The model of adaptive hinging hyperplanes (AHH) is proposed in this paper for black-box modeling. It is based on Multivariate Adaptive Regression Splines (MARS) and Generalized Hinging Hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subarea. It is proved that AHH model is identical to a spec...

A Brody curve, a.k.a. normal curve, is a holomorphic map f from the complex line C to the complex projective space P such that the family of its translations {z 7→ f(z + a) : a ∈ C} is normal. We prove that Brody curves omitting n hyperplanes in general position have growth order at most one, normal type. This generalizes a result of Clunie and Hayman who proved it for n =

In this survey we deal with the location of hyperplanes in n{ dimensional normed spaces, i.e., we present all known results and a unifying approach to the so-called median hyperplane problem in Minkowski spaces. We describe how to nd a hyperplane H minimizing the weighted sum f(H) of distances to a given, nite set of demand points. In robust statistics and operations research such an optimal hy...

We consider logarithmic vector fields parametrized by finite collections of weighted hyperplanes. For a finite collection of weighted hyperplanes in a two-dimensional vector space, it is known that the set of such vector fields is a free module of rank two whose basis elements are homogeneous. We give an algorithm to construct a homogeneous basis for the module.

An arrangement of hyperplanes in E'' is a "plaid" provided its hyperplanes form no multiple flats of intersection and lie in parallel families that are in general position. We develop some geometrically natural formulas for the number of r-faces that are formed by such an arrangement.

The paper evaluates two kernel-based methods on the problem of predicting precipitation based on observable variables. The support vector machine (SVM) method finds the two parallel hyperplanes that provide maximal separation of two subsets, excepting outliers. The minimax probability machine (MPM) method finds an optimal separating hyperplane that minimizes the probability of misclassification...

Gaussian Mixture Models (GMMs) in combination with Support Vector Machine (SVM) classifiers have been shown to give excellent classification accuracy in speaker recognition. In this work we use this approach for language identification, and we compare its performance with the standard approach based on GMMs. In the GMM-SVM framework, a GMM is trained for each training or test utterance. Since i...

In this paper we will extend two known location problems from Euclidean n-space to all n-dimensional normed spaces, n¿ 2. Let X be a "nite set of weighted points whose a2ne hull is n-dimensional. Our "rst objective is to "nd a hyperplane minimizing (among all hyperplanes) the sum of weighted distances with respect to X. Such a hyperplane is called a median hyperplane with respect to X, and we w...