analysing images of curved surfaces a reflectance map makes the relationship between image intensity and surface orientation explicit trade offs between image intensity and surface orientation emerge which cannot be resolved locally in a single view existing methods for determining surface orientation from a single view embody assumptions about surface curvature the hessian matrix is introduced to represent surface curvature properties of surface curvature are expressed as properties of the hessian matrix for several classes of surface image analysis simplifies this result has already been established for planar surfaces forming trihedral corners similar simplification is demonstrated for developable surfaces and for the subclass of surfaces known as generalized cones these studies help to delineate shape information that can be determined from geometric measurements at object boundaries and shape information that can be determined from intensity measurements over sections of smoothly curved surface a novel technique called photometric stereo is discussed the idea of stereo is to obtain multiple images in order to determine the underlying scene precisely in photometric stereo the viewing direction is constant multiple images are obtained by varying the incident illumination it is shown that this provides sufficient information to determine surface orientation at each image point

worst case linear discriminant analysis as scalable semidefinite feasibility problems in this paper we propose an efficient semidefinite programming sdp approach to worst case linear discriminant analysis wlda compared with the traditional lda wlda considers the dimensionality reduction problem from the worst case viewpoint which is in general more robust for classification however the original problem of wlda is non convex and difficult to optimize in this paper we reformulate the optimization problem of wlda into a sequence of semidefinite feasibility problems to efficiently solve the semidefinite feasibility problems we design a new scalable optimization method with a quasi newton method and eigen decomposition being the core components the proposed method is orders of magnitude faster than standard interior point sdp solvers experiments on a variety of classification problems demonstrate that our approach achieves better performance than standard lda our method is also much faster and more scalable than standard interior point sdp solvers based wlda the computational complexity for an sdp with m constraints and matrices of size d by d is roughly reduced from mathcal o m 3 md 3 m 2 d 2 to mathcal o d 3 m d in our case

modified principal component analysis an integration of multiple similarity subspace models we modify the conventional principal component analysis pca and propose a novel subspace learning framework modified pca mpca using multiple similarity measurements mpca computes three similarity matrices exploiting the similarity measurements 1 mutual information 2 angle information and 3 gaussian kernel similarity we employ the eigenvectors of similarity matrices to produce new subspaces referred to as similarity subspaces a new integrated similarity subspace is then generated using a novel feature selection approach this approach needs to construct a kind of vector set termed weak machine cell wmc which contains an appropriate number of the eigenvectors spanning the similarity subspaces combining the wrapper method and the forward selection scheme mpca selects a wmc at a time that has a powerful discriminative capability to classify samples mpca is very suitable for the application scenarios in which the number of the training samples is less than the data dimensionality mpca outperforms the other state of the art pca based methods in terms of both classification accuracy and clustering result in addition mpca can be applied to face image reconstruction mpca can use other types of similarity measurements extensive experiments on many popular real world data sets such as face databases show that mpca achieves desirable classification results as well as has a powerful capability to represent data

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

discriminant subspace analysis a fukunaga koontz approach the fisher linear discriminant fld is commonly used in pattern recognition it finds a linear subspace that maximally separates class patterns according to the fisher criterion several methods of computing the fld have been proposed in the literature most of which require the calculation of the so called scatter matrices in this paper we bring a fresh perspective to fld via the fukunaga koontz transform fkt we do this by decomposing the whole data space into four subspaces with different discriminabilities as measured by eigenvalue ratios by connecting the eigenvalue ratio with the generalized eigenvalue we show where the fisher criterion is maximally satisfied we prove the relationship between fld and fkt analytically and propose a unified framework to understanding some existing work furthermore we extend our theory to the multiple discriminant analysis mda this is done by transforming the data into intraclass and extraclass spaces followed by maximizing the bhattacharyya distance based on our fkt analysis we identify the discriminant subspaces of mda fkt and propose an efficient algorithm which works even when the scatter matrices are singular or too large to be formed our method is general and may be applied to different pattern recognition problems we validate our method by experimenting on synthetic and real data

improved discriminate analysis for high dimensional data and its application to face recognition many pattern recognition applications involve the treatment of high dimensional data and the small sample size problem principal component analysis pca is a common used dimension reduction technique linear discriminate analysis lda is often employed for classification pca plus lda is a famous framework for discriminant analysis in high dimensional space and singular cases in this paper we examine the theory of this framework and find out that even if there is no small sample size problem the pca dimension reduction cannot guarantee the subsequent successful application of lda we thus develop an improved discriminate analysis method by introducing an inverse fisher criterion and adding a constrain in pca procedure so that the singularity phenomenon will not occur experiment results on face recognition suggest that this new approach works well and can be applied even when the number of training samples is one per class

clutter invariant atr one of the central problems in automated target recognition is to accommodate the infinite variety of clutter in real military environments the principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter such metrics are formulated using second order random field models our results indicate that this approach significantly improves detection classification rates of targets in clutter

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic

comments on globally maximizing locally minimizing unsupervised discriminant projection with application to face and palm biometrics this paper develops an unsupervised discriminant projection udp technique for dimensionality reduction of high dimensional data in small sample size cases udp can be seen as a linear approximation of a multimanifolds based learning framework which takes into account both the local and nonlocal quantities udp characterizes the local scatter as well as the nonlocal scatter seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter this characteristic makes udp more intuitive and more powerful than the most up to date method locality preserving projection lpp which considers only the local scatter for clustering or classification tasks the proposed method is applied to face and palm biometrics and is examined using the yale feret and ar face image databases and the polyu palmprint database the experimental results show that udp consistently outperforms lpp and pca and outperforms lda when the training sample size per class is small this demonstrates that udp is a good choice for real world biometrics applications

robust regression for face recognition in this paper we address the problem of robust face recognition by formulating the pattern recognition task as a problem of robust estimation using a fundamental concept that in general patterns from a single object class lie on a linear subspace barsi and jacobs 2003 1 we develop a linear model representing a probe image as a linear combination of class specific galleries in the presence of noise the well conditioned inverse problem is solved using the robust huber estimation and the decision is ruled in favor of the class with the minimum reconstruction error the proposed robust linear regression classification rlrc algorithm is extensively evaluated for two important cases of robustness i e illumination variations and random pixel corruption illumination invariant face recognition is demonstrated on three standard databases under exemplary evaluation protocols reported in the literature comprehensive comparative analysis with the state of art illumination tolerant approaches indicates a comparable performance index for the proposed rlrc algorithm the efficiency of the proposed approach in the presence of severe random noise is validated under several exemplary noise models such as dead pixel problem salt and pepper noise speckle noise and additive white gaussian noise awgn the rlrc algorithm is found to be favorable compared with the benchmark generative approaches

