Research Seminar - February 22, 2001

Abstract

Clifford algebra is well known in mathematics. It has been applied in physics for several decades. Recently it has been identified as extraordinarily useful also in engineering and computer science. Its advantage lies in modelling rich subspace structures of vector spaces from which follows linear access to higher order and multidimensional phenomena.

It will be shown how Clifford algebra extends the neural computing paradigm. Using that frame for computing endows the neural net with constraints and thus results in knowledge based net design. These constraints follow from the Clifford groups related to the chosen algebra. They constitute a bias for learning and thus, result in better generalization and less complexity of learning geometric transformations. We will demonstrate the principles and performance in case of multilayer perceptron. But the principle is general and not limited to that architecture.