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

bilum block versions of multielimination and multilevel ilu preconditioner for general sparse linear systems we introduce block versions of the multielimination incomplete lu ilum factorization preconditioning technique for solving general sparse unstructured linear systems these preconditioners have a multilevel structure and for certain types of problems may exhibit properties that are typically enjoyed by multigrid methods several heuristic strategies for forming blocks of independent sets are introduced and their relative merits are discussed the advantages of block ilum over point ilum include increased robustness and efficiency we compare several versions of the block ilum point ilum and the dual threshold based ilut preconditioners in particular tests with some convection diffusion problems show that it may be possible to obtain convergence that is nearly independent of the reynolds number as well as of the grid size

probabilistic visual learning for object representation we present an unsupervised technique for visual learning which is based on density estimation in high dimensional spaces using an eigenspace decomposition two types of density estimates are derived for modeling the training data a multivariate gaussian for unimodal distributions and a mixture of gaussians model for multimodal distributions those probability densities are then used to formulate a maximum likelihood estimation framework for visual search and target detection for automatic object recognition and coding our learning technique is applied to the probabilistic visual modeling detection recognition and coding of human faces and nonrigid objects such as hands

an improved algorithm for the evaluation of cauchy principal value integrals of oscillatory functions and its application abstract a new interpolatory type quadrature rule is proposed for the numerical evaluation of cauchy principal value integrals of oscillatory kind 1 1 f x x e i x d x where 1 1 the method is based on an interpolatory procedure at clenshaw curtis points and the singular point and the fast computation of the modified moments with cauchy type singularity based on this result a new method is presented for the computation of the oscillatory integrals with logarithmic singularities too these methods enjoy fast implementation and high accuracy convergence rates on are also provided numerical examples support the theoretical analyses

algorithmique et calculs de complexite pour un solveur de type dissections emboitees we consider the nested dissection method based on separator theorems introduced by gilbert tarjan and roman used for solving large sparse systems of linear equations more precisely we study a block storage scheme such as proposed by george for regular square grids and we prove the following results first for families of graphs of bounded degree withn separator theorem 1 2 1 the overhead storage of the block data structure for the factored matrix is linear in system dimension on the other hand by adding a non restrictive assumption on the separation this structure can be constructed by a block symbolic factorization which runs in time linear in matrix dimension numerical experiments illustrating these theoretical results are provided on considere la methode de dissections emboitees basee sur des theoremes de separation introduite par gilbert tarjan et roman utilisee pour la resolution par elimination de gauss de grands systemes lineaires creux plus precisemment on etudie une structure de donnees par blocs similaire a celle proposee par george dans le cadre des graphes en grille et on demontre les proprietes suivantes d une part pour des familles de graphes a degre borne admettant unn theoreme de separation 1 2 1 le stockage secondaire de la structure par blocs contenant la matrice factorisee est lineaire par rapport a la taille du systeme d autre part en rajoutant une hypothese non restrictive sur la maniere d effectuer la separation la structure peut etre construite en temps lineaire par une factorisation logique par blocs des exemples numeriques illustrent ces resultats theoriques

uniform approximation to finite hilbert transform of oscillatory functions and its algorithm abstract for the finite hilbert transform of oscillatory functions q f c 1 1 f x e i x x c d t with a smooth function f and real 0 for c 1 1 in the sense of cauchy principal value or for c 1 of hadamard finite part we present an approximation method of clenshaw curtis type and its algorithm interpolating f by a polynomial p n of degree n and expanding in terms of the chebyshev polynomials with o n log n operations by the fft we obtain an approximation q p n c q f c we write q p n c as a sum of the sine and cosine integrals and an oscillatory integral of a polynomial of degree n 1 we efficiently evaluate the oscillatory integral with a combination of authors previous method and keller s method for f z analytic on the interval 1 1 in the complex plane z the error of q p n c is bounded uniformly with respect to c and numerical examples illustrate the performance of our method

