deterministic error analysis of support vector regression and related regularized kernel methods we introduce a new technique for the analysis of kernel based regression problems the basic tools are sampling inequalities which apply to all machine learning problems involving penalty terms induced by kernels related to sobolev spaces they lead to explicit deterministic results concerning the worst case behaviour of e and svrs using these we show how to adjust regularization parameters to get best possible approximation orders for regression the results are illustrated by some numerical examples

ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids in this paper explicit necessary and sufficient conditions are established for the ordinary and strong ellipticity of the three dimensional field equations in the nonlinear equilibrium theory of incompressible homogeneous and isotropic hyperelastic solids the resulting system of inequalities involves the local principal stretches directly and in addition restricts the first and second partial derivatives of the strain energy density with respect to the deformation invariants or the principal stretches the conditions of ordinary and strong ellipticity are found to coalesce for materials that obey the baker ericksen inequalities and possess a positive shear modulus at infinitesimal deformations various implications of these ellipticity conditions for special classes of materials and deformations are explored

training ν support vector classifiers theory and algorithms the support vector machine svm for classification proposed by scholkopf smola williamson and bartlett 2000 has the advantage of using a parameter on controlling the number of support vectors in this article we investigate the relation between svm and c svm in detail we show that in general they are two different problems with the same optimal solution set hence we may expect that many numerical aspects of solving them are similar however compared to regular c svm the formulation of svm is more complicated so up to now there have been no effective methods for solving large scale svm we propose a decomposition method for svm that is competitive with existing methods for c svm we also discuss the behavior of svm by some numerical experiments

global continuation in displacement problems of nonlinear elastostatics via the leray schauder degree we obtain global solution continua of forced displacement problems of nonlinear elastostatics via a leray schauder scheme we adopt strong ellipticity as a bsic constitutive hypothesis the usual leray schauder approach based in part upon the reduction of the boundary value problem to an operator equation for the zeros of a compact vector field apparently fails on the one hand strong ellipticity alone is not enough to insure invertibility rdquo of the principal quasilinear part of the differential operator more importantly the physical requirement of local injectivity of the deformation and the associated growth of the stored energy function dictate that ellipticity is not uniform we demonstrate how to overcome these difficulties finally with additional physically reasonable restrictions on the stored energy function we obtain unbounded branches of classical globally injective solutions

classical injective solutions in the large in incompressible nonlinear elasticity we consider a general class of parametrized displacement boundary value problems in incompressible nonlinear elasticity we prove the existence of an unbounded solution branch of classical injective solutions emanating from the unforced stress free reference configuration a sharp global implicit function theorem the ramifications of this are that there exists at least one solution for any given applied loading and or there exists solutions of arbitrarily large there norm for some finite loading we refer to this as solutions in the large the nonlinear constraint equation enforcing incompressibility obviates the direct use of either the leray schauder degree or an oriented degree previously developed for compressible problems instead we employ the nonlinear fredholm degree for proper maps constructed in fitzpatrick et al j reine angew math 427 1 33 1992 pejsachowicz and rabier j anal math 76 265 288 1998 we establish the requisite admissibility properties in the presence of the constraint equation before proving the main results

existence and uniqueness of an inverse source problem for a fractional integrodifferential equation abstract we study an inverse source problem for a fractional integrodifferential equation this inverse problem aims to determine a time varying source term in the fractional integrodifferential equation from the measurement data at a fixed point x 0 by using the fixed point theorem in suitable sobolev space the existence and uniqueness of this inverse problem are obtained

efficient computation and model selection for the support vector regression in this letter we derive an algorithm that computes the entire solution path of the support vector regression svr we also propose an unbiased estimate for the degrees of freedom of the svr model which allows convenient selection of the regularization parameter

uniqueness and stability of an inverse problem for a phase field model using data from one component we study an inverse problem of determining a spatial varying coefficient in a parabolic hyperbolic phase field model with the following observation data of only one component the order parameter in a subdomain w satisfying email protected email protected email protected along a sufficiently large time interval and at a suitable time over the whole spatial domain based on a carleman estimate for the parabolic hyperbolic phase field system we prove the lipschitz stability and uniqueness for this inverse problem

