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

computations of wall distances based on differential equations the use of differential equations such as eikonal hamilton jacobi and poisson for the economical calculation of the nearest wall distance d which is needed by some turbulence models is explored modifications that could palliate some turbulence modeling anomalies are also discussed economy is of especial value for deforming adaptive grid problems for these ideally d is repeatedly computed it is shown that the eikonal and hamilton jacobi equations can be easy to implement when written in implicit or iterated advection and advection diffusion equation analogous forms respectively these like the poisson laplacian term are commonly occurring in cfd solvers allowing the re use of efficient algorithms and code components the use of the nasa cfl3d cfd program to solve the implicit eikonal and hamilton jacobi equations is explored the re formulated d equations are easy to implement and are found to have robust convergence for accurate eikonal solutions upwind metric differences are required the poisson approach is also found effective and easiest to implement modified distances are not found to affect global outputs such as lift and drag significantly at least in common situations such as airfoil flows

on the shape of a set of points in the plane a generalization of the convex hull of a finite set of points in the plane is introduced and analyzed this generalization leads to a family of straight line graphs alpha shapes which seem to capture the intuitive notions of fine shape and crude shape of point sets it is shown that a shapes are subgraphs of the closest point or furthest point delaunay triangulation relying on this result an optimal o n log n algorithm that constructs alpha shapes is developed

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

simple finite element based computation of distance functions in unstructured grids a distance field is a representation of the closest distance from a point to a given surface distance fields are widely used in applications ranging from computer vision physics and computer graphics and have been the subject of research of many authors in the last decade most of the methods for computing distance fields are devoted to cartesian grids while little attention has been paid to unstructured grids finite element methods are well known for their ability to deal with partial differential equations in unstructured grids therefore we propose an extension of the fast marching method for computing a distance field in a finite element context employing the element interpolation to hold the eikonal property 1 a simple algorithm to develop the computations is also presented and its efficiency demonstrated through various unstructured grid examples we observed that the presented algorithm has processing times proportional to the number of mesh nodes

representation complexity of adaptive 3d distance fields in this paper we study the representation complexity of a kind of data structure that stores the information necessary to compute the distance from a point to a geometric body these data structures called adaptive splitting based on cubature distance fields asbcdf are binary search trees generated by the adaptive splitting based on cubature asbc algorithm that adaptively subdivides the space surrounding the body into tetrahedra their representation complexity is measured by the number of nodes in the tree two times the number of tetrahedra in the resulting tessellation in the case of convex polyhedra we prove that this quantity remains bounded as the number of vertices of the polyhedra increases to infinity experimental results show that the number of tetrahedra in the tessellations is almost independent of the combinatorial complexity of the polyhedra this means that the average compute time of the distance to arbitrary convex polyhedra is almost constant therefore asbcdfs are especially suitable for real time applications involving rapidly changing environments modelized with complex polyhedra

discriminative transfer subspace learning via low rank and sparse representation in this paper we address the problem of unsupervised domain transfer learning in which no labels are available in the target domain we use a transformation matrix to transfer both the source and target data to a common subspace where each target sample can be represented by a combination of source samples such that the samples from different domains can be well interlaced in this way the discrepancy of the source and target domains is reduced by imposing joint low rank and sparse constraints on the reconstruction coefficient matrix the global and local structures of data can be preserved to enlarge the margins between different classes as much as possible and provide more freedom to diminish the discrepancy a flexible linear classifier projection is obtained by learning a non negative label relaxation matrix that allows the strict binary label matrix to relax into a slack variable matrix our method can avoid a potentially negative transfer by using a sparse matrix to model the noise and thus is more robust to different types of noise we formulate our problem as a constrained low rankness and sparsity minimization problem and solve it by the inexact augmented lagrange multiplier method extensive experiments on various visual domain adaptation tasks show the superiority of the proposed method over the state of the art methods the matlab code of our method will be publicly available at http www yongxu org lunwen html

finite volume distance field and its application to medial axis transforms accurate and efficient computation of the nearest wall distance d or level set is important for many areas of computational science engineering differential equation based distance level set algorithms such as the hyperbolic natured eikonal equation have demonstrated valuable computational efficiency here in the context as an auxiliary equation to the main flow equations the eikonal equation is solved efficiently with two different finite volume approaches the cell vertex and cell centered the application of the distance solution is studied for various geometries moreover a procedure using the differential field to obtain the medial axis transform mat for different geometries is presented the latter provides a skeleton representation of geometric models that has many useful analysis properties as an alternative to other methods the current d mat procedure bypasses difficulties that are usually encountered by pure geometric methods e g the voronoi approach especially in three dimensions and provides better accuracy than pure thinning methods it is also shown that the d mat approach provides the potential to sculpt control the mat form for specialized solution purposes

