Their main advantage lies in the possibility of solving the adaptation task directly. Building on this basic technology , complex and high-performance classifier structures (trees, networks) were developed, which were able to demonstrate their performance in very different fields of application, for example for address readers, postal automation or form readers.
A polynomial classifier is a mapping of vectors from the -dimensional real feature space onto a set of classes:
It is defined as the most significant component of the following vector
The multivariate polynomials can be interpreted as probability functions that a given feature vector belongs to the class . Overall, the following applies .
The above notation can be simplified by calculating only one polynomial instead of many polynomials . Then it holds with a real-valued coefficient vector. Overall follows .
A new feature vector is thus classified by .
J. Schürmann: Pattern Classification: A Unified View of Statistical and Neural Approaches . Wiley & Sons, 1996, ISBN 0471135348 .