In this paper, we investigate the applicability of backtrack technique to solve the vertex enumeration problem and the face enumeration problem for a convex polyhedron given by a system of linear inequalities. We show that there is a linear-time backtrack algorithm for the face enumeration problem whose space complexity is polynomial in the input size, but the vertex enumeration problem require...

Motivated by nonparallel hyperplanes support vector machine (NHSVM), a new regression method of data, named as nonparallel hyperplanes support vector regression (NHSVR), is proposed in this paper. The advantages of NHSVR have two aspects, one is considering the minimization of structure risk by introducing a regularization term in objective function, and another is finding two nonparallel hyper...

This paper explores the use of thresholded hyperplanes as the building blocks of a classifier for face detection. We are motivated by the work of Viola and Jones [10] who used Haar-like wavelet features as their weak classifiers in the AdaBoost learning algorithm. These weak classifiers were chosen for their speed. We explore how much may be gained by using more powerful but less computationall...

In this article we completely determine the possible dimensions of integral points and holomorphic curves on the complement of a union of hyperplanes in projective space. Our main theorems generalize a result of Evertse and Györy, who determined when all sets of integral points (over all number fields) on the complement of a union of hyperplanes are finite, and a result of Ru, who determined wh...

Conventional binary classiication trees such as CART either split the data using axis-aligned hyperplanes or they perform a compu-tationally expensive search in the continuous space of hyperplanes with unrestricted orientations. We show that the limitations of the former can be overcome without resorting to the latter. For every pair of training data-points, there is one hyperplane that is orth...

Let V be a vector space of dimension d over a field K and let A be a central arrangement of hyperplanes in V . To answer a question posed by K. Aomoto, P. Orlik and H. Terao construct a commutative K-algebra U(A) in terms of the equations for the hyperplanes ofA. In the course of their work the following question naturally occurred: ◦ Is U(A) determined by the intersection lattice L(A) of the h...

One says that Veldkamp lines exist for a point-line geometry Γ if, for any three distinct (geometric) hyperplanes A, B and C (i) A is not properly contained in B and (ii) A ∩ B ⊆ C implies A ⊂ C or A ∩ B = A ∩ C. Under this condition, the set V of all hyperplanes of Γ acquires the structure of a linear space – the Veldkamp space – with intersections of distinct hyperplanes playing the role of l...

Abstract In hyperbolic space, the angle of intersection and distance classify pairs totally geodesic hyperplanes. A similar algebraic invariant classifies hyperplanes in Einstein universe. dimension 3, symplectic splittings a 4-dimensional real vector space model is determinant. The classification contributes to complete disjointness criterion for crooked surfaces 3-dimensional

A Naive (or Idiot) Bayes network is a network with a single hypothesis node and several observations that are conditionally independent given the hypothesis. We recently surveyed a number of members of the UAI community and discovered a general lack of understanding of the implications of the Naive Bayes assumption on the kinds of problems that can be solved by these networks. It has long been ...