high order methods for low reynolds number flows around moving obstacles based on universal meshes summary we propose a family of methods for simulating two dimensional incompressible low reynolds number flow around a moving obstacle whose motion is prescribed the methods make use of a universal mesh a fixed background mesh that adapts to the geometry of the immersed obstacle at all times by adjusting a few elements in the neighborhood of the obstacle s boundary the resulting mesh provides a conforming triangulation of the fluid domain over which discretizations of any desired order of accuracy in space and time can be constructed using standard finite element spaces together with off the shelf time integrators we demonstrate the approach by using taylor hood elements to approximate the fluid velocity and pressure to integrate in time we consider implicit runge kutta schemes as well as a fractional step scheme we illustrate the methods and study their convergence numerically via examples that involve flow around obstacles that undergo prescribed deformations copyright 2015 john wiley sons ltd

component based discriminative classification for hidden markov models hidden markov models hmms have been successfully applied to a wide range of sequence modeling problems in the classification context one of the simplest approaches is to train a single hmm per class a test sequence is then assigned to the class whose hmm yields the maximum a posterior map probability this generative scenario works well when the models are correctly estimated however the results can become poor when improper models are employed due to the lack of prior knowledge poor estimates violated assumptions or insufficient training data to improve the results in these cases we propose to combine the descriptive strengths of hmms with discriminative classifiers this is achieved by training feature based classifiers in an hmm induced vector space defined by specific components of individual hidden markov models we introduce four major ways of building such vector spaces and study which trained combiners are useful in which context moreover we motivate and discuss the merit of our method in comparison to dynamic kernels in particular to the fisher kernel approach

similarity based classification of sequences using hidden markov models hidden markov models hmm are a widely used tool for sequence modelling in the sequence classification case the standard approach consists of training one hmm for each class and then using a standard bayesian classification rule in this paper we introduce a novel classification scheme for sequences based on hmms which is obtained by extending the recently proposed similarity based classification paradigm to hmm based classification in this approach each object is described by the vector of its similarities with respect to a predetermined set of other objects where these similarities are supported by hmms a central problem is the high dimensionality of resulting space and to deal with it three alternatives are investigated synthetic and real experiments show that the similarity based approach outperforms standard hmm classification schemes

a generalized kernel approach to dissimilarity based classification usually objects to be classified are represented by features in this paper we discuss an alternative object representation based on dissimilarity values if such distances separate the classes well the nearest neighbor method offers a good solution however dissimilarities used in practice are usually far from ideal and the performance of the nearest neighbor rule suffers from its sensitivity to noisy examples we show that other more global classification techniques are preferable to the nearest neighbor rule in such cases for classification purposes two different ways of using generalized dissimilarity kernels are considered in the first one distances are isometrically embedded in a pseudo euclidean space and the classification task is performed there in the second approach classifiers are built directly on distance kernels both approaches are described theoretically and then compared using experiments with different dissimilarity measures and datasets including degraded data simulating the problem of missing values

k nn classification of handwritten characters via accelerated gat correlation this paper addresses the problem of reinforcing the ability of the k nn classification of handwritten characters via distortion tolerant template matching techniques with a limited quantity of data we compare three kinds of matching techniques the conventional simple correlation the tangent distance and the global affine transformation gat correlation although the k nn classification method is straightforward and powerful it consumes a lot of time therefore to reduce the computational cost of matching in k nn classification we propose accelerating the gat correlation method by reformulating its computational model and adopting efficient lookup tables recognition experiments performed on the iptp cdrom1b handwritten numerical database show that the matching techniques of the simple correlation the tangent distance and the accelerated gat correlation achieved recognition rates of 97 07 97 50 and 98 70 respectively the computation time ratios of the tangent distance and the accelerated gat correlation to the simple correlation are 26 3 and 36 5 to 1 0 respectively we enhance k nn classification via a distortion tolerant gat correlation technique we accelerate gat correlation using separation of variables and lookup tables we examine both shape matching and discrimination abilities of gat correlation gat correlation is far superior in recognition accuracy to the tangent distance computational cost of gat correlation is reduced to about 6 of the original cost

