A fast SVM learning algorithm is proposed according to incremental learning and center convex hull operator. It is established on analyzing the relevance of support vector and convex hull from the angle of calculation geometry. The convex hull of current training samples is solved in the first place. Further, Euclidean distance elimination is applied to convex hull. Meanwhile, every time when t...

We propose a hull operator, the reflex-free hull, that allows us to define a 3D analogue to bays in polygons. The reflex-free hull allows a rich set of topological types, yet for polyhedral input with n edges, it remains a polyhedral set with O(n) edges. This is in contrast to other possible hull definitions that give non-planar surfaces and higher combinatorial complexity. The reflex-free hull...

Convexity predicates and the convex hull operator continue to play an important role in theories of spatial representation and reasoning, yet their firstorder axiomatization is still a matter of controversy. In this paper, we present a new approach to adding convexity to a mereotopological theory with boundary elements by specifying first-order axioms for a binary segment operator s. We show th...

Given two quasi-Banach ideals A and B we investigate the regular hull of their composition (A ◦ B). In concrete situations this regular hull appears more often than the composition itself. As a first example we obtain a description for the regular hull of the nuclear operators which is a ”reflected” Grothendieck representation: N reg 1 = I ◦W (theorem 2.1). Further we recognize that the class o...

Let S be a finite set with n elements in a real linear space. Let JS be a set of n intervals in R. We introduce a convex operator co(S,JS) which generalizes the familiar concepts of the convex hull conv S and the affine hull aff S of S. We establish basic properties of this operator. It is proved that each homothet of conv S that is contained in aff S can be obtained using this operator. A vari...

The hidden point removal (HPR) operator introduced by Katz et al. [KTB07] provides an elegant solution for the problem of estimating the visibility of points in point samplings of surfaces. Since the method requires computing the three-dimensional convex hull of a set with the same cardinality as the original cloud, the method has been largely viewed as impractical for real-time rendering of me...

let  be a hilbert space of functions analytic on a plane domain  such that for every  in  the functional of evaluation at  is bounded. assume further that  contains the constants and admits multiplication by the independent variable , , as a bounded operator. we give sufficient conditions for  to be reflexive for all positive integers .

A bounded linear operator acting on a Hilbert space is a generalized quadratic operator if it has an operator matrix of the form [ aI cT dT ∗ bI ] . It reduces to a quadratic operator if d = 0. In this paper, spectra, norms, and various kinds of numerical ranges of generalized quadratic operators are determined. Some operator inequalities are also obtained. In particular, it is shown that for a...

As appropriate generalizations of convex combinations with uncountably many terms, we introduce the so-called Choquet combinations, decomposable and as well their corresponding hull operators acting on power sets Lebesgue-Bochner spaces. We show that coincides in finite-dimensional setting, yet tends to be larger infinite dimensions. also provide a quantitative characterization hull, without an...