eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

lp stability of solutions of boltzmann equation with external force in soft potentials in this paper we present a uniform lp stability theory for the solutions to boltzmann equation with small or large external forces in vacuum in soft potentials we assume that the initial data are sufficiently small and a fast decay in space and velocity our stability analysis is divided into two parts for small external forces we first consider the time derivative of the pth power of lp norm of the distance between two mild solutions f and g then define nonlinear functionals and apply the gronwall s inequality to obtain the lp stability for large external forces we make use of the constructive assumptions on external force minkowski s inequality and gronwall s inequality to derive the lp stability estimate

bayesian approaches to gaussian mixture modeling a bayesian based methodology is presented which automatically penalizes overcomplex models being fitted to unknown data we show that with a gaussian mixture model the approach is able to select an optimal number of components in the model and so partition data sets the performance of the bayesian method is compared to other methods of optimal model selection and found to give good results the methods are tested on synthetic and real data sets

uniform stability of solutions of boltzmann equation for soft potential with external force abstract the study of cauchy problem of the boltzmann equation is important in both theory and applications existence of global solutions to the equation and uniform stability of solutions in the absence of external force were introduced in the previous work on the boltzmann equation in this paper we will investigate the uniform stability of solutions in l 1 for the cauchy problem of the boltzmann equation when there is an external force for the case of soft potentials

the same class of stationary solutions to some multidimensional kinetic systems with extensive background density abstract in this study we investigate the existence and uniqueness of the same class of stationary solutions for some kinetic systems comprising the vlasov poisson fokker planck system vlasov poisson boltzmann system and vlasov maxwell boltzmann system in arbitrary space dimensions n n 3 essentially the problem can be reduced to solving the problem of a second order elliptic equation with exponential nonlinearity this result had been proved in three spatial dimensions but the extension to a higher dimensional setting makes the existence proof nontrivial in particular it necessary to highlight that the requirement regarding the background density function is relaxed compared with previous studies in the case of three spatial dimensions

spherical homoscedastic distributions the equivalency of spherical and normal distributions in classification many feature representations as in genomics describe directional data where all feature vectors share a common norm in other cases as in computer vision a norm or variance normalization step where all feature vectors are normalized to a common length is generally used these representations and pre processing step map the original data from p to the surface of a hypersphere sp 1 such representations should then be modeled using spherical distributions however the difficulty associated with such spherical representations has prompted researchers to model their spherical data using gaussian distributions instead as if the data were represented in p rather than sp 1 this opens the question to whether the classification results calculated with the gaussian approximation are the same as those obtained when using the original spherical distributions in this paper we show that in some particular cases which we named spherical homoscedastic the answer to this question is positive in the more general case however the answer is negative for this reason we further investigate the additional error added by the gaussian modeling we conclude that the more the data deviates from spherical homoscedastic the less advisable it is to employ the gaussian approximation we then show how our derivations can be used to define optimal classifiers for spherical homoscedastic distributions by using a kernel which maps the original space into one where the data adapts to the spherical homoscedastic model we can derive non linear classifiers with potential applications in a large number of problems we conclude this paper by demonstrating the uses of spherical homoscedasticity in the classification of images of objects gene expression sequences and text data

discriminative zernike and pseudo zernike moments for face recognition usually magnitude coefficients of some selected orders of zms and pzms have been used as invariant image features the careful selection of the set of features with higher discrimination competence may increase the recognition performance in this paper the authors have used a statistical method to estimate the discrimination strength of all the extracted coefficients of zms and pzms whereas for classification only the coefficients with estimated higher discrimination strength are used in the feature vector the performance of these selected discriminative zms dzms and discriminative pzms dpzms features have been compared to that of their corresponding conventional approaches on yale orl and feret databases against illumination expression scale and pose variations an extension to these dzms and dpzms have been proposed by combining them with pca and fld it has been observed from the exhaustive experimentation that the recognition rate is improved by 2 6 at reduced dimensions and with less computational complexity than that of using the successive zms and pzms features

