Accessing the null space with nonlinear multilayer neural networks

Shelly D. D. Goggin; Karl E. Gustafson; Kristina M. Johnson

doi:10.1117/12.140097

1 July 1992 Accessing the null space with nonlinear multilayer neural networks

Shelly D. D. Goggin, Karl E. Gustafson, Kristina M. Johnson

Proceedings Volume 1710, Science of Artificial Neural Networks; (1992) https://doi.org/10.1117/12.140097
Event: Aerospace Sensing, 1992, Orlando, FL, United States

Abstract

Nonlinear multilayer neural networks have been successful in solving problems in object recognition and decision making, which cannot be solved with nonlinear decision functions. These problems require the construction of a one-to-one or many-to-one mapping of input vectors to output vectors. If a finite training set is used, this mapping is a transformation between the set of values for the input elements to the set of values for the output elements. If the set of values for the input elements lies in the same subspace as the set of values for the output vectors, then a linear transformation can be made. Otherwise, either a neural network or some other nonlinear function is needed to construct the transformation. Nonlinear decision functions can make the transformation to sets of values for the output elements that are in a different subspace, but not an arbitrary subspace. The nonlinear multilayer neural network can make any transformation between sets of values of input elements and output elements, if enough hidden units are available. An explanation for the neural network's power to access any space, including the null space, is presented, along with some examples of the applicability of this result.

Citation Download Citation

Shelly D. D. Goggin, Karl E. Gustafson, and Kristina M. Johnson "Accessing the null space with nonlinear multilayer neural networks", Proc. SPIE 1710, Science of Artificial Neural Networks, (1 July 1992); https://doi.org/10.1117/12.140097

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available