operads and knot spaces let em denote the space of embeddings of the interval i 1 1 in the cube im with endpoints and tangent vectors at those endpoints fixed on opposite faces of the cube equipped with a homotopy through immersions to the unknot see definition 5 1 by proposition 5 17 em is homotopy equivalent to emb i im x i lmm l im in 28 mcclure and smith define a cosimplicial object o associated to an operad with multiplication 0 whose homotopy invariant totalization we denote tot see definition 2 17 and definition 2 5 below let cm denote the rath kontsevich operad introduced in 22 whose entries are compactified configuration spaces and which is weakly equivalent to the little ra disks operad 37 see definition 4 1 and theorem 4 5

on minimum class locality preserving variance support vector machine in this paper a so called minimum class locality preserving variance support machine mclpv svm algorithm is presented by introducing the basic idea of the locality preserving projections lpp which can be seen as a modified class of support machine svm and or minimum class variance support machine mcvsvm mclpv svm in contrast to svm and mcvsvm takes the intrinsic manifold structure of the data space into full consideration and inherits the characteristics of svm and mcvsvm we discuss in the paper the linear case the small sample size case and the nonlinear case of the mclpv svm similar to mcvsvm the mclpv svm optimization problem in the small sample size case is solved by using dimensionality reduction through principal component analysis pca and one in the nonlinear case is transformed into an equivalent linear mclpv svm problem under kernel pca kpca experimental results on real datasets indicate the effectiveness of the mclpv svm by comparing it with svm and mcvsvm

the analysis of decomposition methods for support vector machines the support vector machine svm is a promising technique for pattern recognition it requires the solution of a large dense quadratic programming problem traditional optimization methods cannot be directly applied due to memory restrictions up to now very few methods can handle the memory problem and an important one is the decomposition method however there is no convergence proof so far we connect this method to projected gradient methods and provide theoretical proofs for a version of decomposition methods an extension to bound constrained formulation of svm is also provided we then show that this convergence proof is valid for general decomposition methods if their working set selection meets a simple requirement

least squares recursive projection twin support vector machine for classification in this paper we formulate a least squares version of the recently proposed projection twin support vector machine ptsvm for binary classification this formulation leads to extremely simple and fast algorithm called least squares projection twin support vector machine lsptsvm for generating binary classifiers different from ptsvm we add a regularization term ensuring the optimization problems in our lsptsvm are positive definite and resulting better generalization ability instead of usually solving two dual problems we solve two modified primal problems by solving two systems of linear equations whereas ptsvm need to solve two quadratic programming problems along with two systems of linear equations our experiments on publicly available datasets indicate that our lsptsvm has comparable classification accuracy to that of ptsvm but with remarkably less computational time

convergence of the homology spectral sequence of a cosimplicial space we produce new convergence conditions for the homology spectral sequence of a cosimplicial space by requiring that each codegree of the cosimplicial space has finite type mod p homology specifically we find conditions which ensure strong convergence if and only if the total space has p good components we also find exotic convergence conditions for cosimplicial spaces not covered by the strong convergence conditions these results give new convergence conditions for example for the eilenberg moore spectral sequence and for mapping spaces

cross domain soft partition clustering with diversity measure and knowledge reference conventional soft partition clustering approaches such as fuzzy c means fcm maximum entropy clustering mec and fuzzy clustering by quadratic regularization fc qr are usually incompetent in those situations where the data are quite insufficient or much polluted by underlying noise or outliers in order to address this challenge the quadratic weights and gini simpson diversity based fuzzy clustering model qwgsd fc is first proposed as a basis of our work based on qwgsd fc and inspired by transfer learning two types of cross domain soft partition clustering frameworks and their corresponding algorithms referred to as type i type ii knowledge transfer oriented c means ti kt cm and tii kt cm are subsequently presented respectively the primary contributions of our work are four fold 1 the delicate qwgsd fc model inherits the most merits of fcm mec and fc qr with the weight factors in the form of quadratic memberships similar to fcm it can more effectively calculate the total intra cluster deviation than the linear form recruited in mec and fc qr meanwhile via gini simpson diversity index like shannon entropy in mec and equivalent to the quadratic regularization in fc qr qwgsd fc is prone to achieving the unbiased probability assignments 2 owing to the reference knowledge from the source domain both ti kt cm and tii kt cm demonstrate high clustering effectiveness as well as strong parameter robustness in the target domain 3 ti kt cm refers merely to the historical cluster centroids whereas tii kt cm simultaneously uses the historical cluster centroids and their associated fuzzy memberships as the reference this indicates that tii kt cm features more comprehensive knowledge learning capability than ti kt cm and tii kt cm consequently exhibits more perfect cross domain clustering performance and 4 neither the historical cluster centroids nor the historical cluster centroid based fuzzy memberships involved in ti kt cm or tii kt cm can be inversely mapped into the raw data this means that both ti kt cm and tii kt cm can work without disclosing the original data in the source domain i e they are of good privacy protection for the source domain in addition the convergence analyses regarding both ti kt cm and tii kt cm are conducted in our research the experimental studies thoroughly evaluated and demonstrated our contributions on both synthetic and real life data scenarios the novel qwgsd fc model is designed for soft partition clustering two cross domain clustering methods ti tii kt cm are subsequently proposed ti tii kt cm are superior to or competitive with other existing methods the convergences of both ti kt cm and tii kt cm are proved