log determinant relaxation for approximate inference in discrete markov random fields graphical models are well suited to capture the complex and non gaussian statistical dependencies that arise in many real world signals a fundamental problem common to any signal processing application of a graphical model is that of computing approximate marginal probabilities over subsets of nodes this paper proposes a novel method applicable to discrete valued markov random fields mrfs on arbitrary graphs for approximately solving this marginalization problem the foundation of our method is a reformulation of the marginalization problem as the solution of a low dimensional convex optimization problem over the marginal polytope exactly solving this problem for general graphs is intractable for binary markov random fields we describe how to relax it by using a gaussian bound on the discrete entropy and a semidefinite outer bound on the marginal polytope this combination leads to a log determinant maximization problem that can be solved efficiently by interior point methods thereby providing approximations to the exact marginals we show how a slightly weakened log determinant relaxation can be solved even more efficiently by a dual reformulation when applied to denoising problems in a coupled mixture of gaussian model defined on a binary mrf with cycles we find that the performance of this log determinant relaxation is comparable or superior to the widely used sum product algorithm over a range of experimental conditions

fast computation of a class of highly oscillatory integrals in this paper the problem of numerical evaluation of a class of highly oscillatory integrals a b f x x a b x k 1 n x k k e i x dx where 1 k 1 a k b and 1 has been discussed based on analytic continuation the integrals are transformed into the problems of integrating the forms on 0 with the integrand does not oscillate and decays exponentially fast which can be efficiently computed by using general gauss laguerre quadrature rule theoretical results and numerical experiments perform that the method is very efficient in obtaining very high precision approximations if is sufficiently large

discriminative common vectors for face recognition in face recognition tasks the dimension of the sample space is typically larger than the number of the samples in the training set as a consequence the within class scatter matrix is singular and the linear discriminant analysis lda method cannot be applied directly this problem is known as the small sample size problem in this paper we propose a new face recognition method called the discriminative common vector method based on a variation of fisher s linear discriminant analysis for the small sample size case two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database one algorithm uses the within class scatter matrix of the samples in the training set while the other uses the subspace methods and the gram schmidt orthogonalization procedure to obtain the discriminative common vectors then the discriminative common vectors are used for classification of new faces the proposed method yields an optimal solution for maximizing the modified fisher s linear discriminant criterion given in the paper our test results show that the discriminative common vector method is superior to other methods in terms of recognition accuracy efficiency and numerical stability

a well conditioned levin method for calculation of highly oscillatory integrals and its application abstract this paper is devoted to studying efficient calculation of generalized fourier transform 1 x f t e i g t d t for the general phase function g t we develop a modified levin method by the spectral coefficient approach a sparse and well conditioned linear system is constructed to help accelerate calculation of highly oscillatory integrals numerical examples are included to show the convergence properties of the new method with respect to both quantities of collocation points and the frequency furthermore we apply this approach to solving oscillatory volterra integral equations

optimizing the kernel in the empirical feature space in this paper we present a method of kernel optimization by maximizing a measure of class separability in the empirical feature space an euclidean space in which the training data are embedded in such a way that the geometrical structure of the data in the feature space is preserved employing a data dependent kernel we derive an effective kernel optimization algorithm that maximizes the class separability of the data in the empirical feature space it is shown that there exists a close relationship between the class separability measure introduced here and the alignment measure defined recently by cristianini extensive simulations are carried out which show that the optimized kernel is more adaptive to the input data and leads to a substantial sometimes significant improvement in the performance of various data classification algorithms

asymptotic expansions and fast computation of oscillatory hilbert transforms in this paper we study the asymptotics and fast computation of the one sided oscillatory hilbert transforms of the form begin aligned h f t e i omega t x int nolimits 0 infty e i omega t frac f t t x dt quad omega 0 quad x ge 0 end aligned where the bar indicates the cauchy principal value and f is a real valued function with analytic continuation in the first quadrant except possibly a branch point of algebraic type at the origin when x 0 the integral is interpreted as a hadamard finite part integral provided it is divergent asymptotic expansions in inverse powers of omega are derived for each fixed x ge 0 which clarify the large omega behavior of this transform we then present efficient and affordable approaches for numerical evaluation of such oscillatory transforms depending on the position of x we classify our discussion into three regimes namely x mathcal o 1 or x gg 1 0 x ll 1 and x 0 numerical experiments show that the convergence of the proposed methods greatly improve when the frequency omega increases some extensions to oscillatory hilbert transforms with bessel oscillators are briefly discussed as well