new hermite orthogonal polynomial kernel and combined kernels in support vector machine classifier support vector machine is a desired method for classification of different types of data but the main obstacle to using this method is the considerable reduction of classification speed upon increase in the size of problem in this paper a new kernel function is proposed for svm which is derived from hermite orthogonal polynomials this function improves classification accuracy as well as reduction in the number of support vectors and increases the classification speed the overall kernel performance has been evaluated on real world data sets from uci repository by the ten fold cross validation method the combinations of hermite function with common kernels are proposed in this paper experimental results reveal that the hermite chebyshev kernel which is obtained from combination of hermite and chebyshev kernel has the best performance in the number of support vectors and hermite gussian kernel that is produced from combination hermite and gussian kernel has the first rank in the error rate among all experimental kernels on the other hand the hermite proposed method has the least number of support vectors and best performance in the error rate in comparison with common kernels and lowest required time among all kernels a new kernel function has been proposed by using hermite orthogonal polynomial new combined kernels resulted by combining hermite and common kernels have been proposed the proposed methods have been compared with three common kernels on real and synthetic data sets hermite kernel function has the lowest required time for classification the proposed methods yield better error rate and they have the best support vectors reduction significantly

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

shape representation using a generalized potential field model this paper is concerned with efficient derivation of the medial axis transform of a 2d polygonal region instead of using the shortest distance to the region border a potential field model is used for computational efficiency the region border is assumed to be charged and the valleys of the resulting potential field are used to estimate the axes for the medial axis transform the potential valleys are found by following the force field thus avoiding 2d search the potential field is computed in closed form using equations of the border segments the simple newtonian potential is shown to be inadequate for this purpose a higher order potential is defined which decays faster with distance than the inverse of distance it is shown that as the potential order becomes arbitrarily large the axes approach those computed using the shortest distance to the border algorithms are given for the computation of axes which can run in linear parallel time for part of the axes having initial guesses experimental results are presented for a number of examples

differential equation based wall distance computation for des and rans surprisingly expensive to compute wall distances are still used in a range of key turbulence and peripheral physics models potentially economical accuracy improving differential equation based distance algorithms are considered these involve elliptic poisson and a hyperbolic natured eikonal equation approaches numerical issues relating to non orthogonal curvilinear grid solution of the latter are addressed eikonal extension to a hamilton jacob equation is discussed use of this extension to improve turbulence model accuracy and along with the eikonal enhance detached eddy simulation des techniques is considered application of the distance approaches is studied for various geometries these include a plane channel flow with a wire at the centre a wing flap system and a supersonic double delta configuration although less accurate than the eikonal poisson method based flow solutions are extremely close to those using a search procedure for a moving grid case the poisson method is found especially efficient results show that the eikonal equation can be solved on highly stretched non orthogonal and curvilinear grids a key accuracy aspect is that metrics must be upwinded in the propagating front direction the hamilton jacobi equation is found to have qualitative turbulence model improving properties

a new face recognition method based on svd perturbation for single example image per person at present there are many methods for frontal view face recognition however few of them can work well when only one example image per class is available in this paper we present a new method based on svd perturbation to deal with the one example image problem and two generalized eigenface algorithms are proposed in the first algorithm the original image is linearly combined with its derived image gotten by perturbing the image matrix s singular values and then principal component analysis pca is performed on the joined images in the second algorithm the derived images are regarded as independent images that could augment training image set and then pca is performed on all the training images available including the original ones and the derived ones the proposed algorithms are compared with both the standard eigenface algorithm and the pc 2a algorithm which is proposed for addressing the one example image problem on the well known feret database with three different image resolutions experimental results show that the generalized eigenface algorithms are more accurate and use far fewer eigenfaces than both the standard eigenface algorithm and the pc 2a algorithm