relative entropies for kinetic equations in bounded domains irreversibility stationary solutions uniqueness the relative entropy method describes the irreversibility of the vlasov poisson and vlasov boltzmann poisson systems in bounded domains with incoming boundary conditions uniform in time estimates are deduced from the entropy in some cases these estimates are sufficient to prove the convergence of the solution to a unique stationary solution as time goes to infinity the method is also used to analyse other types of boundary conditions such as mass and energy preserving diffuse reflection boundary conditions and to prove the uniqueness of stationary solutions for some special collision terms

a novel bayesian logistic discriminant model an application to face recognition the linear discriminant analysis lda is a linear classifier which has proven to be powerful and competitive compared to the main state of the art classifiers however the lda algorithm assumes the sample vectors of each class are generated from underlying multivariate normal distributions of common covariance matrix with different means i e homoscedastic data this assumption has restricted the use of lda considerably over the years authors have defined several extensions to the basic formulation of lda one such method is the heteroscedastic lda hlda which is proposed to address the heteroscedasticity problem another method is the nonparametric da nda where the normality assumption is relaxed in this paper we propose a novel bayesian logistic discriminant bld model which can address both normality and heteroscedasticity problems the normality assumption is relaxed by approximating the underlying distribution of each class with a mixture of gaussians hence the proposed bld provides more flexibility and better classification performances than the lda hlda and nda a subclass and multinomial versions of the bld are proposed the posterior distribution of the bld model is elegantly approximated by a tractable gaussian form using variational transformation and jensen s inequality allowing a straightforward computation of the weights an extensive comparison of the bld to the lda support vector machine svm hlda nda and subclass discriminant analysis sda performed on artificial and real data sets has shown the advantages and superiority of our proposed method in particular the experiments on face recognition have clearly shown a significant improvement of the proposed bld over the lda

cauchy problem for the vlasov poisson boltzmann system the dynamics of dilute electrons can be modelled by the fundamental vlasov poisson boltzmann system which describes mutual interactions of the electrons through collisions in the self consistent electric field in this paper it is shown that any smooth perturbation of a given global maxwellian leads to a unique global in time classical solution when either the mean free path is small or the background charge density is large moreover the solution converges to the global maxwellian when time tends to infinity the analysis combines the techniques used in the study of conservation laws with the decomposition of the boltzmann equation introduced in 17 19 by obtaining new entropy estimates for this physical model

existence of stationary solutions to the vlasov poisson boltzmann system abstract in this paper we study the existence of stationary solutions to the vlasov poisson boltzmann system when the background density function tends to a positive constant with a very mild decay rate as x in fact the stationary vlasov poisson boltzmann system can be written into an elliptic equation with exponential nonlinearity under the assumption on the decay rate being ln e x for some 0 it is shown that this elliptic equation has a unique solution this result generalizes the previous work r glassey j schaeffer y zheng steady states of the vlasov poisson fokker planck system j math anal appl 202 1996 1058 1075 where the decay rate 1 x 1 2 is assumed

asymptotic behavior of an initial boundary value problem for the vlasov poisson fokker planck system the asymptotic behavior for the vlasov poisson fokker planck system in bounded domains is analyzed in this paper boundary conditions defined by a scattering kernel are considered it is proven that the distribution of particles tends for large time to a maxwellian determined by the solution of the poisson boltzmann equation with dirichlet boundary condition in the proof of the main result the conservation law of mass and the balance of energy and entropy identities are rigorously derived an important argument in the proof is to use a lyapunov type functional related to these physical quantities

