Geometric preprocessing and neurocomputing for pattern recognition and pose estimation

This paper shows the analysis and design of feed-forward neural networks using the coordinate-free system of Clifford or geometric algebra. It is shown that real-, complex- and quaternion-valued neural networks are simply particular cases of the geometric algebra multidimensional neural networks and that they can be generated using Support Multi-Vector Machines. Particularly, the generation of RBF for neurocomputing in geometric algebra is easier using the SMVM that allows to find the optimal parameters automatically. The use of SVM in the geometric algebra framework expands its sphere of applicability for multidimensional learning.

We introduce a novel method of geometric preprocessing utilizing hypercomplex or Clifford moments. This method is applied together with geometric MLPs for tasks of 2D pattern recognition. Interesting examples of non-linear problems like the grasping of an object along a non-linear curve and the 3D pose recognition show the effect of the use of adequate Clifford or geometric algebras that alleviate the training of neural networks and that of Support Multi-Vector Machines.