hexahedral meshing using midpoint subdivision and integer programming abstract the generation of finite element meshes of 3d hexahedral elements can be performed by subdividing the model into a number of simple bodies like hexahedra triangular prisms etc within these bodies regular or simple transition meshes can be generated in this paper a method called midpoint subdivision will be discussed which enables the user to build the model using a number of high level subregions which satisfy certain simple topological conditions these subregions can be automatically subdivided into meshes of hexahedral elements for analysis the distribution of elements within the mesh is typically controlled by specifying the division numbers of certain edges however for a given set of subregions there are a number of constraints on the edge division numbers that will yield a compatible mesh the use of integer programming will be discussed this finds the compatible division numbers which are nearest to but not less than the target values specified

ranking the best instances we formulate a local form of the bipartite ranking problem where the goal is to focus on the best instances we propose a methodology based on the construction of real valued scoring functions we study empirical risk minimization of dedicated statistics which involve empirical quantiles of the scores we first state the problem of finding the best instances which can be cast as a classification problem with mass constraint next we develop special performance measures for the local ranking problem which extend the area under an roc curve auc criterion and describe the optimal elements of these new criteria we also highlight the fact that the goal of ranking the best instances cannot be achieved in a stage wise manner where first the best instances would be tentatively identified and then a standard auc criterion could be applied eventually we state preliminary statistical results for the local ranking problem

exploiting the relationships among several binary classifiers via data transformation the structural resemblance among several existing classifiers has motivated us to investigate their underlying relationships by exploring into the mapping solutions of these classifiers we found that they can be linked by simple feature data scaling in other words the key to these relationships lies upon how the replica of feature data are being scaled this finding leads us directly to an exploration of novel classifiers beyond existing settings based on an extensive empirical evaluation we show that the proposed formulation facilitates a tuning capability beyond existing settings for classifier generalization highlightsestablishment of relationship among several binary classifiers exploration of a random projection network for such classifier learning proposal of novel classifier which exploits the established relationship observe the performance of novel classifier on several performance measures

partial auc maximization in a linear combination of dichotomizers classifier combination is a useful and common methodology to design an effective classification system a large number of combination rules has been proposed hitherto mostly aimed at minimizing the error rate recently some methods have been presented that are devoted to maximize the area under the roc curve auc a more suitable performance measure when dealing with two class problems with imprecise environment and or imbalanced class priors however there are several applications that do not operate in the complete range of the roc curve but only in particular regions of it in these cases it is better to analyze the performance only in a part of the curve and to use the partial auc pauc this paper presents a new method that aims at maximizing the pauc by means of linear combination of classifiers the effectiveness of the proposed method has been proved on two biometric databases

efficient multiclass roc approximation by decomposition via confusion matrix perturbation analysis receiver operator characteristic roc analysis has become a standard tool in the design and evaluation of two class classification problems it allows for an analysis that incorporates all possible priors costs and operating points which is important in many real problems where conditions are often nonideal extending this to the multiclass case is attractive conferring the benefits of roc analysis to a multitude of new problems even though the roc analysis extends theoretically to the multiclass case the exponential computational complexity as a function of the number of classes is restrictive in this paper we show that the multiclass roc can often be simplified considerably because some roc dimensions are independent of each other we present an algorithm that analyzes interactions between various roc dimensions identifying independent classes and groups of interacting classes allowing the roc to be decomposed the resulting decomposed roc hypersurface can be interrogated in a similar fashion to the ideal case allowing for approaches such as cost sensitive and neyman pearson optimization as well as the volume under the roc an extensive bouquet of examples and experiments demonstrates the potential of this methodology

a fast sweeping method for eikonal equations in this paper a fast sweeping method for computing the numerical solution of eikonal equations on a rectangular grid is presented the method is an iterative method which uses upwind difference for discretization and uses gauss seidel iterations with alternating sweeping ordering to solve the discretized system the crucial idea is that each sweeping ordering follows a family of characteristics of the corresponding eikonal equation in a certain direction simultaneously the method has an optimal complexity of o n for n grid points and is extremely simple to implement in any number of dimensions monotonicity and stability properties of the fast sweeping algorithm are proven convergence and error estimates of the algorithm for computing the distance function is studied in detail it is shown that 2 n gauss seidel iterations is enough for the distance function in n dimensions an estimation of the number of iterations for general eikonal equations is also studied numerical examples are used to verify the analysis