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

a fast iterative nearest point algorithm for support vector machine classifier design in this paper we give a new fast iterative algorithm for support vector machine svm classifier design the basic problem treated is one that does not allow classification violations the problem is converted to a problem of computing the nearest point between two convex polytopes the suitability of two classical nearest point algorithms due to gilbert and mitchell et al is studied ideas from both these algorithms are combined and modified to derive our fast algorithm for problems which require classification violations to be allowed the violations are quadratically penalized and an idea due to cortes and vapnik and friess is used to convert it to a problem in which there are no classification violations comparative computational evaluation of our algorithm against powerful svm methods such as platt s sequential minimal optimization shows that our algorithm is very competitive

recursive projection twin support vector machine via within class variance minimization in this paper a novel binary classifier coined projection twin support vector machine ptsvm is proposed the idea is to seek two projection directions one for each class such that the projected samples of one class are well separated from those of the other class in its respective subspace in order to further boost performance a recursive algorithm for ptsvm is proposed to generate more than one projection axis for each class to overcome the singularity problem principal component analysis pca is utilized to transform the data in the original space into a low dimensional subspace wherein the optimization problem of ptsvm is convex and can be solved efficiently the experimental results on several uci benchmark data sets and usps digit database show the feasibility and effectiveness of the proposed method

kernel methods in machine learning we review machine learning methods employing positive definite kernels these methods formulate learning and estimation problems in a reproducing kernel hilbert space rkhs of functions defined on the data domain expanded in terms of a kernel working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions the latter include nonlinear functions as well as functions defined on nonvectorial data we cover a wide range of methods ranging from binary classifiers to sophisticated methods for estimation with structured data

solving the small sample size problem in face recognition using generalized discriminant analysis the goal of face recognition is to distinguish persons via their facial images each person s images form a cluster and a new image is recognized by assigning it to the correct cluster since the images are very high dimensional it is necessary to reduce their dimension linear discriminant analysis lda has been shown to be effective at dimension reduction while preserving the cluster structure of the data it is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters the requirement that one of these matrices be nonsingular restricts its application to datasets in which the dimension of the data does not exceed the sample size for face recognition however the dimension typically exceeds the number of images in the database resulting in what is referred to as the small sample size problem recently the applicability of lda has been extended by using the generalized singular value decomposition gsvd to circumvent the nonsingularity requirement thus making lda directly applicable to face recognition data our experiments confirm that lda gsvd solves the small sample size problem very effectively as compared with other current methods

a variable kinematic ritz formulation for vibration study of quadrilateral plates with arbitrary thickness a new variable kinematic ritz method applied to free vibration analysis of arbitrary quadrilateral thin and thick isotropic plates is presented carrera s unified formulation and the versatile pb 2 ritz method are properly combined to build a powerful yet simple modeling and solution framework the proposed technique allows to generate arbitrarily accurate ritz solutions from a large variety of refined two dimensional plate theories by expanding so called ritz fundamental nuclei of the plate mass and stiffness matrices theoretical development of the present methodology is described in detail convergence and accuracy of the method are examined through several examples on thin moderately thick and very thick plates of rectangular skew trapezoidal and general quadrilateral shapes with an arbitrary combination of clamped free and simply supported edges present results are compared with existing three dimensional solutions from open literature maximum and average differences of various higher order plate theories and three dimensional results are also presented with the aim of providing useful guidelines on the choice of appropriate plate theory to get a desired accuracy on frequency parameters