on the evaluation of cauchy principal value integrals of oscillatory functions the problem of the numerical evaluation of cauchy principal value integrals of oscillatory functions 1 1e i w xf x x tdx where 1 t 1 has been discussed based on analytic continuation if f is analytic in a sufficiently large complex region g containing 1 1 the integrals can be transformed into the problems of integrating two integrals on 0 with the integrand that does not oscillate and that decays exponentially fast which can be efficiently computed by using the gauss laguerre quadrature rule the validity of the method has been demonstrated in the provision of two numerical experiments and their results

quadrature formulae for cauchy principal value integrals of oscillatory kind etude de l evaluation numerique d une integrale 7b f 1 1 exp i x f x dx ou f possede un pole simple dans l intervalle 1 1 application de la formule d interpolation de lagrange estimation de l erreur et exemples numeriques

finite element network approximation of conductivity in particle composites a new finite element method computes conductivity in some unstructured particle reinforced composite material the 2 phase material under consideration is composed of a poorly conducting matrix material filled by highly conducting circular inclusions which are randomly dispersed the mathematical model is a poisson type problem with discontinuous coefficients the discontinuities are huge in contrast and quantity the proposed method generalizes classical continuous piecewise affine finite elements to special computational meshes which encode the particles in a network structure important geometric parameters such as the volume fraction are preserved exactly the computational complexity of the method is almost proportional to the number of inclusions this is minimal in the sense that the representation of the underlying geometry via the positions and radii of the inclusions is of the same complexity the discretization error is proportional to the distance of neighboring inclusions and independent of the conductivity contrast in the medium

efficient integration for a class of highly oscillatory integrals abstract this paper presents some quadrature methods for a class of highly oscillatory integrals whose integrands may have singularities at the two endpoints of the interval one is a filon type method based on the asymptotic expansion the other is a clenshaw curtis filon type method which is based on a special hermite interpolation polynomial and can be evaluated efficiently in o n log n operations where n 1 is the number of clenshaw curtis points in the interval of integration in addition we derive the corresponding error bound in inverse powers of the frequency for the clenshaw curtis filon type method for the class of highly oscillatory integrals the efficiency and the validity of these methods are testified by both the numerical experiments and the theoretical results

a unified framework for subspace face recognition pca lda and bayesian analysis are the three most representative subspace face recognition approaches in this paper we show that they can be unified under the same framework we first model face difference with three components intrinsic difference transformation difference and noise a unified framework is then constructed by using this face difference model and a detailed subspace analysis on the three components we explain the inherent relationship among different subspace methods and their unique contributions to the extraction of discriminating information from the face difference based on the framework a unified subspace analysis method is developed using pca bayes and lda as three steps a 3d parameter space is constructed using the three subspace dimensions as axes searching through this parameter space we achieve better recognition performance than standard subspace methods

bayes error estimation using parzen and k nn procedures the use of k nearest neighbor k nn and parzen density estimates to obtain estimates of the bayes error is investigated under limited design set conditions by drawing analogies between the k nn and parzen procedures new procedures are suggested and experimental results are given which indicate that these procedures yield a significant improvement over the conventional k nn and parzen procedures we show that by varying the decision threshold many of the biases associated with the k nn or parzen density estimates may be compensated and successful error estimation may be performed in spite of these biases experimental results are given which demonstrate the effect of kernel size and shape parzen the size of k k nn and the number of samples in the design set

input feature selection by mutual information based on parzen window mutual information is a good indicator of relevance between variables and have been used as a measure in several feature selection algorithms however calculating the mutual information is difficult and the performance of a feature selection algorithm depends on the accuracy of the mutual information in this paper we propose a new method of calculating mutual information between input and class variables based on the parzen window and we apply this to a feature selection algorithm for classification problems

clenshaw curtis type quadrature rule for hypersingular integrals with highly oscillatory kernels abstract the clenshaw curtis type quadrature rule is proposed for the numerical evaluation of the hypersingular integrals with highly oscillatory kernels and weak singularities at the end points for any smooth functions g x based on the fast hermite interpolation this paper provides a stable recurrence relation for these modified moments convergence rates with respect to the frequency k and the number of interpolation points n are considered these theoretical results and high accuracy of the presented algorithm are illustrated by some numerical examples