algebraic feature extraction for image recognition based on an optimal discriminant criterion abstract a novel algebraic feature extraction method for image recognition is presented the main difference between the present method and any other existing algebraic feature extraction method is that the present method uses an optimal discriminant criterion to extract algebraic features for the given training image samples a set of optimal discriminant projection vectors is calculated according to a generalized fisher criterion function on the basis of the optimal discriminant projection vector the projective feature vectors of an image i e algebraic features are extracted by projecting the image onto all optimal discriminant projection vectors the method of calculating the set of optimal discriminant projection vectors is discussed a minimum distance classifier is also proposed for classifying projective feature vectors experimental results showed that the present method has good recognition performance an important conclusion about the present method is that the foley sammon optimal set of discriminant vectors is a special case of the set of optimal discriminant projection vectors

a discussion of stress rates in finite deformation problems abstract it has recently been shown that the finite elastic plastic solution of the simple shear problem exhibits an oscillatory stress response when kinematic hardening is employed while the solution for isotropic hardening gives a monotonically increasing stress this paper analyzes this response on the basis of continuum mechanical descriptions of the problem three objective stress rates are recalled and spatial descriptions of plasticity at finite deformation are reviewed for the usual generalization of the infinitesimal theory as well as a theory based on an invariant measure of true stress in light of the equations for the evolution of the yield surface the hypoelastic solution to the simple shear problem for each of the three stress rates is presented it is shown that the use of the jaumann rate in the generalization of the infinitesimal theory leads to an oscillation in the evolution of the yield surface in simple shear which is explained on the basis of the hypoelastic solution an alternative theory which makes use of the polar decomposition predicts a monotonically increasing shear stress

linear regression for face recognition in this paper we present a novel approach of face identification by formulating the pattern recognition problem in terms of linear regression using a fundamental concept that patterns from a single object class lie on a linear subspace we develop a linear model representing a probe image as a linear combination of class specific galleries the inverse problem is solved using the least squares method and the decision is ruled in favor of the class with the minimum reconstruction error the proposed linear regression classification lrc algorithm falls in the category of nearest subspace classification the algorithm is extensively evaluated on several standard databases under a number of exemplary evaluation protocols reported in the face recognition literature a comparative study with state of the art algorithms clearly reflects the efficacy of the proposed approach for the problem of contiguous occlusion we propose a modular lrc approach introducing a novel distance based evidence fusion def algorithm the proposed methodology achieves the best results ever reported for the challenging problem of scarf occlusion

finding the zeros of a univariate equation proxy rootfinders chebyshev interpolation and the companion matrix when a function f x is holomorphic on an interval x in a b its roots on the interval can be computed by the following three step procedure first approximate f x on a b by a poly

maximal likelihood correspondence estimation for face recognition across pose due to the misalignment of image features the performance of many conventional face recognition methods degrades considerably in across pose scenario to address this problem many image matching based methods are proposed to estimate semantic correspondence between faces in different poses in this paper we aim to solve two critical problems in previous image matching based correspondence learning methods 1 fail to fully exploit face specific structure information in correspondence estimation and 2 fail to learn personalized correspondence for each probe image to this end we first build a model termed as morphable displacement field mdf to encode face specific structure information of semantic correspondence from a set of real samples of correspondences calculated from 3d face models then we propose a maximal likelihood correspondence estimation mlce method to learn personalized correspondence based on maximal likelihood frontal face assumption after obtaining the semantic correspondence encoded in the learned displacement we can synthesize virtual frontal images of the profile faces for subsequent recognition using linear discriminant analysis method with pixel intensity features state of the art performance is achieved on three multipose benchmarks i e cmu pie feret and multipie databases owe to the rational mdf regularization and the usage of novel maximal likelihood objective the proposed mlce method can reliably learn correspondence between faces in different poses even in complex wild environment i e labeled face in the wild database

compound rank k projections for bilinear analysis in many real world applications data are represented by matrices or high order tensors despite the promising performance the existing 2 d discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection making the model less flexible in this paper we propose a novel compound rank k projection crp algorithm for bilinear analysis the crp deals with matrices directly without transforming them into vectors and it therefore preserves the correlations within the matrix and decreases the computation complexity different from the existing 2 d discriminant analysis algorithms objective function values of crp increase monotonically in addition the crp utilizes multiple rank k projection models to enable a larger search space in which the optimal solution can be found in this way the discriminant ability is enhanced we have tested our approach on five data sets including uuim cvl pointing 04 usps and coil20 experimental results show that the performance of our proposed crp performs better than other algorithms in terms of classification accuracy

relations among some low rank subspace recovery models recovering intrinsic low dimensional subspaces from data distributed on them is a key preprocessing step to many applications in recent years a lot of work has modeled subspace recovery as low rank minimization problems we find that some representative models such as robust principal component analysis r pca robust low rank representation r lrr and robust latent low rank representation r latlrr are actually deeply connected more specifically we discover that once a solution to one of the models is obtained we can obtain the solutions to other models in closed form formulations since r pca is the simplest our discovery makes it the center of low rank subspace recovery models our work has two important implications first r pca has a solid theoretical foundation under certain conditions we could find globally optimal solutions to these low rank models at an overwhelming probability although these models are nonconvex second we can obtain significantly faster algorithms for these models by solving r pca first the computation cost can be further cut by applying low complexity randomized algorithms for example our novel filtering algorithm to r pca although for the moment the formal proof of our filtering algorithm is not yet available experiments verify the advantages of our algorithm over other state of the art methods based on the alternating direction method

arithmetic operations on independent random variables a numerical approach dealing with imprecise quantities is an important problem in scientific computation model parameters are known only approximately typically in the form of probability density functions unfortunately there are currently no methods of taking uncertain parameters into account which would at the same time be easy to apply and highly accurate an important special case is operations on independent random variables which occur frequently in obtaining confidence intervals for physical measurements and statistical estimators in this paper we investigate the possibility of implementing arithmetic operations on independent random variables numerically equivalently the problem can be viewed as propagating approximated probability density functions through arithmetic operations we introduce a very broad family of distributions which is closed under the four arithmetic operations and taking powers furthermore we show that the densities of the distributions in the family can be effectively approximated using ch