nonlinear non negative component analysis algorithms in this paper general solutions for nonlinear non negative component analysis for data representation and recognition are proposed motivated by a combination of the non negative matrix factorization nmf algorithm and kernel theory which has lead to a recently proposed nmf algorithm in a polynomial feature space we propose a general framework where one can build a nonlinear non negative component analysis method using kernels the so called projected gradient kernel non negative matrix factorization pgknmf in the proposed approach arbitrary positive definite kernels can be adopted while at the same time it is ensured that the limit point of the procedure is a stationary point of the optimization problem moreover we propose fixed point algorithms for the special case of gaussian radial basis function rbf kernels we demonstrate the power of the proposed methods in face and facial expression recognition applications

wide angle phase slowness approximations in vti media an anisotropic medium with vertical symmetry axis vti often presents a good model for describing real rocks propagation of quasi p and quasi sv waves in such media requires an expression of the vertical phase slowness a complicated function of the horizontal phase slowness and the medium parameters for converted wave phase shift migration methods it is desired to have slowness expressions that are simple and accurate at wide angles of propagation taylor series representations of the squared vertical slowness for quasi p and quasi sv waves result in new wide angle phase slowness approximations based on truncated series and continued fraction representations slowness approximations that are exact for both vertical propagation and at a horizontal slowness corresponding to horizontally traveling qp waves are derived the approximation for quasi sv waves can be used in phase shift migration in media where the quasi sv wavefront contains triplications these approximations are tested on several models and compared to previously published approximations the numerical tests suggest that the new continued fraction approximations are more accurate they can be used in phase shift migration algorithms which are more efficient for large angles than the existing approximations

nearly optimal classification for semimetrics we initiate the rigorous study of classification in semimetric spaces which are point sets with a distance function that is non negative and symmetric but need not satisfy the triangle inequality we define the density dimension dens and discover that it plays a central role in the statistical and algorithmic feasibility of learning in semimetric spaces we compute this quantity for several widely used semimetrics and present nearly optimal sample compression algorithms which are then used to obtain generalization guarantees including fast rates our claim of near optimality holds in both computational and statistical senses when the sample has radius r and margin we show that it can be compressed down to roughly d r dens points and further that finding a significantly better compression is algorithmically intractable unless p np this compression implies generalization via standard occam type arguments to which we provide a nearly matching lower bound

multik mhks a novel multiple kernel learning algorithm in this paper we develop a new effective multiple kernel learning algorithm first we map the input data into m different feature spaces by m empirical kernels where each generated feature space is taken as one view of the input space then through borrowing the motivating argument from canonical correlation analysis cca that can maximally correlate the m views in the transformed coordinates we introduce a special term called inter function similarity loss rifsi into the existing regularization framework so as to guarantee the agreement of multiview outputs in implementation we select the modification of ho kashyap algorithm with squared approximation of the misclassification errors mhks as the incorporated paradigm and the experimental results on benchmark data sets demonstrate the feasibility and effectiveness of the proposed algorithm named multik mhks

a stabilized finite element method for generalized stationary incompressible flows abstract in this paper we describe a finite element formulation for the numerical solution of the stationary incompressible navier stokes equations including coriolis forces and the permeability of the medium the stabilized method is based on the algebraic version of the sub grid scale approach we first describe this technique for general systems of convection diffusion reaction equations and then we apply it to the linearized flow equations the important point is the design of the matrix of stabilization parameters that the method has this design is based on the identification of the stability problems of the galerkin method and a scaling of variables argument to determine which coefficients must be included in the stabilization matrix this together with the convergence analysis of the linearized problem leads to a simple expression for the stabilization parameters in the general situation considered in the paper the numerical analysis of the linearized problem also shows that the method has optimal convergence properties

variational formulations for surface tension capillarity and wetting the interest in the simulation of flows with significant surface tension effects has grown significantly in recent years this has been driven by the substantial advances made in the measurement and manufacturing of microscopic systems since at small length scales surface phenomena are dominant in this article surface tension capillarity and wetting effects are discussed in terms of the virtual work principle and shape sensitivity starting from first principles and arriving at variational formulations that are adequate for numerical treatment by finite elements for example to make the exposition self contained some elements of differential geometry are recalled using a formulation that is fully in cartesian coordinates and may thus be more friendly to readers not familiar with covariant derivatives all necessary results are proved in this cartesian formulation several numerical examples computed with a finite element level set formulation are used to illustrate this challenging physical problem

