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- Publications
- Influence

Top 100 relevant results, sorted by most influential

A theory of neural computation with Clifford algebras

- Sven Buchholz
- Computer Science, Mathematics
- 7 July 2006

The present thesis introduces Clifford Algebra as a framework for neural computation. Neural computation with Clifford algebras is model-based. This principle is established by constructing Clifford… Expand

On Clifford neurons and Clifford multi-layer perceptrons

- Sven Buchholz, G. Sommer
- Computer Science, Mathematics
- Neural Networks
- 1 September 2008

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… Expand

Optimal separation of polarized signals by quaternionic neural networks

- Sven Buchholz, N. Bihan
- Computer Science
- 14th European Signal Processing Conference
- 4 September 2006

Statistical description of polarized signals is proposed in terms of proper quaternionic random processes. Within this framework, the intrinsic nature of such signals is captured well. Simulation… Expand

Optimal Learning Rates for Clifford Neurons

- Sven Buchholz, K. Tachibana, Eckhard M. S. Hitzer
- Computer Science
- ICANN
- 9 September 2007

Neural computation in Clifford algebras, which include familiar complex numbers and quaternions as special cases, has recently become an active research field. As always, neurons are the atoms of… Expand

Geometric Neural Networks

- E. Bayro-Corrochano, Sven Buchholz
- Computer Science
- AFPAC
- 8 September 1997

The representation of the external world in biological creatures appears to be defined in terms of geometry. This suggests that researchers should look for suitable mathematical systems with powerful… Expand

On Averaging in Clifford Groups

- Sven Buchholz, G. Sommer
- Computer Science, Mathematics
- IWMM/GIAE
- 19 May 2004

Averaging measured data is an important issue in computer vision and robotics. Integrating the pose of an object measured with multiple cameras into a single mean pose is one such example. In many… Expand

A Multidimensional Approach to Context-Awareness

- Kevin Goslar, Sven Buchholz, A. Schill, H. Vogler
- Computer Science
- 2003

This paper presents multidimensional context-aware principles for Enterprise Applications. The usage of information about the environment of an application, device or its user can enhance the… Expand

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Control of the transmission phase in an asymmetric four-terminal Aharonov-Bohm interferometer

- Sven Buchholz, S. Fischer, U. Kunze, M. Bell, D. Reuter, A. Wieck
- Physics
- 12 May 2010

Phase sensitivity and thermal dephasing in coherent electron transport in quasi-one-dimensional (1D) waveguide rings of an asymmetric four-terminal geometry are studied by magnetotransport… Expand

Polarized Signal Classification by Complex and quaternionic Multi-Layer Perceptrons

- Sven Buchholz, N. Bihan
- Computer Science, Medicine
- Int. J. Neural Syst.
- 1 April 2008

For polarized signals, which arise in many application fields, a statistical framework in terms of quaternionic random processes is proposed. Based on it, the ability of real-, complex- and… Expand

On the decision boundaries of hyperbolic neurons

- T. Nitta, Sven Buchholz
- Computer Science
- IEEE International Joint Conference on Neural…
- 1 June 2008

In this paper, the basic properties, especially decision boundary, of the hyperbolic neurons used in the hyperbolic neural networks are investigated. And also, a non-split hyperbolic sigmoid… Expand