large correlation analysis in this paper a novel supervised dimensionality reduction method is developed based on both the correlation analysis and the idea of large margin learning the method aims to maximize the minimal correlation between each dimensionality reduced instance and its class label thus named as large correlation analysis lca unlike most existing correlation analysis methods such as cca ccas and cda which all maximize the total or ensemble correlation over all training instances lca devotes to maximizing the individual correlations between given instances and its associated labels and is established by solving a relaxed quadratic programming with box constraints experimental results on real world datasets from both uci and usps show its effectiveness compared to the existing canonical correlation analysis methods

rapid and brief communication face recognition based on 2d fisherface approach two dimensional 2d discrimination analysis using methods such as 2d pca and image lda is of interest in face recognition because it extracts discriminative features faster than one dimensional 1d discrimination analysis however existing 2d methods generally use more discriminative features and take longer to test than 1d methods 2d pca in particular cannot make full use of the fisher discriminant criterion image lda also has drawbacks in that it cannot perform 2d principal component analysis and discards components with poor discriminative capabilities in addition existing 2d methods cannot provide an automatic strategy to choose 2d principal components or discriminant vectors in this paper we propose 2d fisherface a novel discrimination approach that combines the two stage pca lda strategy and 2d discrimination techniques it can extract face discriminative features by automatically selecting two dimensional principal components and discriminant vectors using the ar database as the test data it is shown that the proposed approach is faster and more effective than several representative 1d and 2d discrimination methods

fast computation of low rank matrix approximations given a matrix a it is often desirable to find a good approximation to a that has low rank we introduce a simple technique for accelerating the computation of such approximations when a has strong spectral features that is when the singular values of interest are significantly greater than those of a random matrix with size and entries similar to a our technique amounts to independently sampling and or quantizing the entries of a thus speeding up computation by reducing the number of nonzero entries and or the length of their representation our analysis is based on observing that the acts of sampling and quantization can be viewed as adding a random matrix n to a whose entries are independent random variables with zero mean and bounded variance since with high probability n has very weak spectral features we can prove that the effect of sampling and quantization nearly vanishes when a low rank approximation to a p n is computed we give high probability bounds on the quality of our approximation both in the frobenius and the 2 norm

a new discriminant subspace analysis approach for multi class problems fukunaga koontz transform fkt is a famous feature extraction method in statistical pattern recognition which aims to find a set of vectors that have the best representative power for one class while the poorest representative power for the other class li and savvides 1 propose a one against all strategy to deal with multi class problems in which the two class fkt method can be directly applied to find the presentative vectors of each class motivated by the fkt method in this paper we propose a new discriminant subspace analysis dsa method for the multi class feature extraction problems to solve dsa we propose an iterative algorithm for the joint diagonalization jd problem finally we generalize the linear dsa method to handle nonlinear feature extraction problems via the kernel trick to demonstrate the effectiveness of the proposed method for pattern recognition problems we conduct extensive experiments on real data sets and show that the proposed method outperforms most commonly used feature extraction methods

recovery guarantees for exemplar based clustering for a certain class of distributions we prove that the linear programming relaxation of k medoids clustering a variant of k means clustering where means are replaced by exemplars from within the dataset distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn and the separation distance between any two balls are sufficiently large our results hold in the nontrivial regime where the separation distance is small enough that points drawn from different balls may be closer to each other than points drawn from the same ball in this case clustering by thresholding pairwise distances between points can fail we also exhibit numerical evidence of high probability recovery in a substantially more permissive regime

optimal discriminant plane for a small number of samples and design method of classifier on the plane abstract in a previous work zi quan hong and jing yu yang minimum distance classifier on the optimal discriminant plane we suggested and derived a method for constructing classifier on the optimal discriminant plane using minimum distance criteria in this paper the problem of solving optimal discriminant plane for a small number of samples is discussed which is based on the above paper by the same authors in the case of a small number of samples generalized eigenequation ax bx established for a large number of samples usually has no solution because within class scatter matrix is singular to obtain the solution of the generalized eigenequation a new method is suggested in which the singular value perturbation is added to the within class scatter matrix such that the matrix becomes a nonsingular matrix therefore the generalized eigenequation can be solved using existing algorithms we proved that the generalized eigenequations on the optimal discriminant plane are stable in respect of eigenvalues and the generalized eigenvectors are indeed the optimal discriminant directions if the perturbation is subject to some certain conditions the experimental results have shown that our method works well and the minimum distance classifier on the optimal discriminant plane can be constructed with high performance even in the case of a small number of samples

segmented minimum noise fraction transformation for efficient feature extraction of hyperspectral images in this paper a segmented minimum noise fraction mnf transformation is proposed for efficient feature extraction of hyperspectral images hsis the original bands can be partitioned into several highly correlated subgroups based on the correlation matrix image of the hyperspectral data the mnf is implemented separately on each subgroup of the data and then the bhattacharyya distance is used as the band separability measure for feature extraction consequently the extracted features can then be significantly classified using state of art classifiers i e k nn or svm experiments on two benchmark hsis collected by aviris and rosis demonstrate that the proposed method significantly reduces the transformation time in comparison with the conventional mnf the fisher scalars criterion shows that the class separability with the segmented mnf is the best and the extracted features even exhibit higher classification accuracy compared with the pca or mnf highlightsa segmented minimum noise fraction mnf transformation is proposed for efficient feature extraction of hyperspectral images hsis the proposed method significantly reduces the transformation time in comparison with the conventional mnf the class separability of the extracted features is improved the extracted features by smnf even exhibit higher classification accuracy compared with the pca or mnf

semantic preserving distance metric learning and applications how do we accurately browse a large set of images or efficiently annotate the images from an image library image clustering methods are invaluable tools for applications such as content based image retrieval and image annotation to perform these tasks it is critical to have proper features to describe the visual and semantic content of images and to define an accurate distance metric to measure the dissimilarity between any two images however existing methods which adopt the features of color histograms edge direction histograms and shape context lack the ability to describe semantic content to solve this problem we propose a new approach that utilizes user provided pairwise constraints to describe the semantic relationship between two images a semantic preserving distance metric learning sp dml algorithm is developed to explore the complementary characteristics of the visual features and pairwise constraints in a unified feature space in this space the learned distance metric can be used to measure the dissimilarity between two images specifically the manifold structure adopted in sp dml is revealed by the image s visual features to integrate semantic contents in distance metric learning sp dml utilizes pairwise constraints to build semantic patches and align these patches to obtain the optimal distance metric for the new feature space experimental results in image clustering demonstrate that the performance of sp dml is appealing