feature discovery in non metric pairwise data pairwise proximity data given as similarity or dissimilarity matrix can violate metricity this occurs either due to noise fallible estimates or due to intrinsic non metric features such as they arise from human judgments so far the problem of non metric pairwise data has been tackled by essentially omitting the negative eigenvalues or shifting the spectrum of the associated pseudo covariance matrix for a subsequent embedding however little attention has been paid to the negative part of the spectrum itself in particular no answer was given to whether the directions associated to the negative eigenvalues would at all code variance other than noise related we show by a simple exploratory analysis that the negative eigenvalues can code for relevant structure in the data thus leading to the discovery of new features which were lost by conventional data analysis techniques the information hidden in the negative eigenvalue part of the spectrum is illustrated and discussed for three data sets namely usps handwritten digits text mining and data from cognitive psychology

generalized navier boundary condition and geometric conservation law for surface tension we consider two fluid flow problems in an arbitrary lagrangian eulerian ale framework the purpose of this work is twofold first we address the problem of the moving contact line namely the line common to the two fluids and the wall second we perform a stability analysis in the energy norm for various numerical schemes taking into account the gravity and surface tension effects the problem of the moving contact line is treated with the so called generalized navier boundary conditions owing to these boundary conditions it is possible to circumvent the incompatibility between the classical no slip boundary condition and the fact that the contact line of the interface on the wall is actually moving the energy stability analysis is based in particular on an extension of the geometry conservation law gcl concept to the case of moving surfaces this extension is useful to study the contribution of the surface tension the theoretical and computational results presented in this paper allow us to propose a strategy which offers a good compromise between efficiency stability and artificial diffusion

application of snell s law in weakly anisotropic media snell s law describes the relationship between phase angles and velocities during the reflection or transmission of waves it states that horizontal slowness with respect to an interface is preserved during reflection or transmission evaluation of this relationship at an interface between two isotropic media is straightforward for anisotropic media it is a complicated problem because phase velocity depends on the angle in the anisotropic reflection transmission problem neither is known solving snell s law in the anisotropic case requires a numerical solution for a sixth order polynomial in addition to finding the roots they must be assigned to the correct reflected or transmitted wave type we show that if the anisotropy is weak an approximate solution based on first order perturbation theory can be obtained this approach permits the computation of the full slowness vector and thereby the phase velocity and angle in addition to replacing the need for solving the sixth order polynomial the re

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

p wave slowness surface approximation for tilted orthorhombic media abstractwe have developed an analytic and approximate formula for vertical slowness components of down and upgoing plane p waves in 3d tilted orthorhombic media a perturbation method and shanks transform were used to derive the approximation for slowness surface of p waves in tilted orthorhombic media we have also quantitatively described the validity range of the radial horizontal slowness components for the proposed formula the validity range was affected by the strength of the anellipticity of an orthorhombic medium the stronger the anellipticity the smaller the validity range numerical examples determined that the proposed formula is accurate for tilted orthorhombic media with weak to strong anellipticity we have also evaluated in detail the application of the proposed formula on calculating the p wave intercept time in the p domain for horizontally layered tilted orthorhombic models our formula is useful for ray tracing phase shift migration and p domain intercept time approximation f

indefinite proximity learning a review efficient learning of a data analysis task strongly depends on the data representation most methods rely on symmetric similarity or dissimilarity representations by means of metric inner products or distances providing easy access to powerful mathematical formalisms like kernel or branch and bound approaches similarities and dissimilarities are however often naturally obtained by nonmetric proximity measures that cannot easily be handled by classical learning algorithms major efforts have been undertaken to provide approaches that can either directly be used for such data or to make standard methods available for these types of data we provide a comprehensive survey for the field of learning with nonmetric proximities first we introduce the formalism used in nonmetric spaces and motivate specific treatments for nonmetric proximity data second we provide a systematization of the various approaches for each category of approaches we provide a comparative discussion of the individual algorithms and address complexity issues and generalization properties in a summarizing section we provide a larger experimental study for the majority of the algorithms on standard data sets we also address the problem of large scale proximity learning which is often overlooked in this context and of major importance to make the method relevant in practice the algorithms we discuss are in general applicable for proximity based clustering one class classification classification regression and embedding approaches in the experimental part we focus on classification tasks

unsupervised minor prototype detection using an adaptive population partitioning algorithm this paper presents a new partitioning algorithm designated as the adaptive c populations acp clustering algorithm capable of identifying natural subgroups and influential minor prototypes in an unlabeled dataset in contrast to traditional fuzzy c means clustering algorithms which partition the whole dataset equally adaptive clustering algorithms such as that presented in this study identify the natural subgroups in unlabeled datasets in this paper data points within a small dense region located at a relatively large distance from any of the major cluster centers are considered to form a minor prototype the aim of acp is to adaptively separate these isolated minor clusters from the major clusters in the dataset the study commences by introducing the mathematical model of the proposed acp algorithm and demonstrates its convergence to a stable solution the ability of acp to detect minor prototypes is confirmed via its application to the clustering of three different datasets with different sizes and characteristics

