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[[Pattern recognition]] is a very active field of research intimately bound to [[machine learning]]. Also known as classification or [[statistical classification]], pattern recognition aims at building a [[classifier (mathematics)|classifier]] that can determine the class of an input pattern. This procedure, known as training, corresponds to learning an unknown decision function based only on a set of input-output pairs <math>(\boldsymbol{x}_i,y_i)</math> that form the training data (or training set). Nonetheless, in real world applications such as [[character recognition]], a certain amount of information on the problem is usually known beforehand. The incorporation of this prior knowledge into the training is the key element that will allow an increase of performance in many applications.
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Prior knowledge<ref>B. Scholkopf and A. Smola, "Learning with Kernels", MIT Press 2002.</ref> refers to all information about the problem available in addition to the training data. However, in this most general form, determining a [[Model (abstract)|model]] from a finite set of samples without prior knowledge is an [[ill-posed]] problem, in the sense that a unique model may not exist. Many classifiers incorporate the general smoothness assumption that a test pattern similar to one of the training samples tends to be assigned to the same class.
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