HITZER, Eckhard    Senior Associate Professor    Division of Arts and Sciences, College of Liberal Arts, International Christian University
Language	English
Publication Date	2008
Type	Research Paper (International Conference Proceedings)
Peer Review	With peer review
Title	Coordinate independent update formulas for versor Clifford neurons
Contribution Type	Joint Work
Journal	Proc. Joint 4th Int. Conf. on Soft Comp. and Intel. Sys., and 9th Int. Symp. on Adv. Intel. Sys.
Journal Type	Japan
Volume, Issue, Pages	pp.814-819
Author and coauthor	S. Buchholz, HITZER Eckhard, K. Tachibana
Details	We study the optimization of neural networks with Clifford geometric algebra versor and spinor nodes. For that purpose important multivector calculus results are introduced. Such nodes are generalizations of real, complex and quaternion spinor nodes. In particular we consider nodes that can learn all proper and improper Euclidean transformations with so-called conformal versors. Thus a single node can correctly compute full 3D screws and rotoinversions with off-origin axis and offorigin points of inversion. The latter is a unique property of our proposed versor neuron. Computing inversions by ordinary real-valued networks is not easily possible due to its nonlinear nature. Simulation on learning inversions illustrating these facts are provided in the paper.