an absolutely stabilized finite element method for the stokes problem on presente une formulation a elements finis absolument stabilisee pour le probleme de stokes on etablit des estimations d erreurs optimales dans la norme l 2 pour l approximation des champs de vitesses et de pressions

high order ale schemes for incompressible capillary flows the spatial discretization of problems with moving boundaries is considered incorporating the temporal evolution of not just the mechanical variables but also of the nodal positions of the moving mesh the outcome is a system of differential algebraic equations dae of index 2 or in the case of inertialess flow just 1 from the dae formulation it its possible to define strategies to build schemes of arbitrary accuracy we introduce here several schemes of order 2 and 3 that avoid the solution of a nonlinear system involving simultaneously the mechanical variables and the geometrical ones this class of schemes has been the one adopted by the majority of practitioners of computational fluid dynamics up to now the proposed schemes indeed achieve the design accuracy and further show stability restrictions that are not significantly more severe than those of popular first order schemes the numerical experimentation is performed on capillary problems discretized by both div stable p 2 p 1 p 1 p 1 and equal order p 1 p 1 stabilized finite elements and incorporating surface tension and triple contact line effects

classification with nonmetric distances image retrieval and class representation a key problem in appearance based vision is understanding how to use a set of labeled images to classify new images systems that model human performance or that use robust image matching methods often use nonmetric similarity judgments but when the triangle inequality is not obeyed most pattern recognition techniques are not applicable exemplar based nearest neighbor methods can be applied to a wide class of nonmetric similarity functions the key issue however is to find methods for choosing good representatives of a class that accurately characterize it we show that existing condensing techniques are ill suited to deal with nonmetric dataspaces we develop techniques for solving this problem emphasizing two points first we show that the distance between images is not a good measure of how well one image can represent another in nonmetric spaces instead we use the vector correlation between the distances from each image to other previously seen images second we show that in nonmetric spaces boundary points are less significant for capturing the structure of a class than in euclidean spaces we suggest that atypical points may be more important in describing classes we demonstrate the importance of these ideas to learning that generalizes from experience by improving performance we also suggest ways of applying parametric techniques to supervised learning problems that involve a specific nonmetric distance functions showing how to generalize the idea of linear discriminant functions in a way that may be more useful in nonmetric spaces

theory and algorithm for learning with dissimilarity functions we study the problem of classification when only a dissimilarity function between objects is accessible that is data samples are represented not by feature vectors but in terms of their pairwise dissimilarities we establish sufficient conditions for dissimilarity functions to allow building accurate classifiers the theory immediately suggests a learning paradigm construct an ensemble of simple classifiers each depending on a pair of examples then find a convex combination of them to achieve a large margin we next develop a practical algorithm referred to as dissimilarity based boosting dboost for learning with dissimilarity functions under theoretical guidance experiments on a variety of databases demonstrate that the dboost algorithm is promising for several dissimilarity measures widely used in practice

representation and recognition of handwritten digits using deformable templates we investigate the application of deformable templates to recognition of handprinted digits two characters are matched by deforming the contour of one to fit the edge strengths of the other and a dissimilarity measure is derived from the amount of deformation needed the goodness of fit of the edges and the interior overlap between the deformed shapes classification using the minimum dissimilarity results in recognition rates up to 99 25 percent on a 2 000 character subset of nist special database 1 additional experiments on an independent test data were done to demonstrate the robustness of this method multidimensional scaling is also applied to the 2 000 spl times 2 000 proximity matrix using the dissimilarity measure as a distance to embed the patterns as points in low dimensional spaces a nearest neighbor classifier is applied to the resulting pattern matrices the classification accuracies obtained in the derived feature space demonstrate that there does exist a good low dimensional representation space methods to reduce the computational requirements the primary limiting factor of this method are discussed

