Hyperplanes and hyperplane complements in the Segre product of partial linear spaces are investigated. The parallelism of such a complement is characterized in terms of the point-line incidence. Assumptions, under which the automorphisms of the complement are the restrictions of the automorphisms of the ambient space, are given. An affine covering for the Segre product of Veblenian gamma spaces...

In this paper, weak defining hyperplanes and the anchor points in DEA, as an important subset of the set of extreme efficient points of the Production Possibility Set (PPS), are used to construct unobserved DMUs and in the long run to improve the envelopment of all observed DMUs. There has been a surge of articles on improving envelopment in recent years. What has been done first is in Constant...

Many learning situations involve separation of labeled training instances by hyperplanes. Consistent separation is of theoretical interest, but the real goal is rather to minimize the number of errors using a bounded number of hyperplanes. Exact minimization of empirical error in a high-dimensional grid induced into the feature space by axis-parallel hyperplanes is NP-hard. We develop two appro...

In hyperspectral images, endmembers characterizing one class of ground object may vary due to illumination, weathering, slight variations the materials. This phenomenon is called intra-class endmember variability which important factors affecting performance unmixing. However, often ignored in unmixing, causes a decrease accuracy How deal with focus. To address this problem, we propose novel un...

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 ...