Geometric Algebra Based Neural Networks
In the last period there were introduced some new types of neural networks based on a more general type of algebra. They obey the multidimensional neural activities compared to the one-dimensional neural activity within the standard neural network framework. Instead of using basically the product of two scalar values they utilise some special algebraic product of two multidimensional quantities. Most of them can be considered as a special type of geometric (Clifford) algebra ,  based neural networks (GANNs).
KeywordsOutput Neuron Geometric Algebra Input Element Geometric Product Geometric Multiplication
Unable to display preview. Download preview PDF.
- Arena P., Fortuna L., Re R., and Xibilia MG. On the capability of neural networks with complex neurons in complex-valued function approximation. In Proceedings IEEE International Conference on Circuit and Systems, pages 2168–2171, Chicago, 1993.Google Scholar
- Benvenuto N., Marchesi M., Piazza F., and Uncini A. A comparison between real and complex-valued neural networks in communication applications. In Kohonen et al., editor, Artificial Neural Networks, pages 1177–1180. Elsevier Science Publishers B.V. ( North-Holland ), 1991.Google Scholar
- Arena P., Fortuna L., Muscato G., and Xibilia MG. Multilayer perceptrons to approximate quaternion-valued functions. Neural Networks, 9(6): 1–8, 6 1996.Google Scholar
- Masters T. Signal and Image Processing with Neural Networks: a C++ Sourcebook. John Wiley Sons, 1994.Google Scholar
- Blow Th. and Sommer G. Real multidimensional fourier transform. In SCIA ‘87, 1997. submitted.Google Scholar
- Chudÿ L. and Chudÿ V. Why complex-valued neural networks? (on the possible role of geometric algebra framework for the neural network computation). In Proceedings of IEEE Workshop on Computer-Intensive Methods in Control and Dignal Processing, pages 109–114, Prague, 1996.Google Scholar
- Kalman BL. and Kwasny SC. Why tanh? choosing a sigmoidal function. In Proceedings of Int. Joint Conference on Neural Networks, Baltimore, MD, 1991.Google Scholar
- Friedman JH. An overwiev of predictive learning and function approximation. In V. Cherkassky, J. Friedman, and H. Wechsler, editors, From statistics to neural networks., NATO ASI Series, pages 1–62. Springer-Verlag, 1994.Google Scholar
- Hertz J. and Krogh A. Palmer RG. Introduction to the theory of neural computation. Addison-Wesley, 1991.Google Scholar