the idude framework for grayscale image denoising we present an extension of the discrete universal denoiser dude specialized for the denoising of grayscale images the original dude is a low complexity algorithm aimed at recovering discrete sequences corrupted by discrete memoryless noise of known statistical characteristics it is universal in the sense of asymptotically achieving without access to any information on the statistics of the clean sequence the same performance as the best denoiser that does have access to such information the dude however is not effective on grayscale images of practical size the difficulty lies in the fact that one of the dude s key components is the determination of conditional empirical probability distributions of image samples given the sample values in their neighborhood when the alphabet is relatively large as is the case with grayscale images even for a small sized neighborhood the required distributions would be estimated from a large collection of sparse statistics resulting in poor estimates that would not enable effective denoising the present work enhances the basic dude scheme by incorporating statistical modeling tools that have proven successful in addressing similar issues in lossless image compression instantiations of the enhanced framework which is referred to as idude are described for examples of additive and nonadditive noise the resulting denoisers significantly surpass the state of the art in the case of salt and pepper s p and ary symmetric noise and perform well for gaussian noise

bayesian wavelet based image denoising using the gauss hermite expansion the probability density functions pdfs of the wavelet coefficients play a key role in many wavelet based image processing algorithms such as denoising the conventional pdfs usually have a limited number of parameters that are calculated from the first few moments only consequently such pdfs cannot be made to fit very well with the empirical pdf of the wavelet coefficients of an image as a result the shrinkage function utilizing any of these density functions provides a substandard denoising performance in order for the probabilistic model of the image wavelet coefficients to be able to incorporate an appropriate number of parameters that are dependent on the higher order moments a pdf using a series expansion in terms of the hermite polynomials that are orthogonal with respect to the standard gaussian weight function is introduced a modification in the series function is introduced so that only a finite number of terms can be used to model the image wavelet coefficients ensuring at the same time the resulting pdf to be non negative it is shown that the proposed pdf matches the empirical one better than some of the standard ones such as the generalized gaussian or bessel k form pdf a bayesian image denoising technique is then proposed wherein the new pdf is exploited to statistically model the subband as well as the local neighboring image wavelet coefficients experimental results on several test images demonstrate that the proposed denoising method both in the subband adaptive and locally adaptive conditions provides a performance better than that of most of the methods that use pdfs with limited number of parameters

multilayer airfoil ice accretion simulations using a level set method with b spline representation this paper presents a partial differential equation approach to model the icing front evolution on airfoils via the level set equation offering a high fidelity alternative to common algebraic appr

max min distance analysis by using sequential sdp relaxation for dimension reduction we propose a new criterion for discriminative dimension reduction max min distance analysis mmda given a data set with c classes represented by homoscedastic gaussians mmda maximizes the minimum pairwise distance of these c classes in the selected low dimensional subspace thus unlike fisher s linear discriminant analysis flda and other popular discriminative dimension reduction criteria mmda duly considers the separation of all class pairs to deal with general case of data distribution we also extend mmda to kernel mmda kmmda dimension reduction via mmda kmmda leads to a nonsmooth max min optimization problem with orthonormal constraints we develop a sequential convex relaxation algorithm to solve it approximately to evaluate the effectiveness of the proposed criterion and the corresponding algorithm we conduct classification and data visualization experiments on both synthetic data and real data sets experimental results demonstrate the effectiveness of mmda kmmda associated with the proposed optimization algorithm

optimal mesh topology generation for cfd multiblock structured mesh generation is amongst the most popular meshing techniques for flow simulations however the time consuming and user intensive process of blocking complex domains presents a major bottleneck in structured mesh generation to this end we have considered various automatic blocking strategies where some typical aeroengine domains have been showcased an adjoint based error analysis procedure is then used to assess these methods it is found that in general the medial axis based approaches provide optimal blocking and yields better accuracy in computing the functional of interest this is because the medial axis based methods produce meshes which have better flow alignment especially in case of internal flows a new hybrid blocking approach combining the existing methods with the distance field isosurface is also presented to overcome the shortcomings of the current methods such a blocking technique has the potential to be applied to a wide range of flow domains

geometric mean for subspace selection subspace selection approaches are powerful tools in pattern classification and data visualization one of the most important subspace approaches is the linear dimensionality reduction step in the fisher s linear discriminant analysis flda which has been successfully employed in many fields such as biometrics bioinformatics and multimedia information management however the linear dimensionality reduction step in flda has a critical drawback for a classification task with c classes if the dimension of the projected subspace is strictly lower than c 1 the projection to a subspace tends to merge those classes which are close together in the original feature space if separate classes are sampled from gaussian distributions all with identical covariance matrices then the linear dimensionality reduction step in flda maximizes the mean value of the kullback leibler kl divergences between different classes based on this viewpoint the geometric mean for subspace selection is studied in this paper three criteria are analyzed 1 maximization of the geometric mean of the kl divergences 2 maximization of the geometric mean of the normalized kl divergences and 3 the combination of 1 and 2 preliminary experimental results based on synthetic data uci machine learning repository and handwriting digits show that the third criterion is a potential discriminative subspace selection method which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in flda and its several representative extensions

