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A simple algorithm for approximation by nomographic functions

 
: Limmer, S.; Mohammadi, J.; Stanczak, S.

:

Nedich, A.:
53rd Annual Allerton Conference on Communication, Control, and Computing 2015 : September 29-October 2, 2015
Piscataway, NJ: IEEE, 2015
ISBN: 978-1-5090-1824-6 (electronic)
ISBN: 978-1-5090-1823-9 (USB)
ISBN: 978-1-5090-1825-3 (Print on Demand)
S.453-458
Annual Allerton Conference on Communication, Control, and Computing <53, 2015, Monticello/Ill.>
Englisch
Konferenzbeitrag
Fraunhofer HHI ()

Abstract
This paper introduces a novel algorithmic solution for the approximation of a given continuous multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate continuous inner functions. We show that a suitable approximation can be obtained by solving a cone-constrained Rayleigh-Quotient optimization problem. The proposed approach is based on a combination of a dimensionwise function decomposition known as Analysis of Variance (ANOVA) and optimization over a class of monotone polynomials. An example is given to show that the proposed algorithm can be applied to solve problems in distributed function computation over multiple-access channels.

: http://publica.fraunhofer.de/dokumente/N-422380.html