simulators [9]. There are two main ways of obtaining a DR of a real world object. One is by acquisition with a This paper presents the properties of the discrete analytical hyperplanes. They are defined analytically in the discrete dophysical device like a camera for a 2D DR, a CT or MR main by Diophantine equations. We show that the discrete scanner for a 3D DR, a PET scanner for a 4D DR, etc....

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.

In this paper, we present methods for learning and pruning oblique decision trees. We propose a new function for evaluating different split rules at each node while growing the decision tree. Unlike the other evaluation functions currently used in literature (which are all based on some notion of purity of a node), this new evaluation function is based on the concept of degree of linear separab...

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.

An investigation is carried out to formulate some theoretical results regarding the behavior of a genetic-algorithm-based pattern classification methodology, for an infinitely large number of training data points n, in an N-dimensional space RN. It is proved that for nPR, and for a sufficiently large number of iterations, the performance of this classifier (when hyperplanes are considered to ge...

Online learning is very important for processing sequential data and helps alleviate the computation burden on large scale data as well. Especially, one-pass online learning is to predict a new coming sample’s label and update the model based on the prediction, where each coming sample is used only once and never stored. So far, existing one-pass online learning methods are globally modeled and...

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...