On the hinge-finding algorithm for hinging hyperplanes

This correspondence concerns the estimation algorithm for hinging hyperplane (HH) models, a piecewise-linear model for approximating functions of several variables, suggested in Breiman [1], 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 [1], a stepwise updating procedure is proposed where only a subset of the parameters are changed in each step. This connects closely to some recently suggested greedy algorithms and these greedy algorithms are discussed and compared to a simultaneous updating of all parameters.