on the behaviour of wald statistics for the disjunction of two regular hypotheses occasionally hypotheses arise which although not themselves regular have the logical structure of the disjunction of two or in general several regular hypotheses an example of such a hypothesis is that of collapsibility in a three way contingency table as defined by whittemore when such a hypothesis is to be tested a wald test appears superficially to offer a convenient solution however closer inspection reveals that the irregularity intrinsic to such problems precludes the regularity conditions required for the valid construction of a wald test statistic the purpose of this paper is to describe explicitly the nature of the irregularity and its effect on the asymptotic behaviour of the wald test statistic

subclass discriminant analysis over the years many discriminant analysis da algorithms have been proposed for the study of high dimensional data in a large variety of problems each of these algorithms is tuned to a specific type of data distribution that which best models the problem at hand unfortunately in most problems the form of each class pdf is a priori unknown and the selection of the da algorithm that best fits our data is done over trial and error ideally one would like to have a single formulation which can be used for most distribution types this can be achieved by approximating the underlying distribution of each class with a mixture of gaussians in this approach the major problem to be addressed is that of determining the optimal number of gaussians per class i e the number of subclasses in this paper two criteria able to find the most convenient division of each class into a set of subclasses are derived extensive experimental results are shown using five databases comparisons are given against linear discriminant analysis lda direct lda dlda heteroscedastic lda hlda nonparametric da nda and kernel based lda k lda we show that our method is always the best or comparable to the best

some statistical properties of a family of continuous univariate distributions abstract a new two parameter family of continuous univariate distributions on the interval 1 1 is introduced and some properties are given it is shown that parameters and v are globally orthogonal in the fisher information sense and that to some extent they have the properties of a location parameter and a precision parameter respectively a pivotal statistic is constructed whose distribution is independent of the location parameter finally the connection with ultraspherical functions and brownian motion is described

steady states of the vlasov poisson fokker planck system abstract the form of steady state solutions to the vlasov poisson fokker planck system is known from the works of dressler and others in these papers an external potential is present which tends to infinity as x it is shown here that this assumption is needed to obtain nontrivial steady states this is achieved by showing that for a given nonnegative background density satisfying certain integrability conditions only the trivial solution is possible this result is sharp and exactly matches the known existence criteria of f bouchut and j dolbeault differential integral equations 8 1995 487 514 and others these steady states are solutions to a nonlinear elliptic equation with an exponential nonlinearity for a given background density which is asymptotically constant it is directly shown by elementary means that this nonlinear elliptic equation possesses a smooth and uniquely determined global solution

weighted pseudometric discriminatory power improvement using a bayesian logistic regression model based on a variational method in this paper we investigate the effectiveness of a bayesian logistic regression model to compute the weights of a pseudometric in order to improve its discriminatory capacity and thereby increase image retrieval accuracy in the proposed bayesian model the prior knowledge of the observations is incorporated and the posterior distribution is approximated by a tractable gaussian form using variational transformation and jensen s inequality which allow a fast and straightforward computation of the weights the pseudometric makes use of the compressed and quantized versions of wavelet decomposed feature vectors and in our previous work the weights were adjusted by the classical logistic regression model a comparative evaluation of the bayesian and classical logistic regression models is performed for content based image retrieval as well as for other classification tasks in a decontextualized evaluation framework in this same framework we compare the bayesian logistic regression model to some relevant state of the art classification algorithms experimental results show that the bayesian logistic regression model outperforms these linear classification algorithms and is a significantly better tool than the classical logistic regression model to compute the pseudometric weights and improve retrieval and classification performance finally we perform a comparison with results obtained by other retrieval methods

generalized discriminant analysis using a kernel approach we present a new method that we call generalized discriminant analysis gda to deal with nonlinear discriminant analysis using kernel function operator the underlying theory is close to the support vector machines svm insofar as the gda method provides a mapping of the input vectors into high dimensional feature space in the transformed space linear properties make it easy to extend and generalize the classical linear discriminant analysis lda to nonlinear discriminant analysis the formulation is expressed as an eigenvalue problem resolution using a different kernel one can cover a wide class of nonlinearities for both simulated data and alternate kernels we give classification results as well as the shape of the decision function the results are confirmed using real data to perform seed classification