training ν support vector classifiers theory and algorithms the support vector machine svm for classification proposed by scholkopf smola williamson and bartlett 2000 has the advantage of using a parameter on controlling the number of support vectors in this article we investigate the relation between svm and c svm in detail we show that in general they are two different problems with the same optimal solution set hence we may expect that many numerical aspects of solving them are similar however compared to regular c svm the formulation of svm is more complicated so up to now there have been no effective methods for solving large scale svm we propose a decomposition method for svm that is competitive with existing methods for c svm we also discuss the behavior of svm by some numerical experiments

the eckmann hilton argument and higher operads abstract the classical eckmann hilton argument shows that two monoid structures on a set such that one is a homomorphism for the other coincide and moreover the resulting monoid is commutative this argument immediately gives a proof of the commutativity of the higher homotopy groups a reformulation of this argument in the language of higher categories is suppose we have a one object one arrow 2 category then its hom set is a commutative monoid a similar argument due to a joyal and r street shows that a one object one arrow tricategory is the same as a braided monoidal category in this paper we begin to investigate how one can extend this argument to arbitrary dimension we provide a simple categorical scheme which allows us to formalise the eckmann hilton type argument in terms of the calculation of left kan extensions in an appropriate 2 category then we apply this scheme to the case of n operads in the author s sense and classical symmetric operads we demonstrate that there exists a functor of symmetrisation sym n from a certain subcategory of n operads to the category of symmetric operads such that the category of one object one arrow one n 1 arrow algebras of a is isomorphic to the category of algebras of sym n a under some mild conditions we present an explicit formula for sym n a which involves taking the colimit over a remarkable categorical symmetric operad we will consider some applications of the methods developed to the theory of n fold loop spaces in the second paper of this series

batalin vilkovisky algebras and two dimensional topological field theories by a batalin vilkovisky algebra we mean a graded commutative algebraa together with an operator a a 1 such that 2 0 and a a is a graded derivation ofa for alla a in this article we show that there is a natural structure of a batalin vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions we make use of a technique from algebraic topology the theory of operads

dc algorithm for extended robust support vector machine nonconvex variants of support vector machines svms have been developed for various purposes for example robust svms attain robustness to outliers by using a nonconvex loss function while extended svm e svm extends the range of the hyperparameter by introducing a nonconvex constraint here we consider an extended robust support vector machine er svm a robust variant of e svm er svm combines two types of nonconvexity from robust svms and e svm because of the two nonconvexities the existing algorithm we proposed needs to be divided into two parts depending on whether the hyperparameter value is in the extended range or not the algorithm also heuristically solves the nonconvex problem in the extended range in this letter we propose a new efficient algorithm for er svm the algorithm deals with two types of nonconvexity while never entailing more computations than either e svm or robust svm and it finds a critical point of er svm furthermore we show that er svm includes the existing robus

on the deformation complex of homotopy affine actions abstract an affine action of an associative algebra a on a vector space v is an algebra morphism a v end v where v is a vector space and v end v is the algebra of affine transformations of v the one dimensional version of the swiss cheese operad denoted sc 1 is the operad whose algebras are affine actions of associative algebras this operad is koszul and admits a minimal model denoted by sc 1 algebras over this minimal model are called homotopy affine actions they consist of an a morphism a v end v where a is an a algebra in this paper we prove a relative version of deligne s conjecture in other words we show that the deformation complex of a homotopy affine action has the structure of an algebra over an sc 2 operad that structure is naturally compatible with the e 2 structure on the deformation complex of the a algebra

multivariable cochain operations and little cubes this paper has two goals the first see theorem 2 15 and remark 2 16 a is to construct a small em chain operad s which acts naturally on the normalized cochains s x of a topological space x this is of interest in view of a theorem of mandell 15 page 44 which states that if 9 is any e chain operad over f the algebraic closure of the field with p elements which acts naturally on s x 0 f then the homotopy category of connected p complete nilpotent spaces of finite type

free vibration analysis of a flat plate using the hierarchical finite element method abstract the hierarchical finite element method is used to determined the natural frequencies and modes of a flat rectangular plate ten different boundary conditions including free edges and point supports are considered in this paper extensive results are presented for each case including the variation of frequency with the aspect ratio and the poisson ratio and these are shown to be in very good agreement with the work of other investigators this confirms both the applicability and accuracy of solution of the hfem to problem of this type

