Name
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. Furthermore, it will be shown that Multi-Layer Percerptrons (MLP) based on such neurons are similar to Radial Basis Function (RBF) networks. It is also found that such MLPs can give better results than RBF networks of the same complexity. The abilities of the proposed MLPs are demonstrated on some classical data for neural computing, as well as on real data from a particular computer vision problem. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1007/978-3-540-45243-0_2 | Lecture Notes in Computer Science |
Keywords | Field | DocType |
euclidean space,radial basis function,scalar product,computer vision,higher order,computational complexity | Topology,Radial basis function network,Embedding,Hypersphere,Euclidean space,Hyperplane,Artificial neural network,Perceptron,Mathematics,Computational complexity theory | Conference |
Volume | ISSN | Citations |
2781 | 0302-9743 | 2 |
PageRank | References | Authors |
0.68 | 7 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Christian Perwass | 1 | 225 | 22.03 |
| Vladimir Banarer | 2 | 17 | 2.22 |
| Gerald Sommer | 3 | 269 | 21.93 |