general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

complete stress field in sandwich panels with a new triangular finite element of single layer theory abstract an alternative to conventional three dimensional solid elements or elements based on the layerwise zig zag theory is an element based on a single layer plate theory in which the weighted average field variables capture the panel displacement and stress fields this study presents a new triangular finite element for modeling thick sandwich panels based on a 3 2 order single layer plate theory it utilizes seven weighted average field variables arising from the cubic and quadratic representations of the in plane and transverse displacement fields respectively in order to satisfy the c1 interelement continuity requirement this triangular sandwich element is developed by utilizing the hybrid energy functional

semi supervised orthogonal discriminant analysis via label propagation trace ratio is a natural criterion in discriminant analysis as it directly connects to the euclidean distances between training data points this criterion is re analyzed in this paper and a fast algorithm is developed to find the global optimum for the orthogonal constrained trace ratio problem based on this problem we propose a novel semi supervised orthogonal discriminant analysis via label propagation differing from the existing semi supervised dimensionality reduction algorithms our algorithm propagates the label information from the labeled data to the unlabeled data through a specially designed label propagation and thus the distribution of the unlabeled data can be explored more effectively to learn a better subspace extensive experiments on toy examples and real world applications verify the effectiveness of our algorithm and demonstrate much improvement over the state of the art algorithms

hierarchic models for laminated composites the principles governing the formulation of hierarchic models for laminated composites are discussed the essential features of the hierarchic models described herein are a the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness and b the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity examples are presented

trace ratio problem revisited dimensionality reduction is an important issue in many machine learning and pattern recognition applications and the trace ratio tr problem is an optimization problem involved in many dimensionality reduction algorithms conventionally the solution is approximated via generalized eigenvalue decomposition due to the difficulty of the original problem however prior works have indicated that it is more reasonable to solve it directly than via the conventional way in this brief we propose a theoretical overview of the global optimum solution to the tr problem via the equivalent trace difference problem eigenvalue perturbation theory is introduced to derive an efficient algorithm based on the newton raphson method theoretical issues on the convergence and efficiency of our algorithm compared with prior literature are proposed and are further supported by extensive empirical results

multi view intact space learning it is practical to assume that an individual view is unlikely to be sufficient for effective multi view learning therefore integration of multi view information is both valuable and necessary in this paper we propose the multi view intact space learning misl algorithm which integrates the encoded complementary information in multiple views to discover a latent intact representation of the data even though each view on its own is insufficient we show theoretically that by combing multiple views we can obtain abundant information for latent intact space learning employing the cauchy loss a technique used in statistical learning as the error measurement strengthens robustness to outliers we propose a new definition of multi view stability and then derive the generalization error bound based on multi view stability and rademacher complexity and show that the complementarity between multiple views is beneficial for the stability and generalization misl is efficiently optimized using a novel iteratively reweight residuals irr technique whose convergence is theoretically analyzed experiments on synthetic data and real world datasets demonstrate that misl is an effective and promising algorithm for practical applications

discriminative embedded clustering a framework for grouping high dimensional data in many real applications of machine learning and data mining we are often confronted with high dimensional data how to cluster high dimensional data is still a challenging problem due to the curse of dimensionality in this paper we try to address this problem using joint dimensionality reduction and clustering different from traditional approaches that conduct dimensionality reduction and clustering in sequence we propose a novel framework referred to as discriminative embedded clustering which alternates them iteratively within this framework we are able not only to view several traditional approaches and reveal their intrinsic relationships but also to be stimulated to develop a new method we also propose an effective approach for solving the formulated nonconvex optimization problem comprehensive analyses including convergence behavior parameter determination and computational complexity together with the relationship to other related approaches are also presented plenty of experimental results on benchmark data sets illustrate that the proposed method outperforms related state of the art clustering approaches and existing joint dimensionality reduction and clustering methods

recoupling lie algebra and universal ω algebra we formulate the algebraic version of recoupling theory suitable for commutation quantization over any gradation this gives a generalization of graded lie algebra underlying this is the new notion of an algebra defined in this paper algebra is a generalization of algebra that goes beyond nonassociativity we construct the universal enveloping algebra of recoupling lie algebras and prove a generalized poincare birkhoff witt theorem as an example we consider the algebras over an arbitrary recoupling of zn graded heisenberg lie algebra finally we uncover the usual coalgebra structure of a universal envelope and substantiate its hopf structure

