The hypersphere neuron

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. Furthermore, in this setup, a reliability measure can be associated with data points in a straight forward way.

• Type: Conference
• Year: 2003
• Where: ESANN
• Authors: Vladimir Banarer, Christian Perwass, Gerald Sommer
• Keywords: Conformal Space, ESANN 2003, ESANN 2007, Euclidean Space, Hypersphere Neuron