On finding global optima for the hinge fitting problem
Computers and Operations Research
Brief paper: Identification of dynamic systems using Piecewise-Affine basis function models
Automatica (Journal of IFAC)
Estimation of a regression function by maxima of minima of linear functions
IEEE Transactions on Information Theory
A neural network of smooth hinge functions
IEEE Transactions on Neural Networks
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
Identification of piecewise affine systems via mixed-integer programming
Automatica (Journal of IFAC)
Hinging hyperplane models for multiple predicted variables
SSDBM'12 Proceedings of the 24th international conference on Scientific and Statistical Database Management
Hinging hyperplane based regression tree identified by fuzzy clustering and its application
Applied Soft Computing
| Hi-index | 754.90 |
This correspondence concerns the estimation algorithm for hinging hyperplane (HH) models, a piecewise-linear model for approximating functions of several variables, suggested in Breiman (1993). The estimation algorithm is analyzed and it is shown that it is a special case of a Newton algorithm applied to a sum of squared error criterion. This insight is then used to suggest possible improvements of the algorithm so that convergence to a local minimum can be guaranteed. In addition, the way of updating the parameters in the HH model is discussed. In Breiman, a stepwise updating procedure is proposed where only a subset of the parameters are changed in each step. This connects closely to some previously suggested greedy algorithms and these greedy algorithms are discussed and compared to a simultaneous updating of all parameters