Learning Geometric Transformations with Clifford Neurons

In this paper we propose a new type of neuron developed in the framework of Clifford algebra. It is shown how this novel Clifford neuron covers complex and quaternionic neurons and that it can compute orthogonal transformations very efficiently. 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 Clifford neuron that computes the cross-ratio via the corresponding Möbius transformation. Experimental results for the proposed novel neural models are reported