In this paper we propose a modified framework of support vector machines, called Oblique Support Vector Machines(OSVMs), to improve the capability of classification. The principle of OSVMs is joining an orthogonal vector into weight vector in order to rotate the support hyperplanes. By this way, not only the regularized risk function is revised, but the constrained functions are also modified. ...

Abstract Many results about mass partitions are proved by lifting $\mathds {R}^d$ to a higher-dimensional space and dividing the into pieces. We extend such methods use arguments polyhedral surfaces. Among other results, we prove existence of equipartitions $d+1$ measures in parallel hyperplanes $d+2$ concentric spheres. For whose supports sufficiently well separated, where one can cut fixed (p...

We study the problem of separating n points in the plane, no two of whi h have the same xor yoordinate, using a minimum number of verti al and horizontal lines avoiding the points, so that ea h ell of the subdivision ontains at most one point. Extending previous NP-hardness results due to Freimer et al. we prove that this problem and some variants of it are APX-hard. We give a 2-approximation a...

State-of-the-art methods for clustering data drawn from a union of subspaces are based on sparse and low-rank representation theory. Existing results guaranteeing the correctness of such methods require the dimension of the subspaces to be small relative to the dimension of the ambient space. When this assumption is violated, as is, for example, in the case of hyperplanes, existing methods are ...

A theoretical testing method for fully characterising the Mooney-Rivlin three-parameter hyper-elastic material model is proposed by capturing full-field digital image correlation (DIC) data, namely displacement field and indentation force data. finite element with known parameters will act as experimental against which all data be referenced (a preliminary test case). Going forward this stand-i...

The trace properties of the sample paths of suuciently regular generalized random elds are studied. In particular, nice localisation properties are shown in the case of hyperplanes. Using techniques of Euclidean quantum eld theory a constructive description of the conditional expectation values with respect to some Gibbs measures describing Euclidean quantum eld theory models and the-algebras l...

Given a set of n hyperplanes h1, . . . , hn ∈ R d the hyperplane depth of a point P ∈ R is the minimum number of hyperplanes that a ray from P can meet. The hyperplane depth of the arrangement is the maximal depth of points P not in any hi. We give an optimal O(n logn) deterministic algorithm to compute the hyperplane depth of an arrangement in dimension d = 2.