traveltime approximations for a layered transversely isotropic medium we consider multiple transmitted reflected and converted qp qsv waves or multiple transmitted and reflected sh waves in a horizontally layered medium that is transversely isotropic with a vertical symmetry axis vti traveltime and offset horizontal distance between a source and receiver not necessarily in the same layer are expressed as functions of horizontal slowness these functions are given in terms of a taylor series in slowness in exactly the same form as for a layered isotropic medium the coefficients depend on the parameters of the anisotropic layers through which the wave has passed and there is no weak anisotropy assumption using classical formulas the traveltime or traveltime squared can then be expressed as a taylor series in even powers of offset these taylor series give rise to a shifted hyperbola traveltime approximation and a new continued fraction approximation described by four parameters that match the taylor series up to the sixth power in offset further approximations give several simplified continued fraction approximations all of which depend on three parameters zero offset traveltime nmo velocity and a heterogeneity coefficient the approximations break down when there is a cusp in the group velocity for the qsv wave numerical studies indicate that approximations of traveltime squared are generally better than those for traveltime a new continued fraction approximation that depends on three parameters is more accurate than the commonly used continued fraction approximation and the shifted hyperbola

classification with truncated ell _ 1 distance kernel this brief proposes a truncated ell 1 distance tl1 kernel which results in a classifier that is nonlinear in the global region but is linear in each subregion with this kernel the subregion structure can be trained using all the training data and local linear classifiers can be established simultaneously the tl1 kernel has good adaptiveness to nonlinearity and is suitable for problems which require different nonlinearities in different areas though the tl1 kernel is not positive semidefinite some classical kernel learning methods are still applicable which means that the tl1 kernel can be directly used in standard toolboxes by replacing the kernel evaluation in numerical experiments the tl1 kernel with a pregiven parameter achieves similar or better performance than the radial basis function kernel with the parameter tuned by cross validation implying the tl1 kernel a promising nonlinear kernel for classification tasks

an acoustic wave equation for anisotropic media a wave equation derived using the acoustic medium assumption for p waves in transversely isotropic ti media with a vertical symmetry axis vti media yields a good kinematic approximation to the familiar elastic wave equation for vti media the wavefield solutions obtained using this vti acoustic wave equation are free of shear waves which significantly reduces the computation time compared to the elastic wavefield solutions for exploding reflector type applications from this vti acoustic wave equation the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a ti medium are derived these equations based on the acoustic assumption shear wave velocity 0 are much simpler than their elastic counterparts yet they yield an accurate description of traveltimes and geometrical amplitudes numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex ti models

exact seismic velocities for transversely isotropic media and extended thomsen formulas for stronger anisotropies a different type of approximation to the exact anisotropic wave velocities as a function of incidence angle in transversely isotropic ti media is explored this formulation extends thomsen s weak anisotropy approach to stronger deviations from isotropy without significantly affecting the equations simplicity one easily recognized improvement is that the extreme value of the quasi sv wave speed vsv is located at the correct incidence angle ex rather than always being at the position 45 this holds universally for thomsen s approximation although ex 45 actually is never correct for any ti anisotropic medium wave speed magnitudes are more closely approximated for most values of the incidence angle although there may be some exceptions depending on actual angular location of the extreme value furthermore a special angle m close to theextreme point of the sv wave speed and also needed by the new formulas can be deduced from the same data normally used in weak anisotropy data analy

convergence of traveltime power series for a layered vti medium for a multiply reflected sh wave or a multiply reflected and converted qp qsv wave in a layered vti medium traveltime and offset can be expressed by power series in horizontal slowness as for a stack of isotropic layers these can be used to express traveltime as a series of even powers of offset the existence and behavior of this power series depend on the derivative of offset with respect to horizontal slowness formally expressed as traveltime multiplied by nmo velocity squared when the nmo velocity squared is different from zero the power series always exists for sufficiently small offset the nmo velocity squared is always positive for sh waves and for qp waves in media with normal polarization for which there are no triplications in traveltime as function of offset for qsv wave propagation insome layers the nmo velocity squared may be positive zero or negative when it is positive the power series exists but there may be an off axis triplication in traveltime when the nmo squared veloci

image clustering using local discriminant models and global integration in this paper we propose a new image clustering algorithm referred to as clustering using local discriminant models and global integration ldmgi to deal with the data points sampled from a nonlinear manifold for each data point we construct a local clique comprising this data point and its neighboring data points inspired by the fisher criterion we use a local discriminant model for each local clique to evaluate the clustering performance of samples within the local clique to obtain the clustering result we further propose a unified objective function to globally integrate the local models of all the local cliques with the unified objective function spectral relaxation and spectral rotation are used to obtain the binary cluster indicator matrix for all the samples we show that ldmgi shares a similar objective function with the spectral clustering sc algorithms e g normalized cut ncut in contrast to ncut in which the laplacian matrix is directly calculated based upon a gaussian function a new laplacian matrix is learnt in ldmgi by exploiting both manifold structure and local discriminant information we also prove that k means and discriminative k means diskmeans are both special cases of ldmgi extensive experiments on several benchmark image datasets demonstrate the effectiveness of ldmgi we observe in the experiments that ldmgi is more robust to algorithmic parameter when compared with ncut thus ldmgi is more appealing for the real image clustering applications in which the ground truth is generally not available for tuning algorithmic parameters