global bifurcation of periodic solutions in nonlinear evolution problems with periodic forcing abstract this paper discusses the global bifurcation of 2 periodic solutions of u t p x u f t u with a homogeneous dirichlet boundary condition where p x is linear elliptic and the nonlinearity f is 2 periodic in t the main differences from existing theories devoted to this type of problem can roughly be summarized as follows i the bifurcation analysis makes no use of evolution operators or related concepts poincare maps floquet multipliers etc ii the bifurcation nonbifurcation points are characterized through an associated stationary problem iii the functional setting allows for nonlinearities f exhibiting time discontinuities among other things the results include various partial generalizations of the bifurcation from the principal eigenvalue theorem which unlike the classical version do not require linear parameter dependence

identification of orthotropic elastic constants using the eigenfunction virtual fields method abstract the virtual fields method vfm pierron and grediac 2012 an inverse method based on the principle of virtual work pvw is being increasingly used to estimate mechanical properties of materials from full field deformations obtained from techniques such as digital image correlation moire and speckle interferometry and grid methods by making specific choices for virtual fields vfs in pvw one obtains a system of algebraic equations which is then solved for the unknown material constants recently a new variant of vfm known as the eigenfunction virtual fields method evfm has been proposed subramanian 2013 in evfm principal components of the measured i e true strain fields are used to systematically generate vfs we extend evfm to orthotropic elastic materials in this work and estimate the relevant material parameters from full field strain data generated from a finite element model of an unnotched iosipescu test varying levels of gaussian white noise are added to the synthetic strain data to evaluate the sensitivity of evfm to input noise it is observed that for low to moderate noise the material properties estimated by the proposed method are relatively insensitive to noise however when noise levels are high the proposed method yields large variance in some of the computed properties when compared to the state of the art optimized piecewise continuous vfm toussaint et al 2006 pierron and grediac 2012 some of the large variance in properties estimated from noisy data using evfm is traced to the sensitivity of the third dominant eigenfunction and modifications to the proposed method to address this issue are suggested

quasiconvexity and uniqueness of equilibrium solutions in nonlinear elasticity in this paper we prove the uniqueness of the solution to certain simple displacement boundary value problems in the nonlinear theory of homogeneous hyperelasticity for a body occupying a star shaped reference configuration rn whose boundary is subjected to an affine deformation i e there exists a constant n n matrix f and a constant n vector b such that x fx b for all x we consider all smooth equilibrium configurations satisfying this boundary condition clearly the homogeneous deformation x fx b for all x in bar omega is one such solution our aim is to prove under suitable hypotheses that it is the only such solution

an inverse problem for estimation of bending stiffness in kirchhoff love plates this work deals with the development of a numerical method for solving an inverse problem for bending stiffness estimation in a kirchhoff love plate from overdetermined data the coefficient is identified using a technique called the method of variational imbedding where the original inverse problem is replaced by a minimization problem the euler lagrange equations for minimization comprise higher order equations for the solution of the displacement and an equation for the bending stiffness the correctness of the embedded problem is discussed a difference scheme and a numerical algorithm for solving the parameter identification problem are developed numerical results for the obtained values of the bending stiffness as an inverse problem are presented

new support vector algorithms we propose a new class of support vector algorithms for regression and classification in these algorithms a parameter lets one effectively control the number of support vectors while this can be useful in its own right the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm the accuracy parameter epsilon in the regression case and the regularization constant c in the classification case we describe the algorithms give some theoretical results concerning the meaning and the choice of and report experimental results

