Journal
NEURAL NETWORKS
Volume 21, Issue 7, Pages 925-935Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.neunet.2008.03.004
Keywords
Clifford (geometric) algebra; Clifford neural networks; Clifford neurons; Multi-layer perceptrons; Backpropagation; Function approximation
Funding
- DFG [So-320-2-1, So-320-202]
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We study the framework of Clifford algebra for the design of neural architectures capable of processing different geometric entities. The benefits of this model-based computation over standard real-valued networks are demonstrated. One particular example thereof is the new class of so-called Spinor Clifford neurons. The paper provides a sound theoretical basis to Clifford neural computation. For that purpose the new concepts of isomorphic neurons and isomorphic representations are introduced. A unified training rule for Clifford MLPs is also provided. The topic of activation functions for Clifford MLPs is discussed in detail for all two-dimensional Clifford algebras for the first time. (C) 2008 Elsevier Ltd. All rights reserved.
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