Support vector machines (SVMs) appeared in the early nineties as optimal margin classifiers in the context of Vapnik's statistical learning theory. Since then SVMs have been successfully applied to real-world data analysis problems, often providing improved results compared with other techniques. The SVMs operate within the framework of regularization theory by minimizing an empirical risk in a well-posed and consistent way. A clear advantage of the support vector approach is that sparse solutions to classification and regression problems are usually obtained: only a few samples are involved in the determination of the classification or regression functions. This fact facilitates the application of SVMs to problems that involve a large amount of data, such as text processing and bioinformatics tasks. This paper is intended as an introduction to SVMs and their applications, emphasizing their key features. In addition, some algorithmic extensions and illustrative real-world applications of SVMs are shown.

This paper commented in: [math/0612820], [math/0612821], [math/0612822], [math/0612824]. Rejoinder in [math.ST/0612825]. Published at http://dx.doi.org/10.1214/088342306000000493 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)