Abstract
In this paper a special higher order neuron, the hypersphere neuron, is introduced. By embedding Euclidean space in a conformal space, hyperspheres can be expressed as vectors. The scalar product of points and spheres in conformal space, gives a measure for how far a point lies inside or outside a hypersphere. It will be shown that a hypersphere neuron may be implemented as a perceptron with two bias inputs. By using hyperspheres instead of hyperplanes as decision surfaces, a reduction in computational complexity can be achieved for certain types of problems. This is shown in two experiments using classical test data for neural computing. Furthermore, in this setup, a reliability measure can be associated with data points in a straight forward way.
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Banarer, V., Perwass, C., Sommer, G. (2003). Design of a Multilayered Feed-Forward Neural Network Using Hypersphere Neurons. In: Petkov, N., Westenberg, M.A. (eds) Computer Analysis of Images and Patterns. CAIP 2003. Lecture Notes in Computer Science, vol 2756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45179-2_70
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DOI: https://doi.org/10.1007/978-3-540-45179-2_70
Publisher Name: Springer, Berlin, Heidelberg
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