# Polynomial classifier

**Polynomial classifiers** for pattern recognition were developed from statistical decision theory and have the key function in text recognition (OCR), a branch of pattern recognition.

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.

## Mathematical definition

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 .

## literature

- J. Schürmann:
*Pattern Classification: A Unified View of Statistical and Neural Approaches*. Wiley & Sons, 1996, ISBN 0471135348 . - H. Niemann:
*Classification of Patterns*. Springer, Berlin 1983, ISBN 3-540-12642-2 . (2nd edition, without publisher, 2003: PDF file; 6.5 MB ).