large time behavior of solutions to vlasov poisson fokker planck equations from evanescent collisions to diffusive limit the present contribution investigates the dynamics generated by the two dimensional vlasov poisson fokker planck equation for charged particles in a steady inhomogeneous background of opposite charges we provide global in time estimates that are uniform with respect to initial data taken in a bounded set of a weighted l 2 space and where dependencies on the mean free path tau and the debye length delta are made explicit in our analysis the mean free path covers the full range of possible values from the regime of evanescent collisions tau to infty to the strongly collisional regime tau to0 as a counterpart the largeness of the debye length that enforces a weakly nonlinear regime is used to close our nonlinear estimates accordingly we pay a special attention to relax as much as possible the tau dependent constraint on delta ensuring exponential decay with explicit tau dependent rates towards the stationary solution in the strongly collisional limit tau to0 we also examine all possible asymptotic regimes selected by a choice of observation time scale here also our emphasis is on strong convergence uniformity with respect to time and to initial data in bounded sets of a l 2 space our proofs rely on a detailed study of the nonlinear elliptic equation defining stationary solutions and a careful tracking and optimization of parameter dependencies of hypocoercive hypoelliptic estimates

global existence of classical solutions to the vlasov poisson boltzmann system the time evolution of the distribution function for the charged particles in a dilute gas is governed by the vlasov poisson boltzmann system when the force is self induced and its potential function satisfies the poisson equation in this paper we give a satisfactory global existence theory of classical solutions to this system when the initial data is a small perturbation of a global maxwellian moreover the convergence rate in time to the global maxwellian is also obtained through the energy method the proof is based on the theory of compressible navier stokes equations with forcing and the decomposition of the solutions to the boltzmann equation with respect to the local maxwellian introduced in 23 and elaborated in 31

linear dimensionality reduction via a heteroscedastic extension of lda the chernoff criterion we propose an eigenvector based heteroscedastic linear dimension reduction ldr technique for multiclass data the technique is based on a heteroscedastic two class technique which utilizes the so called chernoff criterion and successfully extends the well known linear discriminant analysis lda the latter which is based on the fisher criterion is incapable of dealing with heteroscedastic data in a proper way for the two class case the between class scatter is generalized so to capture differences in co variances it is shown that the classical notion of between class scatter can be associated with euclidean distances between class means from this viewpoint the between class scatter is generalized by employing the chernoff distance measure leading to our proposed heteroscedastic measure finally using the results from the two class case a multiclass extension of the chernoff criterion is proposed this criterion combines separation information present in the class mean as well as the class covariance matrices extensive experiments and a comparison with similar dimension reduction techniques are presented

existence and uniqueness of a global smooth solution for the vlasov poisson fokker planck system in three dimensions abstract studying precisely the regularity of the force field created by the solution of the linear vlasov fokker planck equation we prove existence and uniqueness of a smooth solution to the vlasov poisson fokker planck system in three dimensions the attractive and repulsive cases are treated the method involves an analysis of the effect of the fokker planck kernel without any force field on non linear expressions coming from the vlasov term

simple and robust solver for the poisson boltzmann equation a variational approach is used to develop a robust numerical procedure for solving the nonlinear poisson boltzmann equation following maggs and rossetto phys rev lett 88 196402 2002 we construct an appropriate constrained free energy functional such that its euler lagrange equations are equivalent to the poisson boltzmann equation this is a formulation that searches for a true minimum in function space in contrast to previous variational approaches that rather searched for a saddle point we then develop implement and test an algorithm for its numerical minimization which is quite simple and unconditionally stable the analytic solution for planar geometry is used for validation some results are presented for a charged colloidal sphere surrounded by counterions and optimizations based upon fast fourier transforms and hierarchical preconditioning are briefly discussed