Universal Consistency and Robustness of Localized Support Vector Machines

This paper analyses properties of localized kernel based, nonparametric statistical machine learning methods, in particular of support vector machines (SVMs) and methods close to them. Caused by the enormous research activities there is abundance of general introductions to this field of computer science and statistics. Beside many publications in international journals there are summarizing textbooks like for example Cristianini & Shawe-Taylor (2000), Schölkopf & Smola (2001), Steinwart & Christmann (2008) or Cucker & Zhou (2007) from a mathematical or statistical point of view. Nevertheless, we want to give a short overview over the analyzed topic. Support vector machines were initially introduced by Boser, Guyon & Vapnik (1992) und Cortes & Vapnik (1995), based on earlier work like the Russian original of Vapnik, Chervonenkis & Červonenkis (1979).