flexible manifold embedding a framework for semi supervised and unsupervised dimension reduction we propose a unified manifold learning framework for semi supervised and unsupervised dimension reduction by employing a simple but effective linear regression function to map the new data points for semi supervised dimension reduction we aim to find the optimal prediction labels f for all the training samples x the linear regression function h x and the regression residue f0 f h x simultaneously our new objective function integrates two terms related to label fitness and manifold smoothness as well as a flexible penalty term defined on the residue f0 our semi supervised learning framework referred to as flexible manifold embedding fme can effectively utilize label information from labeled data as well as a manifold structure from both labeled and unlabeled data by modeling the mismatch between h x and f we show that fme relaxes the hard linear constraint f h x in manifold regularization mr making it better cope with the data sampled from a nonlinear manifold in addition we propose a simplified version referred to as fme u for unsupervised dimension reduction we also show that our proposed framework provides a unified view to explain and understand many semi supervised supervised and unsupervised dimension reduction techniques comprehensive experiments on several benchmark databases demonstrate the significant improvement over existing dimension reduction algorithms

towards robust discriminative projections learning via non greedy l2 1 norm minmax linear discriminant analysis lda is one of the most successful supervised dimensionality reduction methods and has been widely used in many real world applications however the l 2 norm is employed as the distance measure in objective of lda which is sensitive to outliers many previous works improve the robustness of lda by using l1 norm distance however the robustness against outliers is limited and the solver of l1 norm are mostly based on greedy search strategy which is time consuming and easy to get stuck in a local optimum in this paper we propose a novel robust lda measured by l 2 1 norm to learn robust discriminative projections since the proposed model needs to minimize and maximize minmax l 2 1 norm terms simultaneously it is challenging to solve as a result we first systematically derive an efficient iterative optimization algorithm to solve a general ratio minimization problem and rigorously prove its convergence more importantly an efficient non greedy iterative re weighted optimization algorithm is developed based on preceding approach for solving proposed l 2 1 norm minmax problem besides an optimal weighted mean mechanism is driven according to designed objective and solver which can be applied to other approach for robustness improvement extensive experimental results on several real world datasets show the effectiveness of proposed method

optimal fisher discriminant analysis using the rank decomposition abstract the fisher optimal discriminant vector is a very efficient means in high dimensional pattern analysis in the case of a small number of samples the within class scatter matrix s w is singular therefore the calculation of the fisher optimal discriminant vector becomes very important in this paper the conception of the rank decomposition of matrices is first introduced and a new method for calculating the fisher optimal discriminant vector is presented which is particularly well suited to the case of a small number of samples in the sense that the scatter matrices are rank deficient the new method is compared with the pseudoinverse and perturbation methods in tian j opt soc am a 5 1670 1672 1988 and hong and yang pattern recognition 24 317 324 1991 an important conclusion is proved in the three methods our method is the best one for calculating the fisher optimal discriminant vectors in the cases of both a large and a small number of samples the experimental results have also shown that our method can give the highest recognition rate in the case of a small number of samples among the three methods

general subspace learning with corrupted training data via graph embedding we address the following subspace learning problem supposing we are given a set of labeled corrupted training data points how to learn the underlying subspace which contains three components an intrinsic subspace that captures certain desired properties of a data set a penalty subspace that fits the undesired properties of the data and an error container that models the gross corruptions possibly existing in the data given a set of data points these three components can be learned by solving a nuclear norm regularized optimization problem which is convex and can be efficiently solved in polynomial time using the method as a tool we propose a new discriminant analysis i e supervised subspace learning algorithm called corruptions tolerant discriminant analysis ctda in which the intrinsic subspace is used to capture the features with high within class similarity the penalty subspace takes the role of modeling the undesired features with high between class similarity and the error container takes charge of fitting the possible corruptions in the data we show that ctda can well handle the gross corruptions possibly existing in the training data whereas previous linear discriminant analysis algorithms arguably fail in such a setting extensive experiments conducted on two benchmark human face data sets and one object recognition data set show that ctda outperforms the related algorithms

a novel feature extraction method for image recognition based on similar discriminant function sdf abstract the extraction of image features is the most fundamental and important problem in image recognition in this paper a similarity measure of matrices is first presented and a similar discriminant function sdf of images is established based on the discriminant function we further propose a novel feature extraction method for image recognition for each class of training image samples an optimal projection axis maximizing the similarity among these training image samples for the class is calculated unlike the common methods of feature extraction we extract a projective feature vector for a training image sample by projecting the image on the optimal projection axis of the class itself and a set of projective feature vectors for a testing image sample by projecting the image on all the optimal projection axes finally a hierarchical classifier in the optimal discriminant space is designed to recognize images in order to test the efficiency of our method it is used to recognize human faces and english characters experimental results have shown that our method has good recognition performance and the extracted projective feature vectors contain more recognition information than commonly used image features

algebraic feature extraction of image for recognition abstract the extraction of image features is one of the fundamental tasks in image recognition up until now there have been several kinds of features to be used for the purpose of image recognition as follows 1 visual features 2 statistical features of pixel 3 transform coefficient features in addition there is another kind of feature which the author believes is very useful i e 4 algebraic features which represent intrinsic attributions of an image singular values sv of image are this kind of feature in this paper we prove that sv feature vector has some important properties of algebraic and geometric invariance and insensitiveness to noise these properties are very useful for the description and recognition of images as an example sv feature vector is used for the problem of recognizing human facial images in this paper using sv feature vector samples of facial images a normal pattern bayes classification model based on sammon s optimal descriminant plane is constructed the experimental result shows that sv feature vector has good performance of class separation

description and discrimination of planar shapes using shape matrices a shape descriptor has been developed which can describe a shape independent of its translation rotation and scaling the description is in the form of a matrix and it is obtained by a polar quantization of a shape the quantization process takes into consideration not only a shape s outer geometry but its inner geometry as well the descriptor is information preserving and if the quantization parameters are selected properly it is possible to reconstruct an original shape from its description in this technique shape discrimination is possible by a simple exclusive or operation on shape descriptions

