Some Comments on the Application of SVM in Chemistry

As a newly developed method for chemical data processing, SVM has following obvious advantages in comparison with classical chemometrical methods (1) It can treat both linear and nonlinear data sets so the trouble of underfitting can be depressed or controlled in some problems (2) It is so designed that the overfitting can be depressed or controlled by the capacity control of the indicator functions used so that the prediction results are often more reliable (3) As compared with ANN, SVM has no local minimum problem and the solution is unique. As 

On the other hand, we should not forget that every new method or theory has its limitations. Although the strict system of statistical learning theory has been established on the basis of more than 30 years research work of Vapnik and others, the practical calculation of VC dimension is still not successful for many indicator functions and machine learning methods (for example, the estimation of the VC dimension of early stopping ANN is still not successful). 

Before the end of this chapter, we wish to emphasize that the different methods of data processing have different fields of applications. They are not competitive, but complementary to each other. The application of SVM does not mean that the traditional methods are useless. On the contrary, the traditional methods and SVM should be considered as mutually complementary to each other, since many traditional methods also have their advantages as compared with SVM. For example, the traditional methods, including PCA, PLS and Fisher methods can give many linear projection figures. These figures contain plentiful information. Domain experts, including chemists and chemical 

At last, it should be emphasized that the results of SVC or SVR obtained by using normalized data sets are usually better than that without normalization in data processing. In this book, all mathematical models are expressed by normalized data sets. 

In this chapter, we will give a comprehensive introduction to support vector machine (SVM) in an accessible and self-contained way. The organization of this chapter is as follows We start from the central concepts about margin, from which the support vector methods are developed Second, the SVM for classification problems are introduced and the derivation in both linear and nonlinear cases will be described in detail Third, we discuss the support vector regression, i.e. the SVM in regression problems. At last, a variant of SVM, v-SVM is briefly introduced. 

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