert system" became almost taboo. Recently, however, they have reappeared under the name of decision support systems, incorporated among others in chemical instruments. In combination with the numerical chemometric methods they can be very useful. The inductive reasoning process learning from examples is implemented in the inductive expert systems see Chapter Neural networks can also be considered as an implementation of the inductive reasoning process Chapter In Chapter 2, we introduce the first elements of statistical process control SPC , and Chapter 7 is entirely devoted to quality control.
Chapters 13 and 14 describe an important element of quality assurance in the laboratory, namely, how to validate measure- ment methods, i. Chapter 14 also describes how to measure proficiency of analytical laboratories. It makes no sense to carry out excellent analysis on samples that are not representative of the product or the process: the statistics of sampling are described in Chapter The treatment of sensory data is described in Chapter Their importance for certain products is evident.
However, sensory characteristics are not easy to 11 measure and require expert statistical and ehemometrical attention. Chapter 40 is devoted to the analysis of signals and their improvement. It is also evident that in many cases the experimental design in Chapters has as its final objective to achieve better quality measurements or products. However, the book is not intended to be an introduction to statistics, and therefore we have not tried to be complete.
In certain cases, where we consider that chemomet- ricians do not need that knowledge, we have provided less material than statistics books usually do. For instcince, we have attached relatively little importance to the description of statistical distributions, and, while we need of course to use degrees of freedom in many calculations, we have not tried to explain the concept, but have restricted ourselves to operational and context-dependent definitions.
Most chapters describe techniques that often can only be applied to data that are continuous and measured on so-called ratio or interval scales lengths, concentra- tions, temperatures, etc. The use of other types of data often requires different techniques or leads to other results.
Chapters 12, 15, 16, 18 and 19 are devoted to such data. Chapter 12 describes how to carry out hypothesis tests and regression on ranked data or on continuous data that violate the common assumption of normal distribution of measurement errors; Chapter 15 describes distributions that are obtained when the data are counts or binary data i.
Chapter 18 describes information theory and how this is used mainly to characterize the performance of qualitative measurements, and Chapter 19 discusses techniques that can be used with fuzzy data.
Figure 1. Mathematically, the columns are vectors and the tables are matrices. It is therefore important to be able to work with vectors and matrices; an introduction is given first in Chapter 9 and a fuller account later in Chapter In the first volume Part A the emphasis is on the classical statistical methods for hypothesis testing and regression and the methods for experimental design.
In the second volume Part B more attention is given to multivariate methods, often based on latent variables, to signal processing and to some of the more recent methods that are considered to belong to the artificial intelligence area.
One can certainly not state that the methods described in Volume I are all simpler, older, or used more generally than those described in Volume For instance, techniques such as non-linear regression using ACE or cubic splines Chapter 11 , robust regression Chapter 12 , fuzzy regression Chapter 19 or genetic algorithms Chapter 27 are certainly not commonplace. However, the general level of mathematics is higher in Part B than in Part A. For that reason certain subjects are discussed twice, once at a more introductory level in Part A, and once at a higher level of abstraction in Part B.
This is the case for matrix algebra Chapters 9 and 29 and principal component analysis Chapters 17 and The roots of chemometrics go back to when Jurs, Kowalski and Isenhour published a series of papers in Analytical Chemistry  on the application of a linear learning machine to classify low resolution mass spectra.
These papers introduced an innovative way of thinking to transform large amounts of analytical data into meaningful information. The incentive for this new kind of research in analytical chemistry was that "for years experimental scientists have filled labora- tory notebooks which often has been disregarded because lack of proper data interpretation techniques" .
How true this statement still is today, more than 25 years later! This new way of thinking was developed further by Wold into what he called "soft modelling"  when he introduced the SIMCA algorithm for model- ling multivariate data.
The common interest of these groups was to take advantage of the increasing calculation power offered by computers to extract information from large data-sets or to solve difficult optimization problems. Dijkstra applied infor- mation theory to compress libraries of mass spectra . Compression was neces- sary to store spectra in the limited computer memory available at that time and to speed up the retrieval process.
At the same time Massart became active in this field. His interest was to optimize the process of developing new chromatographic methods by the application of principles from operations research . These developments coincided with a fundamental discussion about the scientific basis of analytical chemistry. All this coincided with the growing belief of analytical chemists that "some of the newer mathemati- cal methods or theories, such as pattern recognition, information theory, operations research, etc.
Also in other fields outside analytical chemistry, the application of pattern recognition received a great deal of attention. An important area was the study of relationships between chemical structures and their biological activity, e.
It took until June before this research was called "chemometrics". This name was mentioned for the first time by Wold in a paper published in a Swedish journal  on the application of splines to fit data. He christened his group "Forskningsgruppen for Kemometri", an example which would be followed by Kowalski, who named his group the "Laboratory of Chemometrics". The collaboration between Wold and Kowalski resulted in the foundation of the Chemometrics Society in A year later, the society defined chemometrics as follows: "it is the chemical discipline that uses mathematical and statistical meth- ods to design or select optimal measurement procedures and experiments and to provide maximum chemical information by analysing chemical data" .
As one may notice, in this book we have adapted this definition by including a third objective "to obtain knowledge about chemical systems" and we have specified that the chemical information should be "relevant". This book already indicated some of the main directions chemometrics would follow: design of experiments, optimiza- tion and multivariate data analysis.
Two years later, in , three European chemometricians, Kateman, Massart and Smit organized the international "Computers in Analytical Chemistry CAC " conference in Amsterdam the first of what was to be a long series. On this occasion more than analytical chemists from all over the world gathered to hear about a new and exciting discipline. After the first book on chemometrics was published by the ACS, other textbooks rapidly followed in by Massart et al.
Other, no less important, textbooks are mentioned in the suggested reading list. Wold and coworkers in , based on the early work of H. Wold . This was a formal recognition of the appearance of a new discipline in analytical chemistry, which was emphasized by the special attention on chemometrics at a symposium organized on the occasion of the celebration of the 50th anniversary of Analytical Chemistry .
Since , the field of research expanded rapidly and several new centres in Europe and the USA emerged which became actively involved in chemometrics. Norway, Italy and Spain, for instance, are three of the centres of chemometrics in Europe. In two teams became active in chemometrics in Italy, those of Forina in Genova and of Clementi in Perugia. Around this time, other chemists began to pay more attention to the statistical side of analytical chemistry, such as Dondi in Ferrara.
Elsevier - Handbook of Qualimetrics Part A.pdf
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