Mathematical pattern-recognition

The actual value of pattern recognition methods in chemistry seems to be uncertain at the moment C47, 3633. The future will show whether mathematical pattern recognition methods are useful only for some specialized problems in chemistry or whether they represent a powerful and advantageous problem solving tool for a variety of data interpretations. Three points will require more attention than in the past to clarify the situation. 

Easy and intuitive data analysis The data analysis process is easy and intuitive, because the pattern recognition only requires the knowledge and intuition of the scientists. DifEcult statistical and mathematical methods are not necessary. 

Throughout the 1970s, appHcations of pattern recognition were found in the chemical sciences. Other methods of multivariate mathematics and statistics were borrowed or invented, and a new discipline called chemometrics arose. In 1974, the Chemometrics Society was formed, and the first Chemometrics newsletter came out in 1976 (12). 

H. C. Andrews, Introduction to Mathematical Techniques in Pattern Recognition, Wiley-Interscience, New York, 1972. 

Many current multidimensional methods are based on instruments that combine measurements of several luminescence variables and present a multiparameter data set. The challenge of analyzing such complex data has stimulated the application of special mathematical methods (80-85) that are made practical only with the aid of computers. It is to be expected that future analytical strategies will rely heavily on computerized pattern recognition methods (79, 86) applied to libraries of standardized multidimensional spectra, a development that will require that published luminescence spectra be routinely corrected for instrumental artifacts. Warner et al, (84) have discussed the multiparameter nature of luminescence measurements in detail and list fourteen different parameters that can be combined in various combinations for simultaneous measurement, thereby maximizing luminescence selectivity with multidimensional measurements. Table II is adapted from their paper with the inclusion of a few additional parameters. 

Mathematically, this means that one needs to assign portions of an 8-dimensionaI space to the three classes. A new sample is then assigned to the class which occupies the portion of space in which the sample is located. Supervised pattern recognition is distinct from unsupervised pattern recognition. In the latter one applies essentially clustering methods (Chapter 30) to classify objects into classes that are not known beforehand. In supervised pattern recognition, one knows the classes and has to decide in which of those an object should be classified. 

When describing mathematical modeling in general (not just for classification of bacteria), it is important to point out the mathematical meaning of pattern recognition the mapping of an n-dimensional function to describe a set of... 

Because of their ability to classify complex data types that have no explicit mathematical model, neural networks have become a powerful and widely used approach to pattern recognition problems in general. A neural network is a series of mathematical operations performed on input data that ultimately... 

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. 

Relevant examples of the use of classification techniques range from the simple to the complex. Schaper et al. (1985) developed and used a very simple classification of response methodology to identify those airborne chemicals which alter the normal respiratory response induced by C02. At the other end of the spectrum, Kowalski and Bender (1972) developed a more mathematically based system to classify chemical data (a methodology they termed pattern recognition). 

In the earlier time of chemometrics until about 1990, a number of books have been published that may be rather of historical interest. Chemometrics—Applications of Mathematics and Statistics to Laboratory Systems (Brereton 1990), Chemical Applications of Pattern Recognition (Jurs and Isenhour 1975), Factor Analysis in... 

A great variety of different methods for multivariate classification (pattern recognition) is available (Table 5.6). The conceptually most simply one is fc-NN classification (Section 5.3.3), which is solely based on the fundamental hypothesis of multivariate data analysis, that the distance between objects is related to the similarity of the objects. fc-NN does not assume any model of the object groups, is nonlinear, applicable to multicategory classification, and mathematically very simple furthermore, the method is very similar to spectral similarity search. On the other hand, an example for a rather sophisticated classification method is the SVM (Section 5.6). 

The mathematical techniques employed in pattern recognition permit rapid and efficient identification of relationships and key aspects that otherwise might remain hidden in the large mass of numbers. Since the data base was not well characterized we set the following objectives for the interpretive study ... 

To a significant extent, the theoretical basis of modern communication theory arose from the work of Claude Shannon at Bell Labs. [80]. In these seminal works, the concept of the information entropy associated with an arbitrary signal arose. In 1981, Watanabe realised the close association between entropy minimization and pattern recognition [81]. An association between entropy minimization and the principle of simplicity is also recognized [82]. The basic mathematical form of signal... 

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