Global and Local Rejection Option in Multi–classification Task Marcin Luckner Warsaw University of Technology, Faculty of Mathematics and Information Science, Koszykowa 75, 00–662 Warszawa, Poland mluckner@mini.pw.edu.pl http://www.mini.pw.edu.pl/ ~ lucknerm/en/ Abstract. This work presents two rejection options. The global rejec- tion option separates the foreign observations – not defined in the classi- fication task – from the normal observations. The local rejection option works after the classification process and separates observations indi- vidually for each class. We present implementation of both methods for binary classifiers grouped in a graph structure (tree or directed acyclic graph). Next, we prove that the quality of rejection is identical for both options and depends only on the quality of binary classifiers. The meth- ods are compared on the handwritten digits recognition task. The local rejection option works better for the most part. Keywords: Rejection Option, Support Vector Machines, Graph Ensem- ble, Pattern Recognition 1 Introduction Pattern recognition tasks very often omit the aspect of rejection of foreign ob- servations. The foreign observations do not belong to the normal classes, where the normal classes are defined by the classification task. The examples of foreign elements in the recognition of printed texts are: blots, fragments of damaged symbols, or symbols omitted in the definition of the classification task. The multi–classification task is described by the classification function φ α (x, n  i=1 L i )= i, (1) where i is decision that classifies the observation x to one of the n normal classes C i described by the learning sets L i using a classification method defined by the coefficient α. Theoretically, the rejection option can be implemented by extending the clas- sification function by an additional class. However, we have an intuition that the class of foreign observations may be significantly different from the normal classes.