on hidden markov models and cyclic strings for shape recognition abstract shape descriptions and the corresponding matching techniques must be robust to noise and invariant to transformations for their use in recognition tasks most transformations are relatively easy to handle when contours are represented by strings however starting point invariance is difficult to achieve one interesting possibility is the use of cyclic strings which are strings that have no starting and final points we propose new methodologies to use hidden markov models to classify contours represented by cyclic strings experimental results show that our proposals outperform other methods in the literature

generative models for similarity based classification a maximum entropy approach to generative similarity based classifiers model is proposed first a descriptive set of similarity statistics is assumed to be sufficient for classification then the class conditional distributions of these descriptive statistics are estimated as the maximum entropy distributions subject to empirical moment constraints the resulting exponential class conditional distributions are used in a maximum a posteriori decision rule forming the similarity discriminant analysis sda classifier simulated and real data experiments compare performance to the k nearest neighbor classifier the nearest centroid classifier and the potential support vector machine psvm

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

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

handwritten chinese radical recognition using nonlinear active shape models handwritten chinese characters can be recognized by first extracting the basic shapes radicals of which they are composed radicals are described by nonlinear active shape models and optimal parameters found using the chamfer distance transform and a dynamic tunneling algorithm the radical recognition rate is 96 5 percent correct writer independent on 280 000 characters containing 98 radical classes

on some pressure segregation methods of fractional step type for the finite element approximation of incompressible flow problems abstract in this paper we treat several aspects related to time integration methods for the incompressible navier stokes equations that allow to uncouple the calculation of the velocities and the pressure the first family of schemes consists of classical fractional step methods of which we discuss several possibilities for the pressure extrapolation and the time integration of first and second order the second family consists of schemes based on an explicit treatment of the pressure in the momentum equation followed by a poisson equation for the pressure it turns out that this staggered treatment of the velocity and the pressure is stable finally we present predictor corrector methods based on the above schemes that aim to converge to the solution of the monolithic time integration method apart from presenting these schemes and check its numerical performance we also present a complete set of stability results for the fractional step methods that are independent of the space stability of the velocity pressure interpolation that is of the classical inf sup condition

the immersed interface method for elliptic equations with discontinuous coefficients and singular sources the authors develop finite difference methods for elliptic equations of the form nabla cdot beta x nabla u x kappa x u x f x in a region omega in one or two space dimension

localization of shapes using statistical models and stochastic optimization in this paper we present a new model for deformations of shapes a pseudolikelihood is based on the statistical distribution of the gradient vector field of the gray level the prior distribution is based on the probabilistic principal component analysis ppca we also propose a new model based on mixtures of ppca that is useful in the case of greater variability in the shape a criterion of global or local object specificity based on a preliminary color segmentation of the image is included into the model the localization of a shape in an image is then viewed as minimizing the corresponding gibbs field we use the exploration selection e s stochastic algorithm in order to find the optimal deformation this yields a new unsupervised statistical method for localization of shapes in order to estimate the statistical parameters for the gradient vector field of the gray level we use an iterative conditional estimation ice procedure the color segmentation of the image can be computed with an exploration selection estimation ese procedure

affine transformation and 2d projection invariant k nn classification of handwritten characters via a new matching measure pattern recognition based on matching remains important because it is a fundamental technique it does not require a learning process and the result of matching provides intuitive and geometrical information wakahara et al proposed global affine transformation gat correlation matching which can compensate for affine transformations imposed on a pattern gat correlation matching with an acceleration method and a new matching measure called the nearest neighbor distance of equi gradient direction nndegd achieved high performance in experiments using the mnist database the gat matching measure was extended to a global projection transformation gpt matching measure to allow deformation by 2d projection transformations the purpose of this paper is threefold first we develop an acceleration method for gpt correlation matching second in order to improve recognition performance we apply the curvature of edges in strokes to the matching measure curvature is often used as a feature of characters however in this paper we use it as a weight in the nndegd third to investigate the performance of the proposed methods we apply them to image matching and recognition from the mnist and the iptp databases for k nearest neighbors k nn in the experiment with the mnist database the gpt correlation matching with the curvature weighted nndegd matching measure achieves the lowest error rate of 0 30 among k nn based methods highlightswe enhance k nn classification by affine and 2d projection invariant matchings we develop acceleration methods for those distortion tolerant matching techniques we propose a matching measure using similarity in direction and curvature of edges experiments using the mnist database show a very low error rate of 0 30 the source code used in the above mentioned experiments is uploaded