universal approximation using incremental constructive feedforward networks with random hidden nodes according to conventional neural network theories single hidden layer feedforward networks slfns with additive or radial basis function rbf hidden nodes are universal approximators when all the parameters of the networks are allowed adjustable however as observed in most neural network implementations tuning all the parameters of the networks may cause learning complicated and inefficient and it may be difficult to train networks with nondifferential activation functions such as threshold networks unlike conventional neural network theories this paper proves in an incremental constructive method that in order to let slfns work as universal approximators one may simply randomly choose hidden nodes and then only need to adjust the output weights linking the hidden layer and the output layer in such slfns implementations the activation functions for additive nodes can be any bounded nonconstant piecewise continuous functions g r r and the activation functions for rbf nodes can be any integrable piecewise continuous functions g r r and rg x dx 0 the proposed incremental method is efficient not only for sflns with continuous including nondifferentiable activation functions but also for slfns with piecewise continuous such as threshold activation functions compared to other popular methods such a new network is fully automatic and users need not intervene the learning process by manually tuning control parameters

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

face recognition from a single training image under arbitrary unknown lighting using spherical harmonics in this paper we propose two novel methods for face recognition under arbitrary unknown lighting by using spherical harmonics illumination representation which require only one training image per subject and no 3d shape information our methods are based on the result which demonstrated that the set of images of a convex lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low dimensional linear subspace we provide two methods to estimate the spherical harmonic basis images spanning this space from just one image our first method builds the statistical model based on a collection of 2d basis images we demonstrate that by using the learned statistics we can estimate the spherical harmonic basis images from just one image taken under arbitrary illumination conditions if there is no pose variation compared to the first method the second method builds the statistical models directly in 3d spaces by combining the spherical harmonic illumination representation and a 3d morphable model of human faces to recover basis images from images across both poses and illuminations after estimating the basis images we use the same recognition scheme for both methods we recognize the face for which there exists a weighted combination of basis images that is the closest to the test face image we provide a series of experiments that achieve high recognition rates under a wide range of illumination conditions including multiple sources of illumination our methods achieve comparable levels of accuracy with methods that have much more onerous training data requirements comparison of the two methods is also provided

a center sliding bayesian binary classifier adopting orthogonal polynomials a center sliding bayesian design adopting orthogonal polynomials for binary pattern classification is studied in this paper essentially a bayesian weight solution is coupled with a center sliding scheme in feature space which provides an easy tuning capability for binary classification the proposed method is compared with several state of the art binary classifiers in terms of their solution forms decision thresholds and decision boundaries based on the center sliding bayesian framework a novel orthogonal polynomial classifier is subsequently developed the orthogonal polynomial classifier is evaluated using two representative orthogonal polynomials for feature mapping our experimental results show promising potential of the orthogonal polynomial classifier since it achieves both desired accuracy and computational efficiency highlightsproposed a center sliding bayesian classifier with deterministic solution proposed to adopt orthogonal polynomials for efficient feature expansion developed an easy tuning mechanism for the classification framework provided an extensive evaluation of the proposed classifier

distance metric learning for large margin nearest neighbor classification the accuracy of k nearest neighbor knn classification depends significantly on the metric used to compute distances between different examples in this paper we show how to learn a mahalanobis distance metric for knn classification from labeled examples the mahalanobis metric can equivalently be viewed as a global linear transformation of the input space that precedes knn classification using euclidean distances in our approach the metric is trained with the goal that the k nearest neighbors always belong to the same class while examples from different classes are separated by a large margin as in support vector machines svms the margin criterion leads to a convex optimization based on the hinge loss unlike learning in svms however our approach requires no modification or extension for problems in multiway as opposed to binary classification in our framework the mahalanobis distance metric is obtained as the solution to a semidefinite program on several data sets of varying size and difficulty we find that metrics trained in this way lead to significant improvements in knn classification sometimes these results can be further improved by clustering the training examples and learning an individual metric within each cluster we show how to learn and combine these local metrics in a globally integrated manner

