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Geometrical Aspects of Discrimination by Multilayer Perceptrons

✍ Scribed by Salvatore Ingrassia

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
107 KB
Volume
68
Category
Article
ISSN
0047-259X

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✦ Synopsis

We investigate some geometrical aspects of the discriminant functions of the kind

for suitable constants a k , c k where { is a sigmoidal transformation. This function is realized by a multilayer perceptron with one hidden layer. These results are applied in the analysis of the discriminating power of f p . In particular, we prove that the class of finite populations 0 1 and 0 2 that can be distinguished by f p is monotonically increasing in p and we give a minimal sufficient p leading to a complete separation between 0 1 and 0 2 .

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We thank the EPSRC for support (EP/E030122), the Cardiff Institute of Tissue Engineering and Repair (CITER), and JREI (JR99BAPAEQ) for a 20 processor Compaq SC cluster at the Rutherford Appleton Laboratory.