on quadrature for cauchy principal value integrals of oscillatory functions the authors develop an algorithm for the numerical evaluation of cauchy principal value integrals of oscillatory functions the method is based on an interpolatory procedure at the zeros of the orthogonal polynomials with respect to a jacobi weight a numerically stable procedure is obtained and the corresponding algorithm can be implemented in a fast way yielding satisfactory numerical results bounds of the error and of the amplification factor are also provided

on the calculation of highly oscillatory integrals with an algebraic singularity abstract in this paper we explore the evaluation of highly oscillatory integrals containing an algebraic singularity based on the change of variable t x r where r is a positive real number and the analytical continuation robust numerical results demonstrate the accuracy and effectiveness of the proposed approach

face recognition using kernel direct discriminant analysis algorithms techniques that can introduce low dimensional feature representation with enhanced discriminatory power is of paramount importance in face recognition fr systems it is well known that the distribution of face images under a perceivable variation in viewpoint illumination or facial expression is highly nonlinear and complex it is therefore not surprising that linear techniques such as those based on principle component analysis pca or linear discriminant analysis lda cannot provide reliable and robust solutions to those fr problems with complex face variations in this paper we propose a kernel machine based discriminant analysis method which deals with the nonlinearity of the face patterns distribution the proposed method also effectively solves the so called small sample size sss problem which exists in most fr tasks the new algorithm has been tested in terms of classification error rate performance on the multiview umist face database results indicate that the proposed methodology is able to achieve excellent performance with only a very small set of features being used and its error rate is approximately 34 and 48 of those of two other commonly used kernel fr approaches the kernel pca kpca and the generalized discriminant analysis gda respectively

efficient evaluation of oscillatory bessel hilbert transforms in this paper we study the asymptotics and evaluation of the oscillatory bessel hilbert transform 0 f x email protected n wx dx with 0 t the singularity of the hilbert transform is transferred to an individual oscillatory integral independent of f x for this singular integral we present two methods one is the combination of a filon type method and a complex integration method the other is the combination of a filon type method and an adaptive clenshaw curtis quadrature the remaining integral which is nonsingular can be well calculated with a combination of a filon type method and a gauss laguerre quadrature the efficiency and accuracy of the proposed methods are illustrated by numerical examples

computing cauchy principal value integrals using a standard adaptive quadrature we investigate the possibility of fast accurate and reliable computation of the cauchy principal value integrals a b f x x 1 d x a b using a standard adaptive quadrature in order to properly control the error tolerance for the adaptive quadrature and to obtain a reliable estimation of the approximation error we research the possible influence of round off errors on the computed result as the numerical experiments confirm the proposed method can successfully compete with other algorithms for computing such type integrals moreover the presented method is very easy to implement on any system equipped with a reliable adaptive integration subroutine

a practical algorithm for computing cauchy principal value integrals of oscillatory functions abstract a new automatic quadrature scheme is proposed for evaluating cauchy principal value integrals of oscillatory functions 1 1 f x exp i x x 1 dx 1 1 r the desired approximation is obtained by expanding the function f in the series of chebyshev polynomials of the first kind and then by constructing the indefinite integral for a properly modified integrand to overcome the singularity the method is proved to converge uniformly with respect to both and for any function f satisfying max 1 x 1 f x

image covariance based subspace method for face recognition this paper proposes a new subspace method that is based on image covariance obtained from windowed features of images a windowed input feature consists of a number of pixels and the dimension of input space is determined by the number of windowed features each element of an image covariance matrix can be obtained from the inner product of two windowed features the 2d pca and 2d lda methods are then obtained from principal component analysis and linear discriminant analysis respectively using the image covariance matrix in the case of 2d lda there is no need for pca preprocessing and the dimension of subspace can be greater than the number of classes because the within class and between class image covariance matrices have full ranks comparative experiments are performed using the feret cmu and orl databases of facial images the experimental results show that the proposed 2d lda provides the best recognition rate among several subspace methods in all of the tests