eigen deformations for elastic matching based handwritten character recognition deformations in handwritten characters have category dependent tendencies in this paper the estimation and the utilization of such tendencies called eigen deformations are investigated for the better performance of elastic matching based handwritten character recognition the eigen deformations are estimated by the principal component analysis of actual deformations automatically collected by the elastic matching from experimental results it was shown that typical deformations of each category can be extracted as the eigen deformations it was also shown that the recognition performance can be improved significantly by using the eigen deformations for the detection of overfitting which is the main cause of the misrecognition in the elastic matching based recognition methods

on deformable models for visual pattern recognition this paper reviews model based methods for non rigid shape recognition these methods model match and classify non rigid shapes which are generally problematic for conventational algorithms using rigid models issues including model representation optimization criteria formulation model matching and classification are examined in detail with the objective to provide interested researchers a roadmap for exploring the field this paper emphasizes on 2d deformable models their potential applications and future research directions particularly on deformable pattern classification are discussed

prototype selection for dissimilarity based classifiers a conventional way to discriminate between objects represented by dissimilarities is the nearest neighbor method a more efficient and sometimes a more accurate solution is offered by other dissimilarity based classifiers they construct a decision rule based on the entire training set but they need just a small set of prototypes the so called representation set as a reference for classifying new objects such alternative approaches may be especially advantageous for non euclidean or even non metric dissimilarities the choice of a proper representation set for dissimilarity based classifiers is not yet fully investigated it appears that a random selection may work well in this paper a number of experiments has been conducted on various metric and non metric dissimilarity representations and prototype selection methods several procedures like traditional feature selection methods here effectively searching for prototypes mode seeking and linear programming are compared to the random selection in general we find out that systematic approaches lead to better results than the random selection especially for a small number of prototypes although there is no single winner as it depends on data characteristics the k centres works well in general for two class problems an important observation is that our dissimilarity based discrimination functions relying on significantly reduced prototype sets 3 10 of the training objects offer a similar or much better classification accuracy than the best k nn rule on the entire training set this may be reached for multi class data as well however such problems are more difficult

nonhyperbolic reflection moveout in anisotropic media the standard hyperbolic approximation for reflection moveouts in layered media is accurate only for relatively short spreads even if the layers are isotropic velocity anisotropy may significantly enhance deviations from hyperbolic moveout nonhyperbolic analysis in anisotropic media is also important because conventional hyperbolic moveout processing on short spreads is insufficient to recover the true vertical velocity hence the depth we present analytic and numerical analysis of the combined influence of vertical transverse isotropy and layering on long spread reflection moveouts qualitative description of nonhyperbolic moveout on intermediate spreads offset to depth ratio x z 1 7 2 is given in terms of the exact fourth order taylor series expansion for p sv and p sv traveltime curves valid for multilayered transversely isotropic media with arbitrary strength of anisotropy we use this expansion to provide an analytic explanation for deviations from hyperbolic moveout such as the strong

an adaptive unsupervised approach toward pixel clustering and color image segmentation this paper proposes an adaptive unsupervised scheme that could find diverse applications in pattern recognition as well as in computer vision particularly in color image segmentation the algorithm named ant colony fuzzy c means hybrid algorithm afha adaptively clusters image pixels viewed as three dimensional data pieces in the rgb color space the ant system as algorithm is applied for intelligent initialization of cluster centroids which endows clustering with adaptivity considering algorithmic efficiency an ant subsampling step is performed to reduce computational complexity while keeping the clustering performance close to original one experimental results have demonstrated afha clustering s advantage of smaller distortion and more balanced cluster centroid distribution over fcm with random and uniform initialization quantitative comparisons with the x means algorithm also show that afha makes a better pre segmentation scheme over x means we further extend its application to natural image segmentation taking into account the spatial information and conducting merging steps in the image space extensive tests were taken to examine the performance of the proposed scheme results indicate that compared with classical segmentation algorithms such as mean shift and normalized cut our method could generate reasonably good or better image partitioning which illustrates the method s practical value