why can lda be performed in pca transformed space abstract pca plus lda is a popular framework for linear discriminant analysis lda in high dimensional and singular case in this paper we focus on building a theoretical foundation for this framework moreover we point out the weakness of the previous lda based methods and suggest a complete pca plus lda algorithm experimental results on orl face image database indicate that the proposed method is more effective than the previous ones

sub domain adaptation learning methodology regarded as global methods maximum mean discrepancy mmd based transfer learning frameworks only reflect the global distribution discrepancy and structural differences between domains they can reflect neither the inner local distribution discrepancy nor the structural differences between domains to address this problem a novel transfer learning framework with local learning ability a sub domain adaptation learning framework sdal is proposed in this framework a projected maximum local weighted mean discrepancy pmlmd is constructed by integrating the theory and method of local weighted mean lwm into mmd pmlmd reflects global distribution discrepancy between domains through accumulating local distribution discrepancies between the local sub domains in domains in particular we formulate in theory that pmlmd is one of the generalized measures of mmd on the basis of sdal two novel methods are proposed by using multi label classifiers mlc and support vector machine svm finally tests on artificial data sets high dimensional text data sets and face data sets show the sdal based transfer learning methods are superior to or at least comparable with benchmarking methods

hilbert space embeddings and metrics on probability measures a hilbert space embedding for probability measures has recently been proposed with applications including dimensionality reduction homogeneity testing and independence testing this embedding represents any probability measure as a mean element in a reproducing kernel hilbert space rkhs a pseudometric on the space of probability measures can be defined as the distance between distribution embeddings we denote this as k indexed by the kernel function k that defines the inner product in the rkhs we present three theoretical properties of k first we consider the question of determining the conditions on the kernel k for which k is a metric such k are denoted characteristic kernels unlike pseudometrics a metric is zero only when two distributions coincide thus ensuring the rkhs embedding maps all distributions uniquely i e the embedding is injective while previously published conditions may apply only in restricted circumstances e g on compact domains and are difficult to check our conditions are straightforward and intuitive integrally strictly positive definite kernels are characteristic alternatively if a bounded continuous kernel is translation invariant on d then it is characteristic if and only if the support of its fourier transform is the entire d second we show that the distance between distributions under k results from an interplay between the properties of the kernel and the distributions by demonstrating that distributions are close in the embedding space when their differences occur at higher frequencies third to understand the nature of the topology induced by k we relate k to other popular metrics on probability measures and present conditions on the kernel k under which k metrizes the weak topology

a triangular fourier p element for the analysis of membrane vibrations abstract a triangular fourier p element for the analysis of membrane vibrations is presented the element s transverse displacement is written in terms of dimensionless area co ordinates and is described by three linear shape functions plus a variable number of trigonometric shape functions the three nodal displacements and the amplitudes of the trigonometric functions on the three edges and in the interior of the element respectively are used as generalized co ordinates inter element compatibility is achieved by matching the generalized co ordinates at the three nodes and the three edges results are obtained for a right isosceles triangular and a square membranes and comparisons are made with exact and linear triangular finite element solutions the results of both membranes confirm that the solutions converge very fast from above to the exact values as the number of trigonometric terms is increased and highly accurate values are obtained with the use of a very few terms the results also show that the triangular fourier p element produces a much higher accuracy than the linear triangular finite element with fewer system degrees of freedom

on minimum distribution discrepancy support vector machine for domain adaptation domain adaptation learning dal is a novel and effective technique to address pattern classification problems where the prior information for training is unavailable or insufficient its effectiveness depends on the discrepancy between the two distributions that respectively generate the training data for the source domain and the testing data for the target domain however dal may not work so well when only the distribution mean discrepancy between source and target domains is considered and minimized in this paper we first construct a generalized projected maximum distribution discrepancy gpmdd metric for dal on reproducing kernel hilbert space rkhs based domain distributions by simultaneously considering both the projected maximum distribution mean and the projected maximum distribution scatter discrepancy between the source and the target domain in the sequel based on both the structure risk and the gpmdd minimization principle we propose a novel domain adaptation kernelized support vector machine daksvm with respect to the classical svm and its two extensions called ls daksvm and m daksvm with respect to the least square svm and the v svm respectively moreover our theoretical analysis justified that the proposed gpmdd metric could effectively measure the consistency not only between the rkhs embedding domain distributions but also between the scatter information of source and target domains hence the proposed methods are distinctive in that the more consistency between the scatter information of source and target domains can be achieved by tuning the kernel bandwidth the better the convergence of gpmdd metric minimization is and thus improving the scalability and generalization capability of the proposed methods for dal experimental results on artificial and real world problems indicate that the performance of the proposed methods is superior to or at least comparable with existing benchmarking methods

