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What is Chemometrics?

Learning Objectives

• To define chemometrics
• To learn how to count with bits and how to perform arithmetic or logical operations in a computer
• To understand the principal terminology for computer systems and the meaning of robotics and automation.

The development of the discipline of chemometrics is strongly related to the use of computers in chemistry. Some analytical groups in the 1970s were already working with statistical and mathematical methods that are ascribed nowadays to chemometric methods. Those early investigations were connected to the use of mainframe computers.

The notation chemometrics was introduced in 1972 by the Swede Svante Wold and the American Bruce R. Kowalski. The foundation of the International Chemometrics Society in 1974 led to the first description of this discipline. In the following years, several conference series were organized, for example, Computer Application in Analytics (COMPANA), Computer-Based Analytical Chemistry (COBAC), and Chemometrics in Analytical Chemistry (CAC). Some journals devoted special sections to papers on chemometrics. Later, novel chemometric journals were started, such as the Journal of Chemometrics (Wiley) and Chemometrics and Intelligent Laboratory Systems (Elsevier).

An actual definition of chemometrics is:

the chemical discipline that uses mathematical and statistical methods, (a) to design or select optimal measurement procedures and experiments, and (b) to provide maximum chemical information by analyzing chemical data.

The discipline of chemometrics originates in chemistry. Typical applications of chemometric methods are the development of quantitative structure-activity relationships and the evaluation of analytical-chemical data. The data flood generated by modern analytical instrumentation is one reason that analytical chemists, in particular, develop applications of chemometric methods. Chemometric methods in analytics are a discipline that uses mathematical and statistical methods to obtain relevant information on material systems.

With the availability of personal computers at the beginning of the 1980s, a new age commenced for the acquisition, processing, and interpretation of chemical data. In fact, today, every scientist uses software, in one form or another, that is related to mathematical methods or processing of knowledge. As a consequence, the necessity emerges for a deeper understanding of those methods.

The education of chemists in mathematics and statistics is usually unsatisfactory. Therefore, one of the initial aims of chemometrics was to make complicated mathematical methods practicable. Meanwhile, the commercialized statistical and numerical software simplifies this process, so that all important chemometric methods can be taught in appropriate computer demonstrations.

Apart from the statistical-mathematical methods, the topics of chemometrics are also related to problems of the computer-based laboratory, to methods for handling chemical or spectroscopic databases, and to methods of artificial intelligence.

In addition, chemometricians contribute to the development of all these methods. As a rule, these developments are dedicated to particular practical requirements, such as the automatic optimization of chromatographic separations or in prediction of the biological activity of a chemical compound.

1.1 The Computer-Based Laboratory

Nowadays, the computer is an indispensable tool in research and development. The computer is linked to analytical instrumentation; it serves as a tool for acquiring data, word processing, and handling databases and quality assurance systems. In addition, the computer is the basis for modern communication techniques such as electronic mails or video conferences. In order to understand the important principles of computer usage, some fundamentals are considered here, that is, coding and processing of digital information, the main components of the computer, programming languages, computer networking, and automation processes.

Analog and Digital Data

The use of digital data provides several advantages over the use of analog data. Digital data are less noise sensitive. The only noise arises from round-off errors due to finite representation of the digits of a number. They are less prone to, for instance, electrical interferences, and they are compatible with digital computers.

As a rule, primary data are generated as analog signals either in a discrete or a continuous mode (Figure 1.1). For example, monitoring the intensity of optical radiation by means of a photocell provides a continuous signal. Weak radiation, however, could be monitored by detecting individual photons with a photomultiplier.

Figure 1.1 Signal dependence on time of an analog (a) and a digital detector (b).

Usually, the analog signals generated are converted into digital data by an analog-to-digital converter (ADC) as explained as follows:

Binary versus Decimal Number System

In a digital measurement, the number of pulses occurring within a specified set of boundary conditions is counted. The easiest way to count is to have the pulses represented as binary numbers. In this way, only two electronic states are required. To represent the decimal numbers from 0 to 9, one would need 10 different states. Typically, the binary numbers 0 and 1 are represented electronically by voltage signals of 0.5 and 5 V, respectively. Binary numbers characterize coefficients of the power of 2, so that any number in the decimal system can be described.

Example 1.1 Binary Number Representation

The decimal number 77 is expressed as binary number by 1001101, that is,

Table 1.1 summarizes further relationships between binary and decimal numbers. Every binary number is composed of individual bits (binary digits). The digit lying farthest to the right is termed the least significant digit, and the one on the left is the most significant digit.

Table 1.1 Relationship between binary and decimal numbers.

How are calculations done using binary numbers? Arithmetic operations are similar but simpler than those for decimal numbers. In addition, for example, four combinations are feasible:

Note that for the addition of the binary numbers 1 plus 1, a 1 is carried over to the next higher power of 2.

Example 1.2 Calculation with Binary Numbers

Consider the addition of 21 + 5 in the case of a decimal (a) and of a binary number (b):

Apart from arithmetic operations in the computer, logical reasoning is necessary too. This might be in the course of an algorithm or in connection with an expert system. Logical operations with binary numbers are summarized in Table 1.2.

Table 1.2 Truth values for logical connectives of predicates p and q based on binary numbers.