Quaternion Spiking and Quaternion Quantum Neural Networks: Theory and Applications

Biological evidence shows that there are neural networks specialized for recognition of signals and patterns acting as associative memories. The spiking neural networks are another kind which receive input from a broad range of other brain areas to produce output that selects particular cognitive or motor actions to perform. An important contribution of this work is to consider the geometric processing in the modeling of feed-forward neural networks. Since quaternions are well suited to represent 3D rotations, it is then well justified to extend real-valued neural networks to quaternion-valued neural networks for task of perception and control of robot manipulators. This work presents the quaternion spiking neural networks which are able to control robots, where the examples confirm that these artificial neurons have the capacity to adapt on-line the robot to reach the desired position. Also, we present the quaternionic quantum neural networks for pattern recognition using just one quaternion neuron. In the experimental analysis, we show the excellent performance of both quaternion neural networks.