the constitutive compatibility method for identification of material parameters based on full field measurements abstract we revisit here the concept of the constitutive relation error for the identification of elastic material parameters based on image correlation an additional concept so called constitutive compatibility of stress is introduced defining a subspace of the classical space of statically admissible stresses the key idea is to define stresses as compatible with the observed deformation field through the chosen class of constitutive equation this makes possible the uncoupling of the identification of stress from the identification of the material parameters as a result the global cost of the identification is strongly reduced this uncoupling also leads to parametrized solutions in cases where the solution is non unique as demonstrated on 2d numerical examples

a cascade optimization methodology for automatic parameter identification and shape process optimization in metal forming simulation computer simulations of metal forming processes using the finite element method fem are today well established this form of simulation uses an increasing number of sophisticated geometrical and material models relying on a certain number of input data which are not always readily available the aim of inverse problems which will be considered here is to determine one or more of the input data relating to these forming process simulations thereby leading to a desired result in this paper we will focus on two categories of such inverse problems the first category consists of parameter identification inverse problems these involve evaluating the material parameters for material constitutive models that would lead to the most accurate results with respect to physical experiments i e minimizing the difference between experimental results and fem simulations the second category consists of shape process optimization inverse problems these involve determining the initial geometry of the specimen and or the shape of the forming tools as well as some parameters of the process itself in order to provide the desired final geometry after the forming process these two categories of inverse problems can be formulated as optimization problems in a similar way i e by using identical optimization algorithms in this paper we intend firstly to solve these two types of optimization problems by using different non linear gradient based optimization methods and secondly to compare their efficiency and robustness in a variety of numerical applications

on the existence of a global minimum in inverse parameters identification by self optimizing inverse analysis method abstract in this paper a mathematical proof of the existence of a global minimum of self optim self optimizing inverse analysis method cost functional is presented based upon weak solution theory of partial differential equations the self optim provides single global minimum rather than having multiple global minima corresponding to unrealistic solutions of the inverse problem furthermore discrete approximation of the inverse problem and computational methods for the cost functional are proposed and the proof is numerically verified this paper provides a rigorous mathematical foundation for applications of the self optim method to various inverse problems in mechanics

leave one out bounds for support vector regression model selection minimizing bounds of leave one out errors is an important and efficient approach for support vector machine svm model selection past research focuses on their use for classification but not regression in this letter we derive various leave one out bounds for support vector regression svr and discuss the difference from those for classification experiments demonstrate that the proposed bounds are competitive with bayesian svr for parameter selection we also discuss the differentiability of leave one out bounds

accurate on line support vector regression batch implementations of support vector regression svr are inefficient when used in an on line setting because they must be retrained from scratch every time the training set is modified following an incremental support vector classification algorithm introduced by cauwenberghs and poggio 2001 we have developed an accurate on line support vector regression aosvr that efficiently updates a trained svr function whenever a sample is added to or removed from the training set the updated svr function is identical to that produced by a batch algorithm applications of aosvr in both on line and cross validation scenarios are presented in both scenarios numerical experiments indicate that aosvr is faster than batch svr algorithms with both cold and warm start

training v support vector regression theory and algorithms we discuss the relation between e support vector regression e svr and support vector regression svr in particular we focus on properties that are different from those of c support vector classification c svc and support vector classification svc we then discuss some issues that do not occur in the case of classification the possible range of e and the scaling of target values a practical decomposition method for svr is implemented and computational experiments are conducted we show some interesting numerical observations specific to regression

face recognition using an enhanced independent component analysis approach this paper is concerned with an enhanced independent component analysis ica and its application to face recognition typically face representations obtained by ica involve unsupervised learning and high order statistics in this paper we develop an enhancement of the generic ica by augmenting this method by the fisher linear discriminant analysis lda hence its abbreviation fica the fica is systematically developed and presented along with its underlying architecture a comparative analysis explores four distance metrics as well as classification with support vector machines svms we demonstrate that the fica approach leads to the formation of well separated classes in low dimension subspace and is endowed with a great deal of insensitivity to large variation in illumination and facial expression the comprehensive experiments are completed for the facial recognition technology feret face database a comparative analysis demonstrates that fica comes with improved classification rates when compared with some other conventional approaches such as eigenface fisherface and the ica itself