a fast simple and stable chebyshev legendre transform using an asymptotic formula a fast simple and numerically stable transform for converting between legendre and chebyshev coefficients of a degree n polynomial in mathcal o n log n 2 log log n operations is derived the fundamental idea of the algorithm is to rewrite a well known asymptotic formula for legendre polynomials of large degree as a weighted linear combination of chebyshev polynomials which can then be evaluated by using the discrete cosine transform numerical results are provided to demonstrate the efficiency and numerical stability since the algorithm evaluates a legendre expansion at an n 1 chebyshev grid as an intermediate step it also provides a fast transform between legendre coefficients and values on a chebyshev grid

limitations to the large strain theory in the formulation of a large strain problem the euler cauchy stokes decomposition and the eulerian objective stress and strain rates used for the formulation of the problem are actually applicable only for some special cases and are not suitable for general large strain and rotation rates in this paper the limitations and applicabilities of the conventional large strain formulation under various deformation cases will be studied

multilinear discriminant analysis for higher order tensor data classification in the past decade great efforts have been made to extend linear discriminant analysis for higher order data classification generally referred to as multilinear discriminant analysis mda existing examples include general tensor discriminant analysis gtda and discriminant analysis with tensor representation dater both the two methods attempt to resolve the problem of tensor mode dependency by iterative approximation gtda is known to be the first mda method that converges over iterations however its performance relies highly on the tuning of the parameter in the scatter difference criterion although dater usually results in better classification performance it does not converge yet the number of iterations executed has a direct impact on dater s performance in this paper we propose a closed form solution to the scatter difference objective in gtda namely direct gtda dgtda which also gets rid of parameter tuning we demonstrate that dgtda outperforms gtda in terms of both efficiency and accuracy in addition we propose constrained multilinear discriminant analysis cmda that learns the optimal tensor subspace by iteratively maximizing the scatter ratio criterion we prove both theoretically and experimentally that the value of the scatter ratio criterion in cmda approaches its extreme value if it exists with bounded error leading to superior and more stable performance in comparison to dater

recognizing imprecisely localized partially occluded and expression variant faces from a single sample per class the classical way of attempting to solve the face or object recognition problem is by using large and representative data sets in many applications though only one sample per class is available to the system in this contribution we describe a probabilistic approach that is able to compensate for imprecisely localized partially occluded and expression variant faces even when only one single training sample per class is available to the system to solve the localization problem we find the subspace within the feature space e g eigenspace that represents this error for each of the training images to resolve the occlusion problem each face is divided into k local regions which are analyzed in isolation in contrast with other approaches where a simple voting space is used we present a probabilistic method that analyzes how good a local match is to make the recognition system less sensitive to the differences between the facial expression displayed on the training and the testing images we weight the results obtained on each local area on the basis of how much of this local area is affected by the expression displayed on the current test image

1d lda vs 2d lda when is vector based linear discriminant analysis better than matrix based recent advances have shown that algorithms with 2d matrix based representation perform better than the traditional 1d vector based ones in particular 2d lda has been widely reported to outperform 1d lda however would the matrix based linear discriminant analysis be always superior and when would 1d lda be better in this paper we investigate into these questions and have a comprehensive comparison between 1d lda and 2d lda in theory and in experiments we analyze the heteroscedastic problem in 2d lda and formulate mathematical equalities to explore the relationship between 1d lda and 2d lda then we point out potential problems in 2d lda it is shown that 2d lda has eliminated the information contained in the covariance information between different local geometric structures such as the rows or the columns which is useful for discriminant feature extraction whereas 1d lda could preserve such information interestingly this new finding indicates that 1d lda is able to gain higher fisher score than 2d lda in some extreme case furthermore sufficient conditions on which 2d lda would be bayes optimal for two class classification problem are derived and comparison with 1d lda in this aspect is also analyzed this could help understand how 2d lda is expected to achieve at its best further discover its relationship with 1d lda and well support other findings after the theoretical analysis comprehensive experimental results are reported by fairly and extensively comparing 1d lda with 2d lda in contrast to the existing view that some 2d lda based algorithms would perform better than 1d lda when the number of training samples for each class is small or when the number of discriminant features used is small we show that it is not always true and show that some standard 1d lda based algorithms could perform better in those cases on some challenging data sets

regularized discriminant analysis and its application to face recognition the linear fisher discriminant analysis lda is a well known and popular statistical method in pattern recognition and classi5cation the basic idea is to optimize the discriminant criteria in which the ratio between the interand the intra class distance is maximized this approach is theoretically sound and a number of papers have shown its superior performance when applying in pattern recognition applications 1 5 however this approach su ers from the small size problem this problem occurs when the sample size is small compared with the size of feature vector which always appears in the face recognition applications this is because the typical image dimension for face image is greater than 32 32 and usually only 2 6 images are used for training thus the within class covariance estimation cw will be singular in this case the eigenvalue problem is ill posed the fisher index in t will be reached at the null space of cw and will always result in in5nity index in t a number of methods have been proposed in the last decade to overcome the limitation of lda on small sample size these methods in applying to face recognition can be roughly grouped into three categories the 5rst approach applied a dimension reduction method such as principal component analysis pca to extract important components for lda this approach is straightforward but the dimension reduction method may remove some useful information for recognition the second approach modi5es the fisher s optimization criteria theoretically this approach can solve the problem but the constraints 1 3 will limit the

a least squares framework for component analysis over the last century component analysis ca methods such as principal component analysis pca linear discriminant analysis lda canonical correlation analysis cca locality preserving projections lpp and spectral clustering sc have been extensively used as a feature extraction step for modeling classification visualization and clustering ca techniques are appealing because many can be formulated as eigen problems offering great potential for learning linear and nonlinear representations of data in closed form however the eigen formulation often conceals important analytic and computational drawbacks of ca techniques such as solving generalized eigen problems with rank deficient matrices e g small sample size problem lacking intuitive interpretation of normalization factors and understanding commonalities and differences between ca methods this paper proposes a unified least squares framework to formulate many ca methods we show how pca lda cca lpp sc and its kernel and regularized extensions correspond to a particular instance of least squares weighted kernel reduced rank regression ls wkrrr the ls wkrrr formulation of ca methods has several benefits 1 provides a clean connection between many ca techniques and an intuitive framework to understand normalization factors 2 yields efficient numerical schemes to solve ca techniques 3 overcomes the small sample size problem 4 provides a framework to easily extend ca methods we derive weighted generalizations of pca lda sc and cca and several new ca techniques

