Results 1  10
of
82,469
Multiple kernel learning, conic duality, and the SMO algorithm
 In Proceedings of the 21st International Conference on Machine Learning (ICML
, 2004
"... While classical kernelbased classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed that the optimiz ..."
Abstract

Cited by 450 (31 self)
 Add to MetaCart
While classical kernelbased classifiers are based on a single kernel, in practice it is often desirable to base classifiers on combinations of multiple kernels. Lanckriet et al. (2004) considered conic combinations of kernel matrices for the support vector machine (SVM), and showed
A NOVEL APPROACH TO ORTHOGONAL DISTANCE LEAST SQUARES FITTING OF GENERAL CONICS
"... Abstract: Fitting of conics to a set of points is a well researched area and is used in many fields of science and engineering. Least squares methods are one of the most popular techniques available for conic fitting and among these, orthogonal distance fitting has been acknowledged as the ’best ’ ..."
Abstract
 Add to MetaCart
’ least squares method. Although the accuracy of orthogonal distance fitting is unarguably superior, the problem so far has been in finding the orthogonal distance between a point and a general conic. This has lead to the development of conic specific algorithms which take the characteristics of the type
Direct least Square Fitting of Ellipses
, 1998
"... This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac  b² = 1 the new method incorporates the ellipticity constraint ..."
Abstract

Cited by 421 (3 self)
 Add to MetaCart
This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4ac  b² = 1 the new method incorporates the ellipticity constraint
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
Abstract

Cited by 800 (26 self)
 Add to MetaCart
of probability distributions — are best studied in the general setting. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, we develop general variational representations of the problems of computing
Superconformal field theory on threebranes at a CalabiYau singularity
 Nucl. Phys. B
, 1998
"... Just as parallel threebranes on a smooth manifold are related to string theory on AdS5 × S 5, parallel threebranes near a conical singularity are related to string theory on AdS5 × X5, for a suitable X5. For the example of the conifold singularity, for which X5 = (SU(2) × SU(2))/U(1), we argue that ..."
Abstract

Cited by 690 (37 self)
 Add to MetaCart
Just as parallel threebranes on a smooth manifold are related to string theory on AdS5 × S 5, parallel threebranes near a conical singularity are related to string theory on AdS5 × X5, for a suitable X5. For the example of the conifold singularity, for which X5 = (SU(2) × SU(2))/U(1), we argue
Hasse's Theorem and Rational Points on the General Conic
"... Diophantine Equations are equations to which only integer solutions or alternatively rational solutions are considered. The study of these equations has fascinated man for thousands of years. The ancient Babylonians enumerated Pythagorean triples, integer solutions to the equation: X2 + y2 = Z 2 The ..."
Abstract
 Add to MetaCart
including elliptic curves is highly nontrivial and incomplete. However, many general theorems exist and the theory is in constant development. In this paper we will detail the theory for conics. We define a point in the plane to be rational if its coordinates are rational. We define a curve to be rational
Sketchpad: A manmachine graphical communication system
, 2003
"... The Sketchpad system uses drawing as a novel communication medium for a computer. The system contains input, output, and computation programs which enable it to interpret information drawn directly on a computer display. It has been used to draw electrical, mechanical, scientific, mathematical, and ..."
Abstract

Cited by 702 (6 self)
 Add to MetaCart
, and animated drawings; it is a general purpose system. Sketchpad has shown the most usefulness as an aid to the understanding of processes, such as the notion of linkages, which can be described with pictures. Sketchpad also makes it easy to draw highly repetitive or highly accurate drawings and to change
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
Abstract

Cited by 5350 (67 self)
 Add to MetaCart
was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
Iterative point matching for registration of freeform curves and surfaces
, 1994
"... A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in ma ..."
Abstract

Cited by 659 (7 self)
 Add to MetaCart
A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately
ChernSimons Gauge Theory as a String Theory
, 2003
"... Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional ChernSimons gaug ..."
Abstract

Cited by 551 (14 self)
 Add to MetaCart
Certain two dimensional topological field theories can be interpreted as string theory backgrounds in which the usual decoupling of ghosts and matter does not hold. Like ordinary string models, these can sometimes be given spacetime interpretations. For instance, threedimensional ChernSimons gauge theory can arise as a string theory. The worldsheet model in this case involves a topological sigma model. Instanton contributions to the sigma model give rise to Wilson line insertions in the spacetime ChernSimons theory. A certain holomorphic analog of ChernSimons theory can also arise as a string theory.
Results 1  10
of
82,469