analysis of thick sandwich construction by a 3 2 order theory abstract this study is an extension of the 1 2 order plate theory to a higher order 3 2 theory based on the equivalent single layer assumptions the in plane and transverse displacement components are expressed as cubic and quadratic expansions through the thickness of the sandwich construction also the transverse stress component is assumed to vary as a cubic function through the thickness utilizing reissner s definitions for kinematics of thick plates the displacement components at any point on the plate are approximated in terms of weighted average quantities displacements and rotations that are functions of the in plane coordinates the undetermined coefficients defining the in plane and transverse displacement fields are then expressed in terms of the weighted average displacements and rotations and their derivatives by directly employing reissner s definitions and enforcing the zero transverse shear stress conditions on the upper and lower surfaces of the sandwich panel the coefficients defining the transverse stress component are obtained by requiring the transverse strain component which is expressed in terms of the unknown coefficients of the transverse stress component from a mixed constitutive relation to be the least squares equivalent of the kinematic definition of the transverse strain component the resulting expressions for the unknown coefficients of the transverse stress component are related to resultant strains and curvatures defined from kinematic relations the equations of equilibrium and boundary conditions of the sandwich plate based on the 3 2 higher order theory are derived by employing the principles of virtual displacements the robustness and accuracy of this 3 2 order plate theory are established through comparisons with exact solutions available in the literature the finite element implementation of the present 3 2 order plate theory is also discussed

computational homogenisation of composite plates consideration of the thickness change with a modified projection strategy in the present paper a method for the modelling of the mechanical behaviour of composite plates especially hybrid laminates and sandwich plates is proposed the chosen method is the computational homogenisation or the so called fe 2 for plates the principle is to split the considered problem into two scales on the one hand the two dimensional fe computation of a plate is performed on the macroscale on the other hand a three dimensional fe problem is computed on the mesoscale which enables the discretisation of the layers organisation from each integration point of the macroscale the deformations are projected to the representative volume element rve on the mesoscale where a dirichlet boundary value problem is solved finally the homogenisation of the stresses is conducted to define the stress resultants of the macroscale the proposed method presents the advantage to take into account any material behaviour without any transformation of the constitutive laws even non linear ones furthermore the new projection strategy presented in this work considers the thickness change of the plate which enables a resolution of the poisson locking the method is illustrated by the simulation of the mechanical behaviour of both sandwich plate and of hybrid laminate

a 1 2 order theory for elastodynamic analysis of thick orthotropic shells abstract a higher order shell theory is developed for elastodynamic analysis of orthotropic shells the theory accounts for all basic deformations including transverse shear and transverse normal strains and stresses the theory is developed in orthogonal curvilinear coordinates in which the reference surface components of the displacement vector vary linearly through the thickness while the transverse displacement is parabolic transverse shear and transverse normal strains are formulated to satisfy physical traction conditions at the top and bottom shell surfaces and are also made least squares compatible with the corresponding strains that are derived directly from the strain displacement relations of three dimensional elasticity in these variational statements of strain compatibility transverse shear and transverse normal correction factors are introduced and are determined from dynamic considerations in the manner originally proposed by mindlin equations of motion and associated engineering poisson boundary conditions are derived from a three dimensional variational principle an important feature of the present theory is the requirement of only simple c0 and c 1 continuity for the shell kinematic variables this aspect makes the theory particularly attractive for the development of efficient shell finite elements suitable for general purpose finite element analysis of thick shell structures analytical solutions for the free vibration of isotropic and orthotropic cylindrical shells are obtained for a wide range of thickness radius and thickness wavelength ratios and found to be in close agreement with the exact elasticity solutions