face recognition using elasticfaces though principle component analysis pca and locality preserving projections lpps are two of the most popular linear methods for face recognition pca can only see the euclidean structure of the training set and lpp preserves the nonlinear submanifold structure hidden in the training set in this paper we propose the elastic preserving projections epps which by incorporating the merits of the local geometry and the global information of the training set epp outputs a sample subspace which simultaneously preserves the local geometrical structure and exploits the global information of the training set different from some other linear dimensionality reduction methods epp can be deemed as learning both the coordinates and the affinities between sample points furthermore the effectiveness of our proposed algorithm is analyzed theoretically and confirmed by some experiments on several well known face databases the obtained results indicate that epp significantly outperforms its other rival algorithms

robust bilateral lp norm two dimensional linear discriminant analysis abstract traditional linear discriminant analysis lda may suffer from a sensitivity to outliers and the small sample size sss problem while the lp norm measure for 0

a fast algorithm for the convolution of functions with compact support using fourier extensions we present a new algorithm for computing the convolution of two compactly supported functions the algorithm approximates the functions to be convolved using fourier extensions and then uses the fast fourier transform to efficiently compute fourier extension approximations to the pieces of the result the complexity of the algorithm is mathcal o bigl n log n 2 bigr where n is the number of degrees of freedom used in each of the fourier extensions

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

approximate orthogonal sparse embedding for dimensionality reduction locally linear embedding lle is one of the most well known manifold learning methods as the representative linear extension of lle orthogonal neighborhood preserving projection onpp has attracted widespread attention in the field of dimensionality reduction in this paper a unified sparse learning framework is proposed by introducing the sparsity or l 1 norm learning which further extends the lle based methods to sparse cases theoretical connections between the onpp and the proposed sparse linear embedding are discovered the optimal sparse embeddings derived from the proposed framework can be computed by iterating the modified elastic net and singular value decomposition we also show that the proposed model can be viewed as a general model for sparse linear and nonlinear kernel subspace learning based on this general model sparse kernel embedding is also proposed for nonlinear sparse feature extraction extensive experiments on five databases demonstrate that the proposed sparse learning framework performs better than the existing subspace learning algorithm particularly in the cases of small sample sizes

on the relationship between the logarithmic strain rate and the stretching tensor abstract in this paper we investigate the relationship between the stretching tensor d and the logarithmic hencky strain in v with v the left stretch tensor we establish the simple formula 1 which holds for arbitrary three dimensional motions here f is the deformation gradient is the time derivative of in v measured in a coordinate system which rotates with the left principal strain axes and is the spin of the right principal strain axes we use this formula to show that or equrvatently the jaumann derivative of ln v if and only if the characteristic spaces of the right stretch tensor u are constant on any time interval in which the number of distinct principal stretches is constant finally we show that the asymptotic approximation 3 holds whenever the displacement gradient h satisfies

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

gender classification from unaligned facial images using support subspaces rough face alignments result in suboptimal performance of face identification in this study we present an approach for identifying the gender based on facial images without proper face alignments instead of just using only the detected face patch for identification a set of patches is randomly cropped around the face detection region each patch set is represented by a linear subspace and compared with other linear subspaces by measuring their canonical correlations a similarity matrix comprised of the canonical correlations is then incorporated into an indefinite kernel support vector machine svm formulation the number of support vectors which we call support subspaces can be decided automatically hence we can avoid the dimension selection problem observed in our previous work our experimental results demonstrate that the proposed approach outperforms state of the art methods

novel fisher discriminant classifiers at the present several applications need to classify high dimensional points belonging to highly unbalanced classes unfortunately when the training set cardinality is small compared to the data dimensionality small sample size problem the classification performance of several well known classifiers strongly decreases similarly the classification accuracy of several discriminative methods decreases when non linearly separable and unbalanced classes are treated in this paper we firstly survey state of the art methods that employ improved versions of linear discriminant analysis lda to deal with the above mentioned problems secondly we propose a family of classifiers based on the fisher subspace estimation which efficiently deal with the small sample size problem non linearly separable classes and unbalanced classes the promising results obtained by the proposed techniques on benchmark datasets and the comparison with state of the art predictors show the efficacy of the proposed techniques

face recognition by exploring information jointly in space scale and orientation information jointly contained in image space scale and orientation domains can provide rich important clues not seen in either individual of these domains the position spatial frequency and orientation selectivity properties are believed to have an important role in visual perception this paper proposes a novel face representation and recognition approach by exploring information jointly in image space scale and orientation domains specifically the face image is first decomposed into different scale and orientation responses by convolving multiscale and multi orientation gabor filters second local binary pattern analysis is used to describe the neighboring relationship not only in image space but also in different scale and orientation responses this way information from different domains is explored to give a good face representation for recognition discriminant classification is then performed based upon weighted histogram intersection or conditional mutual information with linear discriminant analysis techniques extensive experimental results on feret ar and frgc ver 2 0 databases show the significant advantages of the proposed method over the existing ones

discriminative multimanifold analysis for face recognition from a single training sample per person conventional appearance based face recognition methods usually assume that there are multiple samples per person mspp available for discriminative feature extraction during the training phase in many practical face recognition applications such as law enhancement e passport and id card identification this assumption however may not hold as there is only a single sample per person sspp enrolled or recorded in these systems many popular face recognition methods fail to work well in this scenario because there are not enough samples for discriminant learning to address this problem we propose in this paper a novel discriminative multimanifold analysis dmma method by learning discriminative features from image patches first we partition each enrolled face image into several nonoverlapping patches to form an image set for each sample per person then we formulate the sspp face recognition as a manifold manifold matching problem and learn multiple dmma feature spaces to maximize the manifold margins of different persons finally we present a reconstruction based manifold manifold distance to identify the unlabeled subjects experimental results on three widely used face databases are presented to demonstrate the efficacy of the proposed approach