learning a mahalanobis distance metric for data clustering and classification distance metric is a key issue in many machine learning algorithms this paper considers a general problem of learning from pairwise constraints in the form of must links and cannot links as one kind of side information a must link indicates the pair of the two data points must be in a same class while a cannot link indicates that the two data points must be in two different classes given must link and cannot link information our goal is to learn a mahalanobis distance metric under this metric we hope the distances of point pairs in must links are as small as possible and those of point pairs in cannot links are as large as possible this task is formulated as a constrained optimization problem in which the global optimum can be obtained effectively and efficiently finally some applications in data clustering interactive natural image segmentation and face pose estimation are given in this paper experimental results illustrate the effectiveness of our algorithm

three dimensional vibration analysis of thick rectangular plates using chebyshev polynomial and ritz method this paper describes a method for free vibration analysis of rectangular plates with any thicknesses which range from thin moderately thick to very thick plates it utilises admissible functions comprising the chebyshev polynomials multiplied by a boundary function the analysis is based on a linear small strain three dimensional elasticity theory the proposed technique yields very accurate natural frequencies and mode shapes of rectangular plates with arbitrary boundary conditions a very simple and general programme has been compiled for the purpose for a plate with geometric symmetry the vibration modes can be classified into symmetric and antisymmetric ones in that direction in such a case the computational cost can be greatly reduced while maintaining the same level of accuracy convergence studies and comparison have been carried out taking square plates with four simply supported edges as examples it is shown that the present method enables rapid convergence stable numerical operation and very high computational accuracy parametric investigations on the vibration behaviour of rectangular plates with four clamped edges have also been performed in detail with respect to different thickness side ratios aspect ratios and poissons ratios these results may serve as benchmark solutions for validating approximate two dimensional theories and new computational techniques in future 2002 elsevier science ltd all rights reserved

free vibration of skew mindlin plates by p version of f e m abstract accurate natural frequencies and mode shapes of skew plates with and without cutouts are determined by p version finite element method using integrals of legendre polynomials for p 1 14 the hierarchical plate element is formulated based on mindlin s plate theory including rotatory inertia effects and based on a skew co ordinate system non dimensional frequency parameter and mode shapes are presented for a range of skew angle aspect ratio a b thickness width ratio h b cutout dimensions and different boundary conditions the results were verified by comparison with those available in the open literature

the bar complex of an e infinity algebra the standard reduced bar complex b a of a differential graded algebra a inherits a natural commutative algebra structure if a is a commutative algebra we address an extension of this construction in the context of e infinity algebras we prove that the bar complex of any e infinity algebra can be equipped with the structure of an e infinity algebra so that the bar construction defines a functor from e infinity algebras to e infinity algebras we prove the homotopy uniqueness of such natural e infinity structures on the bar construction we apply our construction to cochain complexes of topological spaces which are instances of e infinity algebras we prove that the n th iterated bar complexes of the cochain algebra of a space x is equivalent to the cochain complex of the n fold iterated loop space of x under reasonable connectedness completeness and finiteness assumptions on x

asymptotic behaviors of support vector machines with gaussian kernel support vector machines svms with the gaussian rbf kernel have been popular for practical use model selection in this class of svms involves two hyperparameters the penalty parameter c and the kernel width this letter analyzes the behavior of the svm classifier when these hyperparameters take very small or very large values our results help in understanding the hyperparameter space that leads to an efficient heuristic method of searching for hyperparameter values with small generalization errors the analysis also indicates that if complete model selection using the gaussian kernel has been conducted there is no need to consider linear svm

