Support Vector Machines: Review and Applications in Civil Engineering Yonas B. Dibike, Slavco Velickov and Dimitri Solomatine International Institute for Infrastructural, Hydraulic, and Environmental Engineering, P.O. Box 3015, 2601 DA Delft, The Netherlands, email-ybd@ihe.nl Abstract: The subject of Support Vector Machines (SVM) covers emerging techniques which have proven successful in many traditionally neural network (NN)-dominated applications. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimisation (SRM) induction principle that aims at minimising a bound on the generalisation error of a model, rather than minimising the mean square error over the data set. In this paper, the basic ideas underlying SVM are reviewed and the potential of this method for feature classification and multiple regression (modelling) problems is demonstrated using digital remote sensing data and data on the horizontal force exerted by dynamic waves on a vertical structure, respectively. The relative performance of the SVM is then analysed by comparing its results with the corresponding results obtained in previous studies where NNs have been applied on the same data sets. 1 Introduction The problem of empirical data modelling is pertinent to many engineering applications. In empirical data modelling a process of induction is used to build up a model of the system, from which it is hoped to deduce responses of the system that have yet to be observed. Ultimately the quantity and quality of the observations govern the performance of this model. In most cases, data is finite and sampled and, typically, sampling is non-uniform and, due to the high-dimensional nature of the problem, the data forms only a sparse distribution in the input space. The foundation of the subject of Support Vector Machines (SVM) has been developed principally by Vapnik (Vapnik [13] & [15]) and the corresponding SV devices are gaining popularity due to their many attractive features and promising empirical performance. They can generally be thought as constituting an alternative training technique for Multi-Layer Perceptron and Radial Basis Function classifiers, in which the weights of the network are found by solving a Quadratic Programming (QP) problem with linear inequality and equality constraints, rather than by solving a non-convex, unconstrained minimisation problem, as in standard neural network training techniques (Osuna, et al,[7]) Their formulation embodies the Structural Risk Minimisation (SRM) principle, which has been shown to be superior to the more traditional Empirical Risk Minimisation (ERM) principle employed by many of the other modelling techniques (Osuna, et al,[7], Gunn[3]). SRM minimises an upper bound on the expected risk, as opposed to the ERM, which minimises the error on the training data. It is this difference that provides SVM with a greater ability to generalise, which is the goal in statistical learning. SVMs were first developed to solve the classification problem, but recently they have been extended to the domain of regression problems and it has been shown that this approach can find more general solutions than the maximum likelihood-based least square method (Vapnik[15]). Proc. of the 2 nd Joint Workshop on Application of AI in Civil Engineering March 2000, Cottbus, Germany