roundoff errors in the problem of computing cauchy principal value integrals we investigate the possibility of fast accurate and reliable computation of the cauchy principal value integrals mathrm p int a b f x x tau 1 dx a tau b using standard adaptive quadratures in order to properly control the error tolerance for the adaptive quadrature and to obtain a reliable estimation of the approximation error we research the possible influence of round off errors on the computed result as the numerical experiments confirm the proposed method can successfully compete with other algorithms for computing such type integrals moreover the presented method is very easy to implement on any system equipped with a reliable adaptive integration subroutine

multiclass linear dimension reduction by weighted pairwise fisher criteria we derive a class of computationally inexpensive linear dimension reduction criteria by introducing a weighted variant of the well known k class fisher criterion associated with linear discriminant analysis lda it can be seen that lda weights contributions of individual class pairs according to the euclidean distance of the respective class means we generalize upon lda by introducing a different weighting function

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

efficient computation of highly oscillatory integrals with hankel kernel in this paper we consider the evaluation of two kinds of oscillatory integrals with a hankel function as kernel we first rewrite these integrals as the integrals of fourier type by analytic continuation these fourier type integrals can be transformed into the integrals on 0 the integrands of which are not oscillatory and decay exponentially fast consequently the transformed integrals can be efficiently computed by using the generalized gauss laguerre quadrature rule moreover the error analysis for the presented methods is given the efficiency and accuracy of the methods have been demonstrated by both numerical experiments and theoretical results

on the evaluation of highly oscillatory integrals by analytic continuation we consider the integration of one dimensional highly oscillatory functions based on analytic continuation rapidly converging quadrature rules are derived for a general class of oscillatory integrals with an analytic integrand the accuracy of the quadrature increases both for the case of a fixed number of points and increasing frequency and for the case of an increasing number of points and fixed frequency these results are then used to obtain quadrature rules for more general oscillatory integrals i e for functions that exhibit some smoothness but that are not analytic the approach described in this paper is related to the steepest descent method but it does not employ asymptotic expansions it can be used for small or moderate frequencies as well as for very high frequencies the approach is compared with the oscillatory integration techniques recently developed by iserles and norsett

calculation of incompressible viscous flows by an unconditionally stable projection fem this paper investigates the numerical performance of a finite element implementation of a new incremental fractional step method to compute steady and unsteady incompressible viscous flows under general boundary conditions and using unstructured meshes a variational framework is adopted which accommodates two different spaces for representing and approximating the velocity fields calculated respectively in the viscous and inviscid phases of the method but which leads to a very simple numerical scheme in terms of only one discrete velocity field an unconditionally stable semi implicit approximation of the nonlinear term is used to eliminate any time step restriction as far as the numerical stability is concerned numerical results for five test problems in two dimensions are reported to illustrate the flexibility of the proposed method

numerical calculation of integrals involving oscillatory and singular kernels and some applications of quadratures numerical methods for strongly oscillatory and singular functions are given in this paper beside a summary of standard methods and product integration rules we consider a class of complex integration methods several applications of quadrature processes in problems in telecom munications and physics are also presented 1998 elsevier science ltd all rights reserved integration oscillatory kernel singular kernel orthogonal polynomials product rules gaussian quaclratures error function bessel functions legendre functions

lu decomposition and numerical structure for solving large sparse nonsymmetric linear systems abstract in this work the solution of a large sparse linear system of equations with an arbitrary sparsity pattern is obtained by using lu decomposition method as well as numerical structure approach the lu decomposition method is based on doolittle s method while the numerical structure approach is based on cramer s rule the numerical structure approach produces direct solution without facing fill in problems as encountered in lu decomposition in order to reduce the fill ins in the decomposition the powers of a boolean matrix obtained from the coefficient matrix a are taken so that the fill ins in the structure of a can be known in advance the position of fill ins in a are thus determined in the best choice manner that is it is very effective and memory wise cheap we also outline a method by using numerical structure with reduced computation efforts finally experiments are performed on eight examples to compare the efficiency of the proposed methods the results obtained are reported in a table it is found that the lu decomposition method is much better than numerical structure the usefulness of numerical structure approach is also discussed