soft margin multiple kernel learning multiple kernel learning mkl has been proposed for kernel methods by learning the optimal kernel from a set of predefined base kernels however the traditional l 1 rm mkl method often achieves worse results than the simplest method using the average of base kernels i e average kernel in some practical applications in order to improve the effectiveness of mkl this paper presents a novel soft margin perspective for mkl specifically we introduce an additional slack variable called kernel slack variable to each quadratic constraint of mkl which corresponds to one support vector machine model using a single base kernel we first show that l 1 rm mkl can be deemed as hard margin mkl and then we propose a novel soft margin framework for mkl three commonly used loss functions including the hinge loss the square hinge loss and the square loss can be readily incorporated into this framework leading to the new soft margin mkl objective functions many existing mkl methods can be shown as special cases under our soft margin framework for example the hinge loss soft margin mkl leads to a new box constraint for kernel combination coefficients using different hyper parameter values for this formulation we can inherently bridge the method using average kernel l 1 rm mkl and the hinge loss soft margin mkl the square hinge loss soft margin mkl unifies the family of elastic net constraint regularizer based approaches and the square loss soft margin mkl incorporates l 2 rm mkl naturally moreover we also develop efficient algorithms for solving both the hinge loss and square hinge loss soft margin mkl comprehensive experimental studies for various mkl algorithms on several benchmark data sets and two real world applications including video action recognition and event recognition demonstrate that our proposed algorithms can efficiently achieve an effective yet sparse solution for mkl

successive overrelaxation for support vector machines successive overrelaxation sor for symmetric linear complementarity problems and quadratic programs is used to train a support vector machine svm for discriminating between the elements of two massive datasets each with millions of points because sor handles one point at a time similar to platt s sequential minimal optimization smo algorithm 1999 which handles two constraints at a time and joachims svm sup light 1998 which handles a small number of points at a time sor can process very large datasets that need not reside in memory the algorithm converges linearly to a solution encouraging numerical results are presented on datasets with up to 10 000 000 points such massive discrimination problems cannot be processed by conventional linear or quadratic programming methods and to our knowledge have not been solved by other methods on smaller problems sor was faster than svm sup light and comparable or faster than smo

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

the odd origin of gerstenhaber brackets batalin vilkovisky operators and master equations using five basic principles we treat gerstenhaber lie brackets batalin vilkovisky bv operators and master equations appearing in mathematical and physical contexts in a unified way the different contexts for this are given by the different types of feynman graphs that underlie the particular situation two of the maxims we bring forth are 1 that extending to the non connected graphs gives a commutative multiplication forming a part of the bv structure and 2 that there is a universal odd twist that unifies and explains seemingly ad hoc choices of signs and is responsible for the bv operator being a differential our treatment results in uniform general theorems these allow us to prove new results and recover and connect many constructions that have appeared independently throughout the literature the more general point of view also allows us to disentangle the necessary from the circumstantial

associahedra cyclohedra and a topological solution to the a deligne conjecture abstract we give a topological solution to the a deligne conjecture using associahedra and cyclohedra to this end we construct three cw complexes whose cells are indexed by products of polytopes giving new explicit realizations of the polytopes in terms of different types of trees we are able to show that the cw complexes are cell models for the little discs the cellular chains of one complex in particular which is built out of associahedra and cyclohedra naturally act on the hochschild cochains of an a algebra yielding an explicit topological and minimal solution to the a deligne conjecture along the way we obtain new results about the cyclohedra such as new decompositions into products of cubes and simplices which can be used to realize them via a new iterated blow up construction

semi automatic computer aided lesion detection in dental x rays using variational level set a semi automatic lesion detection framework is proposed to detect areas of lesions from periapical dental x rays using level set method in this framework first a new proposed competitive coupled level set method is used to segment the image into three pathologically meaningful regions using two coupled level set functions tailored for the dental clinical setting a two stage clinical segmentation acceleration scheme is used the method uses a trained support vector machine svm classifier to provide an initial contour for two coupled level sets then based on the segmentation results an analysis scheme is applied firstly the scheme builds an uncertainty map from which those areas with radiolucent will be automatically emphasized by a proposed color emphasis scheme those radiolucent in the teeth or jaw usually suggested possible lesions secondly the scheme employs a method based on the average intensity profile to isolate the teeth and locate two types of lesions periapical lesion pl and bifurcation lesion bl experimental results show that our proposed segmentation method is able to segment the image into pathological meaningful regions for further analysis our proposed framework is able to automatically provide direct visual cues for the lesion detection and when given the orientation of the teeth it is able to automatically locate the pl and bl with a seriousness level marked for further dental diagnosis when used in the clinical setting the framework enables dentist to improve interpretation and to focus their attention on critical areas

