The paper outlines a method for designing near optimal nonlinear classifiers based on a self-organizing technique for estimating probability density functions when only weak assumptions are made about the densities. T...
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The paper outlines a method for designing near optimal nonlinear classifiers based on a self-organizing technique for estimating probability density functions when only weak assumptions are made about the densities. The classical parametric and nonparametric methods for estimating density functions have a number of drawbacks;parametric methods give weak results on unknown distributions, while nonparametric methods require extensive amounts of design samples, storage capacity, and computing power. The present method avoids these disadvantages by parameterizing a set of component densities from which the actual densities are constructed. The parameters of the component densities are optimized by a self-organizing algorithm, reducing to a minimum the labeling of design samples. All the required computations are realized with the simple "sum of product" units commonly used in connectionist models. The density approximations produced by the method are illustrated in two dimensions for a multispectral image classification task. The practical use of the method is illustrated by a small speech recognition problem, that of recognizing 18 Swedish consonants. Related issues of invariant projections, cross-class pooling of data, and subspace partitioning are also discussed.
The characteristics of a project course (160 h of work for the students) oriented towards graphical interaction is described. Project proposals are presented to the students by researchers from different applications....
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The characteristics of a project course (160 h of work for the students) oriented towards graphical interaction is described. Project proposals are presented to the students by researchers from different applications. The students get a high degree of freedom during the project and partly as a result of this they are enthusiastic about the work and produce very impressive prototypes which they present at the end of the course. Copyright (C) 1996 Elsevier science Ltd
The edge focusing method produces a series of edge images ranging from coarser to finer scale resolution. The displacements of these extracted edges in this series are discussed. A three-step method of labelling the e...
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The edge focusing method produces a series of edge images ranging from coarser to finer scale resolution. The displacements of these extracted edges in this series are discussed. A three-step method of labelling the extracted edges as coming from objects or as coming from shadows and other illumination phenomena using this series is tried. More precisely, we show that it seems possible to label edges into the categories ‘diffuse’ and ‘non-diffuse’ from a binary multi-scale representation, i.e. without using the image intensities directly.
The experimental results of viewing 3D objects on a 2D display are presented. The effect of object relationship;presentation quality (wireframe and shaded);and illumination on depth perception were studied. After the ...
A numerical method for simulating incompressible two-dimensional multiphase flow is presented. The method is based on a level-set formulation discretized by a finite-element technique. The treatment of the specific fe...
A numerical method for simulating incompressible two-dimensional multiphase flow is presented. The method is based on a level-set formulation discretized by a finite-element technique. The treatment of the specific features of this problem, such as surface tension forces acting at the interfaces separating two immiscible fluids, as well as the density and viscosity jumps that in general occur across such interfaces, have been integrated into the finite-element framework. Using a method based on the weak formulation of the Navier-Stokes equations has its advantages. In this formulation, the singular surface tension forces are included through line integrals along the interfaces, which are easily approximated quantities. In addition, differentiation of the discontinuous viscosity is avoided. The discontinuous density and viscosity are included in the finite element integrals. A strategy for the evaluation of integrals with discontinuous integrands has been developed based on a rigorous analysis of the errors associated with the evaluation of such integrals. numerical tests have been performed. For the case of a rising buoyant bubble the results are in good agreement with results from a front-tracking method. The run presented here is a run including topology changes, where initially separated areas of one fluid merge in different stages due to buoyancy effects.
Probabilistic neural networks can approximate class conditional densities in optimal (Bayesian) pattern classifiers. In natural pattern recognition applications, the size of the training set is always limited, making ...
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Probabilistic neural networks can approximate class conditional densities in optimal (Bayesian) pattern classifiers. In natural pattern recognition applications, the size of the training set is always limited, making the approximation task difficult. Invariance constraints can significantly simplify the task of density approximation. A technique is presented for learning invariant representations, based on a statistical approach to ground invariance. An iterative method is developed formally for computing the maximum likelihood estimate to the parameters of an invariant mixture model. The method can be interpreted as a competitive training strategy for a radial basis function (RBF) network. It can be used for self-organizing formation of both invariant templates and features.< >
N COMPUTER applications we are used to live with approximation. Var I ious notions of approximation appear, in fact, in many circumstances. One notable example is the type of approximation that arises in numer&#...
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ISBN:
(数字)9783642584121
ISBN:
(纸本)9783540654315;9783642635816
N COMPUTER applications we are used to live with approximation. Var I ious notions of approximation appear, in fact, in many circumstances. One notable example is the type of approximation that arises in numer ical analysis or in computational geometry from the fact that we cannot perform computations with arbitrary precision and we have to truncate the representation of real numbers. In other cases, we use to approximate com plex mathematical objects by simpler ones: for example, we sometimes represent non-linear functions by means of piecewise linear ones. The need to solve difficult optimization problems is another reason that forces us to deal with approximation. In particular, when a problem is computationally hard (i. e. , the only way we know to solve it is by making use of an algorithm that runs in exponential time), it may be practically unfeasible to try to compute the exact solution, because it might require months or years of machine time, even with the help of powerful parallel computers. In such cases, we may decide to restrict ourselves to compute a solution that, though not being an optimal one, nevertheless is close to the optimum and may be determined in polynomial time. We call this type of solution an approximate solution and the corresponding algorithm a polynomial-time approximation algorithm. Most combinatorial optimization problems of great practical relevance are, indeed, computationally intractable in the above sense. In formal terms, they are classified as Np-hard optimization problems.
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