efficient quadrature of highly oscillatory integrals with algebraic singularities in this paper we are concerned with the numerical evaluation of a class of highly oscillatory integrals containing algebraic singularities first we expand such integrals derived by two transformations t x b b 0 t 21 z email protected email protected 1 into asymptotic series in inverse powers of the frequency w then based the asymptotic series two methods are presented one is the filon type method the other is the clenshaw curtis filon type method which is based on a special hermite interpolation polynomial in the clenshaw curtis points and can be evaluated efficiently in o nlogn operations where n 1 is the number of clenshaw curtis points in the interval of integration some error and convergence analysis and robust numerical examples are used to demonstrate the accuracy and effectiveness of the proposed approaches for approximating the class of highly oscillatory singular integrals

a discriminant analysis using composite features for classification problems in this paper we propose a new discriminant analysis using composite features for pattern classification a composite feature consists of a number of primitive features each of which corresponds to an input variable the covariance of composite features is obtained from the inner product of composite features and can be considered as a generalized form of the covariance of primitive features it contains information on statistical dependency among multiple primitive features a discriminant analysis c lda using the covariance of composite features is a generalization of the linear discriminant analysis lda unlike lda the number of extracted features can be larger than the number of classes in c lda which is a desirable property especially for binary classification problems experimental results on several data sets indicate that c lda provides better classification results than other methods based on primitive features

the nearest subclass classifier a compromise between the nearest mean and nearest neighbor classifier we present the nearest subclass classifier nsc which is a classification algorithm that unifies the flexibility of the nearest neighbor classifier with the robustness of the nearest mean classifier the algorithm is based on the maximum variance cluster algorithm and as such it belongs to the class of prototype based classifiers the variance constraint parameter of the cluster algorithm serves to regularize the classifier that is to prevent overfitting with a low variance constraint value the classifier turns into the nearest neighbor classifier and with a high variance parameter it becomes the nearest mean classifier with the respective properties in other words the number of prototypes ranges from the whole training set to only one per class in the experiments we compared the nsc with regard to its performance and data set compression ratio to several other prototype based methods on several data sets the nsc performed similarly to the k nearest neighbor classifier which is a well established classifier in many domains also concerning storage requirements and classification speed the nsc has favorable properties so it gives a good compromise between classification performance and efficiency

nonparametric discriminant analysis a nonparametric method of discriminant analysis is proposed it is based on nonparametric extensions of commonly used scatter matrices two advantages result from the use of the proposed nonparametric scatter matrices first they are generally of full rank this provides the ability to specify the number of extracted features desired this is in contrast to parametric discriminant analysis which for an l class problem typically can determine at most l 1 features second the nonparametric nature of the scatter matrices allows the procedure to work well even for non gaussian data sets using the same basic framework a procedure is proposed to test the structural similarity of two distributions the procedure works in high dimensional space it specifies a linear decomposition of the original data space in which a relative indication of dissimilarity along each new basis vector is provided the nonparametric scatter matrices are also used to derive a clustering procedure which is recognized as a k nearest neighbor version of the nonparametric valley seeking algorithm the form which results provides a unified view of the parametric nearest mean reclassification algorithm and the nonparametric valley seeking algorithm

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

calculs de complexite relatifs a une methode de dissection emboitee nous presentons une numerotation de type nested dissection des inconnues d un systeme lineaireax b pour des ensembles de matricescreuses symetriques definies positives correspondant a des famille de graphes non orientes a degre borne et admettant un sqrt n thereme de separation comparativement aux methodes et resultats de rose 9 l algorithme presente est plus simple mais les theoremes de complexite moins generaux en raison de l hypothese restrictive de degre borne en outre les demonstrations font appel en permanence a la structure d arbre sur la famille des separateurs qui constitue par ailleurs une partition de l ensemble des sommets du graphe initial nous presentons ensuite le schema general d implementation dans le cadre du code d elements finis modulef pourdes problemes plans d elements finis et nous donnons quelques mesures comparatives avec la numerotation plus classique qui tend a minimiser le profil de la matrice a nested dissection ordering is given for solving any system of linear equationsax b for the family ofsparse symmetric positive definite matrices corresponding to the class of undirected graphs withbounded degree and satisfyinga sqrt n separator theorem if we compare the methods and results presented by rose 9 our algorithm is more simple but the complexity results are less general because of the restriction of bounded degree besides our proofs use continually the arborescent structure on the family of separators which is by another way a partition of the set of vertices for the initial graph then the general implementation scheme in the finite element package modulef fortwo dimensional finite element problems is presented and numerical comparisons between our ordering and the standard envelope method are given