a general soft method for learning svm classifiers with l 1 norm penalty based on the geometric interpretation of support vector machines svms this paper presents a general technique that allows almost all the existing l 2 norm penalty based geometric algorithms including gilbert s algorithm schlesinger kozinec s sk algorithm and mitchell dem yanov malozemov s mdm algorithm to be softened to achieve the corresponding learning l 1 svm classifiers intrinsically the resulting soft algorithms are to find e optimal nearest points between two soft convex hulls theoretical analysis has indicated that our proposed soft algorithms are essentially generalizations of the corresponding existing hard algorithms and consequently they have the same properties of convergence and almost the identical cost of computation as a specific example the problem of solving n svms by the proposed soft mdm algorithm is investigated and the corresponding solution procedure is specified and analyzed to validate the general soft technique several real classification experiments are conducted with the proposed l 1 norm based mdm algorithms and numerical results have demonstrated that their performance is competitive to that of the corresponding l 2 norm based algorithms such as sk and mdm algorithms

analytical 3 d p element for quadrilateral plates part 1 thick isotropic plate structures an analytical three dimensional 3 d p version element for the vibration analysis of arbitrary quadrilateral thick plates is presented with the additional hierarchical shape functions and analytically integrated element matrices the computed accuracy is considerably improved the computed natural frequencies of cantilever and simply supported square plates show that the convergence rate of the present element is very fast with respect to the number of hierarchical terms and it can predict very accurate modes the element is applicable to the free vibration analysis of quadrilateral polygonal plates as well as 3 d space structures the continuous wavelet transform cwt is applied for the identification of damping ratios based on the rayleigh damping model the damped vibration response is obtained a simple experiment is performed to verify the predicted vibration responses the results show that the proposed element is also efficient for the vibration response analysis of plates

three dimensional hierarchical finite element free vibration analysis of annular sector plates an annular sector solid hierarchical finite element is presented and applied to three dimensional free vibration analysis of annular sector plates the element s displacements are expressed in terms of a fixed number of linear polynomial shape functions plus a variable number of shape functions which are forms of the shifted legendre orthogonal polynomial the linear polynomial shape functions are used to describe the element s nodal displacements and the higher order shape functions are used to provide additional freedom to the edges faces and interior of the element results of frequency calculations are found for annular sector plates with two straight edges simply supported like a diaphragm condition and comparisons are made with those obtained by the finite prism method the manner of convergence of the solution as a function of the numbers of hierarchical modes is also investigated furthermore contributions to original three dimensional frequencies are made for annular sector plates with other boundary conditions along the two straight edges

on the three dimensional vibrations of the cantilevered rectangular parallelepiped a solution is presented for the three dimensional problem of determining the free vibration frequencies and mode shapes for a rectangular parallelepiped which is completely fixed on one face and free on the other five faces this problem apparently is previously unsolved in the published literature the ritz method is used with displacements assumed in the form of algebraic polynomials convergence is studied numerical results are given for the first five frequencies of each of the four symmetry classes of vibration for five thick parallelepiped configurations including the cube contour plots are exhibited for the modal displacements of the cube the effects of varying poisson s ratio are also observed

three dimensional vibration of rectangular plates variance of simple support conditions and influence of in plane inertia plate models developed on the basis of the three dimensional elasticity theory are crucial to the correct solutions in dynamics problems in a three dimensional setting there exist numerous possible definitions of boundary conditions this paper attempts to identify the variance of three dimensional simple support conditions existing in practice the hard simple support condition assumes vanishing normal stresses at the edges and zero transverse and tangential displacement at the peripheries the soft simple support on the other hand imposes zero transverse displacement with vanishing normal and shear stresses at the boundaries to quantify the relative effects of each boundary condition on the vibratory responses of thick plates a global three dimensional ritz formulation is employed for analysis this technique uses sets of finite polynomial series in cartesian co ordinates to approximate the global normal mode variations of the plate these separable one dimensional polynomials are orthogonally generated within the plate domain such that all the essential edge conditions are identically satisfied the accuracy of the proposed three dimensional ritz method is assured from the convergence and comparison studies numerical experiments have been conducted to study firstly the effects of geometric parameters on the overall normal mode characteristics of simply supported plates and secondly the effects of in plane inertia on the vibration frequencies of plates with different thicknesses the three dimensional deformed mode shapes for selected cases have also been computed these have served to describe more vividly the normal mode characteristics of different types of simply supported rectangular plates

