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Learning Geometric Transformations with Clifford Neurons

By Sven Buchholz and Gerald Sommer

Abstract

. In this paper we propose a new type of neuron developed in the framework of Cliord algebra. It is shown how this novel Cliord neuron covers complex and quaternionic neurons and that it can compute orthogonal transformations very eciently. The introduced framework can also be used for neural computation of non{linear geometric transformations which makes it very promising for applications. As an example we develop a Cliord neuron that computes the cross-ratio via the corresponding M\u7fobius transformation. Experimental results for con- rmation of the proposed novel neural models are presented. 1 Introduction The aim of neural computation is to understand neural and cognitive processes in biological systems, in particular in the human brain, in computational terms and to design and analyze models and algorithms towards these goals. The connectionist approaches among these are known as Neural Networks (NNs). Neural networks are interconnections of articial "neurons" that are greatl..

Year: 2000
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