Brief paper: Adaptive hinging hyperplanes and its applications in dynamic system identification
Automatica (Journal of IFAC)
Urban Traffic Flow Forecasting Based on Adaptive Hinging Hyperplanes
AICI '09 Proceedings of the International Conference on Artificial Intelligence and Computational Intelligence
The hill detouring method for minimizing hinging hyperplanes functions
Computers and Operations Research
A special kind of neural networks: continuous piecewise linear functions
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
| Hi-index | 754.84 |
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.