an algorithm for the convolution of legendre series an mathcal o n 2 algorithm for the convolution of compactly supported legendre series is described the algorithm is derived from the convolution theorem for legendre polynomials and the recurrence relation satisfied by spherical bessel functions combining with previous work yields an mathcal o n 2 algorithm for the convolution of chebyshev series numerical results are presented to demonstrate the improved efficiency over the existing algorithm

efficient and robust feature extraction by maximum margin criterion in pattern recognition feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information principal component analysis pca and linear discriminant analysis lda are the two most popular linear dimensionality reduction methods however pca is not very effective for the extraction of the most discriminant features and lda is not stable due to the small sample size problem in this paper we propose some new linear and nonlinear feature extractors based on maximum margin criterion mmc geometrically feature extractors based on mmc maximize the average margin between classes after dimensionality reduction it is shown that mmc can represent class separability better than pca as a connection to lda we may also derive lda from mmc by incorporating some constraints by using some other constraints we establish a new linear feature extractor that does not suffer from the small sample size problem which is known to cause serious stability problems for lda the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper our extensive experiments demonstrate that the new feature extractors are effective stable and efficient

dimensionality reduction of image features using the canonical contextual correlation projection a linear discriminative supervised technique for reducing feature vectors extracted from image data to a lower dimensional representation is proposed it is derived from classical linear discriminant analysis lda extending this technique to cases where there is dependency between the output variables i e the class labels and not only between the input variables the latter can readily be dealt with in standard lda the novel method is useful for example in supervised segmentation tasks in which high dimensional feature vectors describe the local structure of the image the principal idea is that where standard lda merely takes into account a single class label for every feature vector the new technique incorporates class labels of its neighborhood in the analysis as well in this way the spatial class label configuration in the vicinity of every feature vector is accounted for resulting in a technique suitable for e g image data this extended lda that takes spatial label context into account is derived from a formulation of standard lda in terms of canonical correlation analysis the novel technique is called the canonical contextual correlation projection cccp an additional drawback of lda is that it cannot extract more features than the number of classes minus one in the two class case this means that only a reduction to one dimension is possible our contextual lda approach can avoid such extreme deterioration of the classification space and retain more than one dimension the technique is exemplified on a pixel based medical image segmentation problem in which it is shown that it may give significant improvement in segmentation accuracy

multilinear discriminant analysis for face recognition there is a growing interest in subspace learning techniques for face recognition however the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma in this paper we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order first we propose a discriminant tensor criterion whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction then a novel approach called k mode optimization is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions we call this algorithm multilinear discriminant analysis mda which has the following characteristics 1 multiple interrelated subspaces can collaborate to discriminate different classes 2 for classification problems involving higher order tensors the mda algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem and 3 the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k mode optimization we provide extensive experiments on orl cmu pie and feret databases by encoding face images as second or third order tensors to demonstrate that the proposed mda algorithm based on higher order tensors has the potential to outperform the traditional vector based subspace learning algorithms especially in the cases with small sample sizes

rapid and brief communication generalizing relevance weighted lda in this paper a new variant on linear discriminant analysis lda that we refer to as generalizing relevance weighted lda or grw lda is proposed grw lda extends the applicability to cases that lda cannot handle by combining the advantages of two recent lda enhancements namely generalized singular value decomposition based lda and relevance weighted lda experimental results on feret face database demonstrate the effectiveness of the proposed method

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

blockwise projection matrix versus blockwise data on undersampled problems analysis comparison and applications linear subspace methods are extensively used in many areas such as pattern recognition and machine learning among them block subspace methods are efficient in terms of the computational complexity in this paper we perform a thorough analysis on block subspace methods and give a theoretical framework for understanding block subspace methods it reveals the relationship between block subspace methods and classical subspace methods we theoretically show that blockwise pca has larger reconstruction errors than classical pca and classical lda has stronger discriminant power than blockwise lda in the case of the same number of reduced features in addition based on the fisher criterion we also give a strategy for selecting an approximate block size for classification problems the comprehensive experiments on face images and gene expression data are used to evaluate our results and a comparative analysis for various methods is made experimental results demonstrate that overly combining subspaces of block subspace methods without considering the subspace distance may yield undesirable performance on undersampled problems

gender discriminating models from facial surface normals in this paper we show how to use facial shape information to construct discriminating models for gender classification we represent facial shapes using 2 5d fields of facial surface normals and investigate three different methods to improve the gender discriminating capacity of the model constructed using the standard eigenspace method the three methods are novel variants of principal geodesic analysis pga namely a weighted pga b supervised weighted pga and c supervised pga our starting point is to define a weight map over the facial surface that indicates the importance of different locations in discriminating gender we show how to compute the relevant weights and how to incorporate the weights into the 2 5d model construction we evaluate the performance of the alternative methods using facial surface normals extracted from 3d range images or recovered from brightness images experimental results demonstrate the effectiveness of our methods moreover the classification accuracy which is as high as 97 demonstrates the effectiveness of using facial shape information for gender classification

kernel quadratic discriminant analysis for small sample size problem it is generally believed that quadratic discriminant analysis qda can better fit the data in practical pattern recognition applications compared to linear discriminant analysis lda method this is due to the fact that qda relaxes the assumption made by lda based methods that the covariance matrix for each class is identical however it still assumes that the class conditional distribution is gaussian which is usually not the case in many real world applications in this paper a novel kernel based qda method is proposed to further relax the gaussian assumption by using the kernel machine technique the proposed method solves the complex pattern recognition problem by combining the qda solution and the kernel machine technique and at the same time tackles the so called small sample size problem through a regularized estimation of the covariance matrix extensive experimental results indicate that the proposed method is a more sophisticated solution outperforming many traditional kernel based learning algorithms

on the invariant representation of spin tensors with applications abstract the invariant representation of the spin tensor defined as the rotation rate or a principal triad for a symmetric and non degenerate tensor is derived on the basis of the general solution of a linear tensorial equation the result can be naturally specified to study the spin of the stretch tensors and to investigate the relations between various rotation rate tensors encountered frequently in modern continuum mechanics a remarkable formula which relates the generalized stress conjugate to the generalized strain in hill s sense to cauchy stress is obtained in invariant form through the work conjugate principle particularly a detailed discussion on the time rate of logarithmic strain and its conjugate stress is made as the principal axes ofstrain are not fixed during deformation