between classification error approximation and weighted least squares learning this paper presents a deterministic solution to an approximated classification error based objective function in the formulation we propose a quadratic approximation as the function for achieving smooth error counting the solution is subsequently found to be related to the weighted least squares whereby a robust tuning process can be incorporated the tuning traverses between the least squares estimate and the approximated total error rate estimate to cater to various situations of unbalanced attribute distributions by adopting a linear parametric classifier model the proposed classification error based learning formulation is empirically shown to be superior to that using the original least squares error cost function finally it will be seen that the performance of the proposed formulation is comparable to other classification error based and state of the art classifiers without sacrificing the computational simplicity

maximizing the area under the roc curve by pairwise feature combination the majority of the available classification systems focus on the minimization of the classification error rate this is not always a suitable metric specially when dealing with two class problems with skewed classes and cost distributions in this case an effective criterion to measure the quality of a decision rule is the area under the receiver operating characteristic curve auc that is also useful to measure the ranking quality of a classifier as required in many real applications in this paper we propose a nonparametric linear classifier based on the maximization of auc the approach lies on the analysis of the wilcoxon mann whitney statistic of each single feature and on an iterative pairwise coupling of the features for the optimization of the ranking of the combined feature by the pairwise feature evaluation the proposed procedure is essentially different from other classifiers using auc as a criterion experiments performed on synthetic and real data sets and comparisons with previous approaches confirm the effectiveness of the proposed method

manifold regularized discriminative nonnegative matrix factorization with fast gradient descent nonnegative matrix factorization nmf has become a popular data representation method and has been widely used in image processing and pattern recognition problems this is because the learned bases can be interpreted as a natural parts based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole for practical classification tasks however nmf ignores both the local geometry of data and the discriminative information of different classes in addition existing research results show that the learned basis is unnecessarily parts based because there is neither explicit nor implicit constraint to ensure the representation parts based in this paper we introduce the manifold regularization and the margin maximization to nmf and obtain the manifold regularized discriminative nmf md nmf to overcome the aforementioned problems the multiplicative update rule mur can be applied to optimizing md nmf but it converges slowly in this paper we propose a fast gradient descent fgd to optimize md nmf fgd contains a newton method that searches the optimal step length and thus fgd converges much faster than mur in addition fgd includes mur as a special case and can be applied to optimizing nmf and its variants for a problem with 165 samples in r1600 fgd converges in 28 s while mur requires 282 s we also apply fgd in a variant of md nmf and experimental results confirm its efficiency experimental results on several face image datasets suggest the effectiveness of md nmf

generalization performance of magnitude preserving semi supervised ranking with graph based regularization semi supervised ranking is a relatively new and important learning problem inspired by many applications we propose a novel graph based regularized algorithm which learns the ranking function in the semi supervised learning framework it can exploit geometry of the data while preserving the magnitude of the preferences the least squares ranking loss is adopted and the optimal solution of our model has an explicit form we establish error analysis of our proposed algorithm and demonstrate the relationship between predictive performance and intrinsic properties of the graph the experiments on three datasets for recommendation task and two quantitative structure activity relationship datasets show that our method is effective and comparable to some other state of the art algorithms for ranking

daml domain adaptation metric learning the state of the art metric learning algorithms cannot perform well for domain adaptation settings such as cross domain face recognition image annotation etc because labeled data in the source domain and unlabeled ones in the target domain are drawn from different but related distributions in this paper we propose the domain adaptation metric learning daml by introducing a data dependent regularization to the conventional metric learning in the reproducing kernel hilbert space rkhs this data dependent regularization resolves the distribution difference by minimizing the empirical maximum mean discrepancy between source and target domain data in rkhs theoretically by using the empirical rademacher complexity we prove risk bounds for the nearest neighbor classifier that uses the metric learned by daml practically learning the metric in rkhs does not scale up well fortunately we can prove that learning daml in rkhs is equivalent to learning daml in the space spanned by principal components of the kernel principle component analysis kpca thus we can apply kpca to select most important principal components to significantly reduce the time cost of daml we perform extensive experiments over four well known face recognition datasets and a large scale web image annotation dataset for the cross domain face recognition and image annotation tasks under various settings and the results demonstrate the effectiveness of daml

