Extreme points of vector functions

Extreme Points of Vector Functions

Several previous investigations have appeared in the literature which discuss the nature of the set T in »-dimensional space spanned by the vectors ifsdui, ■ ■ ■ , fsdp.n) where 5 ranges over all measurable sets. It was first shown by Liapounov that xi ui, • • ■ , un are atomless measures, then the set F is convex and closed. Extensions of this result were achieved by D. Blackwell [l] and Dvore...

Concerning weak ∗ - extreme points

Every separable nonreflexive Banach space admits an equivalent norm such that the set of the weak-extreme points of the unit ball is discrete.

Extreme Support Vector Regression

Extreme Support Vector Machine (ESVM), a variant of ELM, is a nonlinear SVM algorithm based on regularized least squares optimization. In this chapter, a regression algorithm, Extreme Support Vector Regression (ESVR), is proposed based on ESVM. Experiments show that, ESVR has a better generalization ability than the traditional ELM.Furthermore, ESVMcan reach comparable accuracy as SVR and LS-SV...

Deep Extreme Cut: From Extreme Points to Object Segmentation

This paper explores the use of extreme points in an object (left-most, right-most, top, bottom pixels) as input to obtain precise object segmentation for images and videos. We do so by adding an extra channel to the image in the input of a convolutional neural network (CNN), which contains a Gaussian centered in each of the extreme points. The CNN learns to transform this information into a seg...

Extreme points of the unit cell in Lebesgue-Bochner functions spaces