on fast multipole methods for volterra integral equations with highly oscillatory kernels abstract this paper explores the fast multipole methods fmms to accelerate the approximation for weakly singular volterra integral equations with highly oscillatory trigonometric kernels by constructing the fast translation path the fmm is utilized to speed up the iterative method which reduces the complexity from o n 2 to o n especially we use the collocation method to discretize the volterra integral equation with constants and linear elements respectively then apply the gmres to solve the dense and non symmetric linear system in addition the highly oscillatory integrals derived from the algorithm are calculated effectively by the steepest descent method the proposed method shows that the numerical solutions become more accurate as the frequency increases both of the optimal convergence rates of truncation and the error bounds analysis are represented in the end

gabor feature based classification using the enhanced fisher linear discriminant model for face recognition this paper introduces a novel gabor fisher 1936 classifier gfc for face recognition the gfc method which is robust to changes in illumination and facial expression applies the enhanced fisher linear discriminant model efm to an augmented gabor feature vector derived from the gabor wavelet representation of face images the novelty of this paper comes from 1 the derivation of an augmented gabor feature vector whose dimensionality is further reduced using the efm by considering both data compression and recognition generalization performance 2 the development of a gabor fisher classifier for multi class problems and 3 extensive performance evaluation studies in particular we performed comparative studies of different similarity measures applied to various classifiers we also performed comparative experimental studies of various face recognition schemes including our novel gfc method the gabor wavelet method the eigenfaces method the fisherfaces method the efm method the combination of gabor and the eigenfaces method and the combination of gabor and the fisherfaces method the feasibility of the new gfc method has been successfully tested on face recognition using 600 feret frontal face images corresponding to 200 subjects which were acquired under variable illumination and facial expressions the novel gfc method achieves 100 accuracy on face recognition using only 62 features

on uniform approximations to hypersingular finite part integrals abstract in this paper new uniform approximation schemes for computation of hypersingular finite part integrals are studied the methods are verified to be supremely qualified for oscillatory integrands in addition based on the results on chebyshev approximations the uniform convergence and computational error bounds are considered preliminary numerical results show the stability and efficiency of the schemes

on the numerical approximation for fourier type highly oscillatory integrals with gauss type quadrature rules in this paper we present an improved numerical steepest descent method for the approximation of fourier type highly oscillatory integrals based on the previous numerical steepest descent method the new method used the integrand information at endpoints and stationary points the asymptotic order is given that is improved both for the case of stationary points and stationary points free several numerical examples are presented which show the high efficiency of the proposed method numerical results support our theoretical analyses

the analysis of a nested dissection algorithm nested dissection is an algorithm invented by alan george for preserving sparsity in gaussian elimination on symmetric positive definite matrices nested dissection can be viewed as a recursive divide and conquer algorithm on an undirected graph it usesseparators in the graph which are small sets of vertices whose removal divides the graph approximately in half george and liu gave an implementation of nested dissection that used a heuristic to find separators lipton and tarjan gave an algorithm to findn1 2 separators in planar graphs and two dimensional finite element graphs and lipton rose and tarjan used these separators in a modified version of nested dissection guaranteeing bounds ofo n logn on fill ando n3 2 on operation count we analyze the combination of the original george liu nested dissection algorithm and the lipton tarjan planar separator algorithm this combination is interesting because it is easier to implement than the lipton rose tarjan version especially in the framework of existing sparse matrix software using some topological graph theory we proveo n logn fill ando n3 2 operation count bounds for planar graphs twodimensional finite element graphs graphs of bounded genus and graphs of bounded degree withn1 2 separators for planar and finite element graphs the leading constant factor is smaller than that in the lipton rose tarjan analysis we also construct a class of graphs withn1 2 separators for which our algorithm does not achieve ano n logn bound on fill