logdet divergence based metric learning with triplet constraints and its applications how to select and weigh features has always been a difficult problem in many image processing and pattern recognition applications a data dependent distance measure can address this problem to a certain extent and therefore an accurate and efficient metric learning becomes necessary in this paper we propose a logdet divergence based metric learning with triplet constraints ldmlt approach which can learn mahalanobis distance metric accurately and efficiently first of all we demonstrate the good properties of triplet constraints and apply it in logdet divergence based metric learning model then to deal with high dimensional data we apply a compressed representation method to learn store and evaluate mahalanobis matrix efficiently besides a dynamic triplets building strategy is proposed to build a feedback from the obtained mahalanobis matrix to the triplet constraints which can further improve the ldmlt algorithm furthermore the proposed method is applied to various applications including pattern recognition facial expression recognition and image retrieval the results demonstrate the improved performance of the proposed approach

robust transfer metric learning for image classification metric learning has attracted increasing attention due to its critical role in image analysis and classification conventional metric learning always assumes that the training and test data are sampled from the same or similar distribution however to build an effective distance metric we need abundant supervised knowledge i e side label information which is generally inaccessible in practice because of the expensive labeling cost in this paper we develop a robust transfer metric learning rtml framework to effectively assist the unlabeled target learning by transferring the knowledge from the well labeled source domain specifically rtml exploits knowledge transfer to mitigate the domain shift in two directions i e sample space and feature space in the sample space domain wise and class wise adaption schemes are adopted to bridge the gap of marginal and conditional distribution disparities across two domains in the feature space our metric is built in a marginalized denoising fashion and low rank constraint which make it more robust to tackle noisy data in reality furthermore we design an explicit rank constraint regularizer to replace the rank minimization np hard problem to guide the low rank metric learning experimental results on several standard benchmarks demonstrate the effectiveness of our proposed rtml by comparing it with the state of the art transfer learning and metric learning algorithms

robust multi source adaptation visual classification using supervised low rank representation abstract how to guarantee the robustness of multi source adaptation visual classification is an important challenge in current visual learning community to this end we address in this paper the problem of robust visual classification with few labeled samples from the target domain of interest by leveraging multiple prior source models motivated by the recent success of low rank representation we formulate this problem as a robust multi source adaptation visual classification rmavc model with supervised low rank representation by combining the strength of discriminative information from the target domain and the prior models from multiple source domains specifically we propose a joint supervised low rank representation and multi source adaptation visual classification framework which achieves dual goals of finding the most discriminative low rank representation and multi source adaptation classifier parameters for the target domain while it is showed in this paper that the proposed rmavc framework is effective and can produce high accuracy on several tasks of multi source adaptation visual classification this framework fails to consider the local geometrical structure of the target data and the heterogeneousness among multiple source domains hence under this framework we further present two effective extensions or variants i e rmavck and rmavc fm by exploiting multiple kernel trick and flexible manifold regularization respectively the proposed framework and its variants are robust for classifying visual objects accurately and the experimental results demonstrate the effectiveness of our methods on several types of image and video datasets

multimodal graph based reranking for web image search this paper introduces a web image search reranking approach that explores multiple modalities in a graph based learning scheme different from the conventional methods that usually adopt a single modality or integrate multiple modalities into a long feature vector our approach can effectively integrate the learning of relevance scores weights of modalities and the distance metric and its scaling for each modality into a unified scheme in this way the effects of different modalities can be adaptively modulated and better reranking performance can be achieved we conduct experiments on a large dataset that contains more than 1000 queries and 1 million images to evaluate our approach experimental results demonstrate that the proposed reranking approach is more robust than using each individual modality and it also performs better than many existing methods

density dependent quantized least squares support vector machine for large data sets based on the knowledge that input data distribution is important for learning a data density dependent quantization scheme dqs is proposed for sparse input data representation the usefulness of the representation scheme is demonstrated by using it as a data preprocessing unit attached to the well known least squares support vector machine ls svm for application on big data sets essentially the proposed dqs adopts a single shrinkage threshold to obtain a simple quantization scheme which adapts its outputs to input data density with this quantization scheme a large data set is quantized to a small subset where considerable sample size reduction is generally obtained in particular the sample size reduction can save significant computational cost when using the quantized subset for feature approximation via the nystrom method based on the quantized subset the approximated features are incorporated into ls svm to develop a data density dependent quantized ls svm dqls svm where an analytic solution is obtained in the primal solution space the developed dqls svm is evaluated on synthetic and benchmark data with particular emphasis on large data sets extensive experimental results show that the learning machine incorporating dqs attains not only high computational efficiency but also good generalization performance

