DocumentCode :
1241395
Title :
Generalization of hinging hyperplanes
Author :
Wang, Shuning ; Sun, Xusheng
Author_Institution :
Dept. of Autom., Tsinghua Univ., Beijing, China
Volume :
51
Issue :
12
fYear :
2005
Firstpage :
4425
Lastpage :
4431
Abstract :
The model of hinging hyperplanes (HH) can approximate a large class of nonlinear functions to arbitrary precision, but represent only a small part of continuous piecewise-linear (CPWL) functions in two or more dimensions. In this correspondence, the influence of this drawback for black-box modeling is first illustrated by a simple example. Then it is shown that the above shortcoming can be amended by adding a sufficient number of linear functions to current hinges. It is proven that any CPWL function of n variables can be represented by a sum of hinges containing at most n+1 linear functions. Hence the model of a sum of such expanded hinges is a general representation for all CPWL functions. The structure of the novel general representation is much simpler than the existing generalized canonical representation that consists of nested absolute-value functions. This characteristic is very useful for black-box modeling. Based on the new general representation, an upper bound on the number of nestings of nested absolute-value functions of a generalized canonical representation is established, which is much smaller than the known result.
Keywords :
approximation theory; computational geometry; identification; nonlinear functions; piecewise linear techniques; CPWL; HH model approximation; arbitrary precision; black-box modeling; continuous piece wise-linear function; generalized canonical representation; hinging hyperplane; nested absolute-value function; nonlinear function; Channel capacity; Decoding; Digital modulation; Fasteners; Function approximation; Information theory; Piecewise linear techniques; Rate distortion theory; Rate-distortion; Source coding; Black-box modeling; canonical representation; continuous piecewise-linear function (CPWL); function approximation; hinging hyperplanes (HHs);
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2005.859246
Filename :
1542439
Link To Document :
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