A hinge function y = h (x) consists of two hyperplanes continuously joined together at a hinge. In regression (prediction), classification (pattern recognition), and noiseless function approximation, use of sums of hinge functions gives a powerful and efficient altemative to neural networks with compute times several orders of magnitude less than fitting neural networks with a comparable number...

We propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes. By the separation property of hyperplane, our method is proved to be globally convergent under very mild assumptions. In addition, we propose a modified version of our algorithm that fin...

Abstract A robust and efficient algorithm for the identification of algebraic surface patches from noisy data is detailed here. The aim is to reconstruct the B-rep of solids made of engineering forms constructs. There is no apriori knowledge on the number of patches. Algebraic surfaces are embedded on hyperplanes in , where is the number of points sufficient to determine an algebraic surface. A...

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...

Currently more and more agents are involved in human routine activities and a mixed human-agent society is thus formed by the humans and the agents involved. The relationship between humans and agents in this mixed society is subtle and it is vital to explore the influence that agents bring into the society. In this paper, we try to investigate a few questions: will humans act differently towar...

Let X1,X2, . . . , be independent random variables with EXi = 0 and write Sn = ∑ n i=1 Xi and V 2 n = ∑ n i=1 X i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum S...

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 ...