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2016 | OriginalPaper | Chapter

10. Mathematical Remarks for Neural Networks

Authors: Rudolf Kruse, Christian Borgelt, Christian Braune, Sanaz Mostaghim, Matthias Steinbrecher

Publisher: Springer London

Published in: Computational Intelligence

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Abstract

The following sections treat mathematical topics that were presupposed in the text (Sect. 10.1 on straight line equations and Sect. 10.2 on regression), or side remarks, which would have disturbed the flow of the exposition (Sect. 10.3 on activation transformation in a Hopfield network).

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Note, however, that this can also be a disadvantage. If the data set contains “outliers” (that is, measurement values that due to random, disproportionally large measurement errors deviate strongly from the true value), the position of the regression line may be influenced heavily by very few measurement points (precisely the outliers), which can lead to an unusable result.

H. Heuser, Lehrbuch der Analysis, Teil 1+2 (Teubner, Stuttgart, Germany, 1988)

Title

Mathematical Remarks for Neural Networks

Book

Computational Intelligence

Print ISBN: 978-1-4471-7294-9

Electronic ISBN: 978-1-4471-7296-3

https://doi.org/10.1007/978-1-4471-7296-3

DOI

https://doi.org/10.1007/978-1-4471-7296-3_10

Authors:

Rudolf Kruse
Christian Borgelt
Christian Braune
Sanaz Mostaghim
Matthias Steinbrecher

Publisher

Springer London

Sequence number

Chapter number

Chapter 10