hidden markov model based weighted likelihood discriminant for 2 d shape classification the goal of this paper is to present a weighted likelihood discriminant for minimum error shape classification different from traditional maximum likelihood ml methods in which classification is based on probabilities from independent individual class models as is the case for general hidden markov model hmm methods proposed method utilizes information from all classes to minimize classification error the proposed approach uses a hmm for shape curvature as its 2 d shape descriptor we introduce a weighted likelihood discriminant function and present a minimum classification error strategy based on generalized probabilistic descent method we show comparative results obtained with our approach and classic ml classification with various hmm topologies alongside fourier descriptor and zernike moments based support vector machine classification for a variety of shapes

simple and efficient ale methods with provable temporal accuracy up to fifth order for the stokes equations on time varying domains we present a class of semi implicit finite element fe schemes that uses arbitrary lagrangian eulerian methods ale to solve the incompressible navier stokes equations nse on time varying domains we use the k th order backward differentiation formula bdf k and taylor hood p m p m 1 finite elements the well known telescope formulas of bdf k have been extended from k 1 2 to k 3 4 5 they enable us to prove that when k le 5 for stokes equations on a fixed domain our schemes converge at rate o delta t k h m 1 when the domain is varying with respect to time and when h delta t o 1 the convergence rate reduces to o delta t k h m for analysis we assume that meshes at different time levels have the same topology consequently our methods do not require the computation of characteristic paths and are jacobian free numerical tests for nse on time varying domains are presented they indicate that our schemes may have full accuracy on time varying domains and can hand

shared farthest neighbor approach to clustering of high dimensionality low cardinality data clustering algorithms are routinely used in biomedical disciplines and are a basic tool in bioinformatics depending on the task at hand there are two most popular options the central partitional techniques and the agglomerative hierarchical clustering techniques and their derivatives these methods are well studied and well established however both categories have some drawbacks related to data dimensionality for partitional algorithms and to the bottom up structure for hierarchical agglomerative algorithms to overcome these limitations motivated by the problem of gene expression analysis with dna microarrays we present a hierarchical clustering algorithm based on a completely different principle which is the analysis of shared farthest neighbors we present a framework for clustering using ranks and indexes and introduce the shared farthest neighbors sfn clustering criterion we illustrate the properties of the method and present experimental results on different data sets using the strategy of evaluating data clustering by extrinsic knowledge given by class labels

shape matching using lat and its application to handwritten numeral recognition this paper describes an iterative technique for gradually deforming a mask binary image with successive local affine transformation lat operations so as to yield the best match to an input binary image as one new and promising approach toward robust handwritten character recognition the method uses local shapes in the sense that the lat of each point at one location is optimized using locations of other points by means of least squares data fitting using gaussian window functions it also uses a multiscale refinement technique that decreases the spread of window functions with each iteration especially in handwritten character recognition structural information is indispensable for robust shape matching or discrimination the method is enhanced to explicitly incorporate structures by weighting the above least squares criterion with similarity measures of both topological and geometric features of the mask and input images moreover deformation constraints are imposed on each iteration not only to promote and stabilize matching convergence but also to suppress an excessive matching process shape matching experiments have been successfully carried out using skeletons of totally unconstrained handwritten numerals

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

nonhyperbolic moveout analysis in vti media using rational interpolation anisotropic velocity analysis using qp waves in transversely isotropic media with a vertical symmetry axis vti usually is done by inferring the anellipticity parameter and the normal moveout velocity vnmo from the nonhyperbolic character of the moveout several approximations explicit in these parameters exist with varying degrees of accuracy here we present a rational interpolation approach to nonhyperbolic moveout analysis in the t x domain this method has no additional computational overhead compared to using expressions explicit in and vnmo the lack of such overhead stems from the observation that for fixed and zero offset two way traveltime t0 the moveout curve for different values of vnmo can be calculated by simple stretching of the offset axis this observation is based on the assumptions that the traveltimes of qp waves in transversely isotropic media mainly depend on and vnmo and that the shear wave velocity along the symmetry axis has a negligibleinfluence on these traveltim

a unified approach to pattern recognition abstract the paper is an outline of a new approach to pattern recognition developed by the author a fuller introduction to the approach will appear soon 1 within the proposed framework the two principal approaches to pattern recognition vector and syntactic are unified