Recently a novel approach to nonlinear function approximation using hinging hyperplanes, was reported by L. Breiman 3]. In this contribution we have combined smooth hinging hyperplanes and the eecient initializa-tion procedure existing for hinging hyperplanes in 3], with a Gauss-Newton procedure, see 4], to perform the nal adjustment of the smooth hinging hyperplanes. This combination uses the ...

We show that there are 6 isomorphism classes of hyperplanes of the dual polar space ∆ = DW (5, 2h) which arise from the Grassmannembedding. If h ≥ 2, then these are all the hyperplanes of ∆ arising from an embedding. If h = 1, then there are 6 extra classes of hyperplanes as has been shown by Pralle [23] with the aid of a computer. We will give a computer free proof for this fact. The hyperplan...

In [MP08] L. Marengo and C. Pasquali present a model of object construction in majority voting and show that, in general, by appropriate changes of such bundles, different social outcomes may be obtained. In this paper we extend and generalize this approach by providing a geometric model of individual preferences and social aggregation based on hyperplanes and their arrangements. As an applicat...

The es-splitting operation on binary matroids is a natural generalization of Slater's <em>n</em>-line splitting graphs. In this paper, we characterize the closure operator matroid M<sup>e</sup><sub>X</sub> in terms original M. We also describe ats and hyperplanes bi- nary hyperplanes, respectively

AbetractRather than iteratively manually examining a variety of pre-specified architectures, a constructive learning algorithm dynamically creates a problem-specific neural network architecture. Here we present an revised version of our parallel constructive neural network learning algorithm which constructs such an architecture. The three steps of searching for points on separating hyperplanes...

We present NeuroLinear, a system for extracting oblique decision rules from neural networks that have been trained for classiication of patterns. Each condition of an oblique decision rule corresponds to a partition of the attribute space by a hyperplane that is not necessarily axis-parallel. Allowing a set of such hyperplanes to form the boundaries of the decision regions leads to a signiicant...