kernel self optimization learning for kernel based feature extraction and recognition kernel learning is becoming an important research topic in the area of machine learning and it has wide applications in pattern recognition computer vision image and signal processing kernel learning provides a promising solution to nonlinear problems including nonlinear feature extraction classification and clustering however in kernel based systems the problem of the kernel function and its parameters remains to be solved methods of choosing parameters from a discrete set of values have been presented in previous studies but these methods do not change the data distribution structure in the kernel based mapping space accordingly performance is not improved because the current kernel optimization does not change the data distribution based on this problem this paper presents a uniform framework for kernel self optimization with the ability to adjust the data structure the data dependent kernel is extended and applied to kernel learning and optimization equations with two criteria for measuring data discrimination are used to solve the optimal parameter values some experiments are performed to evaluate the performance in popular kernel learning methods including kernel principal components analysis kpca kernel discriminant analysis kda and kernel locality preserving projection klpp these evaluations show that the framework of kernel self optimization is feasible for enhancing kernel based learning methods

inexact implementation using krylov subspace methods for large scale exponential discriminant analysis with applications to high dimensionality reduction problems abstract exponential discriminant analysis eda is a generalized discriminant analysis method based on matrix exponential it can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear discriminant analysis lda however for data with high dimensionality one has to solve a large matrix exponential eigenproblem in this method and the time complexity is dominated by the computation of exponential of large matrices in this paper we propose two inexact krylov subspace algorithms for solving the large matrix exponential eigenproblem efficiently the contribution of this work is threefold first we consider how to compute matrix exponential vector products efficiently which is the key step in the krylov subspace method second we compare the discriminant analysis criterion of eda and that of lda from a theoretical point of view third we establish the relationship between the accuracy of the approximate eigenvectors and the distance to nearest neighbor classifier and show why the matrix exponential eigenproblem can be solved approximately in practice numerical experiments on some real world databases show the superiority of our new algorithms over their original counterpart for face recognition

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

spectral approximation of convolution operators we develop a unified framework for constructing matrix approximations to the convolution operator of volterra type defined by functions that are approximated using classical orthogonal polynomials

face recognition using ipca ica algorithm in this paper a fast incremental principal non gaussian directions analysis algorithm called ipca ica is introduced this algorithm computes the principal components of a sequence of image vectors incrementally without estimating the covariance matrix so covariance free and at the same time transforming these principal components to the independent directions that maximize the non gaussianity of the source two major techniques are used sequentially in a real time fashion in order to obtain the most efficient and independent components that describe a whole set of human faces database this procedure is done by merging the runs of two algorithms based on principal component analysis pca and independent component analysis ica running sequentially this algorithm is applied to face recognition problem simulation results on different databases showed high average success rate of this algorithm compared to others

mode kn factor analysis for image ensembles in this corespondence we study the extra factor estimation problem with the assumption that the training image ensemble is expressed as an nth order tensor with the nth dimension characterizing all features for an image and other dimensions for different extra factors such as illuminations poses and identities to overcome the local minimum issue of conventional algorithms designed for this problem we present a novel statistical learning framework called mode kn factor analysis for obtaining a closed form solution to estimating the extra factors of any test image in the learning stage for the kth k ne n dimension of the data tensor the mode kn patterns are constructed by concatenating the feature dimension and the kth extra factor dimension and then a mode kn factor analysis model is learnt based on the mode kn patterns unfolded from the original data tensor in the inference stage for a test image the mode classification of the kth dimension is performed within a probabilistic framework the advantages of mode kn factor analysis over conventional tensor analysis algorithms are twofold 1 a closed form solution instead of iterative sub optimal solution as conventionally is derived for estimating the extra factor mode of any test image and 2 the classification capability is enhanced by interacting with the process of synthesizing data of all other modes in the k th dimension experiments on the pointing 04 and cmu pie databases for pose and illumination estimation both validate the superiority of the proposed algorithm over conventional algorithms for extra factor estimation

formulating robust linear regression estimation as a one class lda criterion discriminative hat matrix linear discriminant analysis such as fisher s criterion is a statistical learning tool traditionally devoted to separating a training dataset into two or even several classes by the way of linear decision boundaries in this paper we show that this tool can formalize the robust linear regression problem as a robust estimator will do more precisely we develop a one class fischer s criterion in which the maximization provides both the regression parameters and the separation of the data in two classes typical data and atypical data or outliers this new criterion is built on the statistical properties of the subspace decomposition of the hat matrix from this angle we improve the discriminative properties of the hat matrix which is traditionally used as outlier diagnostic measure in linear regression naturally we call this new approach discriminative hat matrix the proposed algorithm is fully nonsupervised and needs only the initialization of one parameter synthetic and real datasets are used to study the performance both in terms of regression and classification of the proposed approach we also illustrate its potential application to image recognition and fundamental matrix estimation in computer vision

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

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

quadratic projection based feature extraction with its application to biometric recognition this paper presents a novel quadratic projection based feature extraction framework where a set of quadratic matrices is learned to distinguish each class from all other classes we formulate quadratic matrix learning qml as a standard semidefinite programming sdp problem however the conventional interior point sdp solvers do not scale well to the problem of qml for high dimensional data to solve the scalability of qml we develop an efficient algorithm termed dualqml based on the lagrange duality theory to extract nonlinear features to evaluate the feasibility and effectiveness of the proposed framework we conduct extensive experiments on biometric recognition experimental results on three representative biometric recognition tasks including face palmprint and ear recognition demonstrate the superiority of the dualqml based feature extraction algorithm compared to the current state of the art algorithms highlightsa novel quadratic projection based feature extraction framework is developed a set of quadratic matrices is learnt to distinguish each class from other classes quadratic matrix learning qml is formulated as an sdp problem an efficient algorithm is developed to solve qml based on lagrange duality theory experiments on biometric recognition show the effectiveness of our algorithm

a generalized optimal set of discriminant vectors abstract a generalized optimal set of discriminant vectors for linear feature extraction is presented first the criteria of selecting the generalized optimal discriminant vectors are introduced and then a unified solving method is derived to solve the vectors of the generalized optimal set in both cases of a large number of samples and a small number of samples the experimental results show that the present method is superior to the foley sammon method foley and sammon ieee trans comput 24 281 289 1975 the positive pseudoinverse method tian et al opt engng 25 7 834 839 1986 the perturbation method hong and yang pattern recognition 24 317 324 1991 and the matrix rank decomposition method cheng et al pattern recognition 25 101 111 1992 in terms of correct classification rate