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

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

regularized class specific subspace classifier in this paper we mainly focus on how to achieve the translated subspace representation for each class which could simultaneously indicate the distribution of the associated class and the differences from its complementary classes by virtue of the reconstruction problem the class specific subspace classifier cssc problem could be represented as a series of biobjective optimization problems which minimize and maximize the reconstruction errors of the related class and its complementary classes respectively besides the regularization term is specifically introduced to ensure the whole system s stability accordingly a regularized class specific subspace classifier rcssc method can be further proposed based on solving a general quadratic ratio problem the proposed rcssc method consistently converges to the global optimal subspace and translation under the variations of the regularization parameter furthermore the proposed rcssc method could be extended to the unregularized case which is known as unregularized cssc ucssc method via orthogonal decomposition technique as a result the effectiveness and the superiority of both proposed rcssc and ucssc methods can be verified analytically and experimentally

diagram projection rules for recoupling diagrams in the racah wigner category this paper gives three important techniques for recoupling coefficients of an arbitrary number or irreducible representations factorization as a product of smaller degree recoupling coefficients diagram projection projecting a recoupling diagram to obtain constraints on recoupling coefficients and primitive expansion expressing a recoupling coefficient in terms of primitive recoupling coefficients the first technique reduces a recoupling coefficient to its essential and simplest form the second is many faceted allowing one to work at the recoupling level importantly recoupling diagrams can be used to construct a complete set of constraints on the recoupling coefficients the third allows large degree recoupling coefficients to be expressed in terms of primitive recoupling coefficients an example of this is the fact that the 9j symbol is defined by the 3j and 6j symbols

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

casimir invariants characteristic identities and young diagrams for color algebras and superalgebras the generalized commutation relations satisfied by generators of the general linear special linear and orthosymplectic color super algebras are presented in matrix form tensor operators including casimir invariants are constructed in the enveloping algebra for the general special linear and orthosymplectic cases eigenvalues of the quadratic and higher casimir invariants are given in terms of the highest weight vector correspondingly characteristic polynomial identities satisfied by the matrix of generators are obtained in factorized form classes of finite dimensional representations are identified using young diagram techniques and dimension branching and product rules for these are given finally the connection between color super algebras and generalized particle statistics is elucidated

an improved plate theory of 1 2 order for thick composite laminates abstract a new two dimensional laminate plate theory is developed for the linear elastostatic analysis of thick composite plates the theory employs equivalent single layer assumptions for the displacements transverse shear strains and transverse normal stress the inplane and transverse displacements are respectively linear and quadratic expansions through the laminate thickness where the low order expansion coefficients correspond to the variables of reissner s first order shear deformable theory the transverse shear strains and transverse normal stress are assumed to be quadratic and cubic respectively through the thickness they are expressed in terms of the kinematic variables of the theory by means of a least squares compatibility requirement for the transverse strains and explicit enforcement of exact traction boundary conditions on the top and bottom plate surfaces application of the virtual work principle results in the loth order equations of equilibrium and associated poisson boundary conditions a major advantage of this theory over other higher order theories lies in its perfect suitability for finite element approximation simple c 0 continuous interpolations for the kinematic variables of the first order theory and optionally c 1 interpolations for the two higher order displacements are needed to formulate effective and robust two dimensional plate elements capable of full three dimensional ply by ply strain and stress recovery within the framework of general purpose finite element codes in assessing the predictive capability of the theory analytic solutions for the problem of cylindrical bending are derived and compared with exact three dimensional elasticity results and those of the earlier version of the 1 2 order plate theory

restatement of first order shear deformation theory for laminated plates abstract a restatement of the first order shear deformation theory of plates is offered and verified numerically by exact 3 d elasticity results based on a more appropriate physical assumption the restated theory innovatively interprets its variables and applies elasticity equations in a more pertinent manner it assumes physically that only in some average sense does a straight line originally normal to the midplane remain straight and rotate relative to the normal of the midplane after deformation hence the in plane displacement is still approximated in an average sense as linear and the transverse deflection as constant through the plate thickness the associated nominal uniform transverse shear strain directly derived from these displacement field assumptions is identified as the weighted average transverse shear strain through the plate thickness with the corresponding transverse shear stress as the weighting function while the actual transverse shear strain is permitted to vary through the thickness and satisfies the constitutive law with its stress counterpart likewise the average rotation of the line is identified as its weighted average value instead of the one evaluated from a linear regression of the inplane displacement with the least square method examination of bending energy and transverse shear energy supports this interpretation in addition an effective transverse shear stiffness parameter is identified and proven appropriate this restated first order shear deformation theory yields accurate local as well as global response predictions without employing a shear correction factor