formulating face verification with semidefinite programming this paper presents a unified solution to three unsolved problems existing in face verification with subspace learning techniques selection of verification threshold automatic determination of subspace dimension and deducing feature fusing weights in contrast to previous algorithms which search for the projection matrix directly our new algorithm investigates a similarity metric matrix smm with a certain verification threshold this matrix is learned by a semidefinite programming approach along with the constraints of the kindred pairs with similarity larger than the threshold and inhomogeneous pairs with similarity smaller than the threshold then the subspace dimension and the feature fusing weights are simultaneously inferred from the singular value decomposition of the derived smm in addition the weighted and tensor extensions are proposed to further improve the algorithmic effectiveness and efficiency respectively essentially the verification is conducted within an affine subspace in this new algorithm and is hence called the affine subspace for verification asv extensive experiments show that the asv can achieve encouraging face verification accuracy in comparison to other subspace algorithms even without the need to explore any parameters

enhanced fisher discriminant criterion for image recognition many previous studies have shown that image recognition can be significantly improved by fisher linear discriminant analysis flda technique however flda ignores the variation of data points from the same class which characterizes the most important modes of variability of patterns and helps to improve the generalization capability of flda thus the performance of flda on testing data is not good enough in this paper we propose an enhanced fisher discriminant criterion efdc efdc explicitly considers the intra class variation and incorporates the intra class variation into the fisher discriminant criterion to build a robust and efficient dimensionality reduction function efdc obtains a subspace which best detects the discriminant structure and simultaneously preserves the modes of variability of patterns which will result in stable intraclass representation experimental results on four image database show a clear improvement over the results of flda based methods

cross domain person reidentification using domain adaptation ranking svms this paper addresses a new person reidentification problem without label information of persons under nonoverlapping target cameras given the matched positive and unmatched negative image pairs from source domain cameras as well as unmatched negative and unlabeled image pairs from target domain cameras we propose an adaptive ranking support vector machines adarsvms method for reidentification under target domain cameras without person labels to overcome the problems introduced due to the absence of matched positive image pairs in the target domain we relax the discriminative constraint to a necessary condition only relying on the positive mean in the target domain to estimate the target positive mean we make use of all the available data from source and target domains as well as constraints in person reidentification inspired by adaptive learning methods a new discriminative model with high confidence in target positive mean and low confidence in target negative image pairs is developed by refining the distance model learnt from the source domain experimental results show that the proposed adarsvm outperforms existing supervised or unsupervised learning or non learning reidentification methods without using label information in target cameras moreover our method achieves better reidentification performance than existing domain adaptation methods derived under equal conditional probability assumption

hyperdisk based large margin classifier we introduce a large margin linear binary classification framework that approximates each class with a hyperdisk the intersection of the affine support and the bounding hypersphere of its training samples in feature space and then finds the linear classifier that maximizes the margin separating the two hyperdisks we contrast this with support vector machines svms which find the maximum margin separator of the pointwise convex hulls of the training samples arguing that replacing convex hulls with looser convex class models such as hyperdisks provides safer margin estimates that improve the accuracy on some problems both the hyperdisks and their separators are found by solving simple quadratic programs the method is extended to nonlinear feature spaces using the kernel trick and multi class problems are dealt with by combining binary classifiers in the same ways as for svms experiments on a range of data sets show that the method compares favourably with other popular large margin classifiers

dimensionality reduction by mixed kernel canonical correlation analysis in this paper we propose a novel method named mixed kernel cca mkcca to achieve easy yet accurate implementation of dimensionality reduction mkcca consists of two major steps first the high dimensional data space is mapped into the reproducing kernel hilbert space rkhs rather than the hilbert space with a mixture of kernels i e a linear combination between a local kernel and a global kernel meanwhile a uniform design for experiments with mixtures is also introduced for model selection second in the new rkhs kernel cca is further improved by performing principal component analysis pca followed by cca for effective dimensionality reduction we prove that mkcca can actually be decomposed into two separate components i e pca and cca which can be used to better remove noises and tackle the issue of trivial learning existing in cca or traditional kernel cca after this the proposed mkcca can be implemented in multiple types of learning such as multi view learning supervised learning semi supervised learning and transfer learning with the reduced data we show its superiority over existing methods in different types of learning by extensive experimental results