hochschild homology of structured algebras abstract we give a general method for constructing explicit and natural operations on the hochschild complex of algebras over any prop with a multiplication we think of such algebras as a algebras with extra structure as applications we obtain an integral version of the costello kontsevich soibelman moduli space action on the hochschild complex of open tcfts the tradler zeinalian and kaufmann actions of sullivan diagrams on the hochschild complex of strict frobenius algebras and give applications to string topology in characteristic zero our main tool is a generalization of the hochschild complex

frsde fast reduced set density estimator using minimal enclosing ball approximation reduced set density estimator rsde is an important technique that can be used to replace the classical parzen window estimator pw for saving the computational cost though rsde demonstrates a nicer performance in the density accuracy and the computational time compared with several existing methods it still faces the critical challenge for practical applications because of its high time complexity no less than o n 2 and space complexity o n 2 in training the model weighting coefficients on large data sets in order to overcome this shortcoming a fast reduced set density estimator algorithm frsde is proposed in this study first the relationship between rsde and the minimal enclosing ball problems meb in computational geometry is revealed then the finding that rsde is equivalent to a special meb problem is derived with this finding the fast core set based meb approximation algorithm is introduced to develop the proposed algorithm frsde compared with rsde frsde has the following distinctive advantage it can guarantee that the upper bound of the time complexity is linear with the size n of a large data set and the upper bound of the space complexity is independent of n our experimental results show that the proposed frsde has a competitive performance in the density accuracy and an overwhelming advantage over rsde for large data sets in the data condensation rate and the training time for the weighting coefficients

new support vector algorithms we propose a new class of support vector algorithms for regression and classification in these algorithms a parameter lets one effectively control the number of support vectors while this can be useful in its own right the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm the accuracy parameter epsilon in the regression case and the regularization constant c in the classification case we describe the algorithms give some theoretical results concerning the meaning and the choice of and report experimental results

a unified classification model based on robust optimization a wide variety of machine learning algorithms such as the support vector machine svm minimax probability machine mpm and fisher discriminant analysis fda exist for binary classification the purpose of this letter is to provide a unified classification model that includes these models through a robust optimization approach this unified model has several benefits one is that the extensions and improvements intended for svms become applicable to mpm and fda and vice versa for example we can obtain nonconvex variants of mpm and fda by mimicking perez cruz weston hermann and scholkopf s 2003 extension from convex i svm to nonconvex ei svm another benefit is to provide theoretical results concerning these learning methods at once by dealing with the unified model we give a statistical interpretation of the unified classification model and prove that the model is a good approximation for the worst case minimization of an expected loss with respect to the uncertain probability distribution we also propose a nonconvex optimization algorithm that can be applied to nonconvex variants of existing learning methods and show promising numerical results

kpca plus lda a complete kernel fisher discriminant framework for feature extraction and recognition this paper examines the theory of kernel fisher discriminant analysis kfd in a hilbert space and develops a two phase kfd framework i e kernel principal component analysis kpca plus fisher linear discriminant analysis lda this framework provides novel insights into the nature of kfd based on this framework the authors propose a complete kernel fisher discriminant analysis ckfd algorithm ckfd can be used to carry out discriminant analysis in double discriminant subspaces the fact that it can make full use of two kinds of discriminant information regular and irregular makes ckfd a more powerful discriminator the proposed algorithm was tested and evaluated using the feret face database and the cenparmi handwritten numeral database the experimental results show that ckfd outperforms other kfd algorithms

three dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method this paper presents accurate three dimensional elasticity solutions for free vibrations of six types of plates having free lateral surfaces two opposite sides simply supported and two other sides having combinations of simply supported clamped and free boundary conditions the solution methodology adopted in the present work first reduces the spatial variables in the governing elasticity equations to two by using displacement functions in the forms which satisfy the boundary conditions of the assumed simply supported sides the eigenvalue equations are then formulated from the reduced governing equations and the boundary conditions via the differential quadrature method the numerical results include the first nine natural frequencies of the six plate configurations for combinations of three aspect ratios and two thickness ratios these results are supported by appropriate convergence studies and comparisons with the results of other authors

a hierarchical functions set for predicting very high order plate bending modes with any boundary conditions in this paper a new hierarchical functions set is proposed to predict flexural motion of plate like structures in the medium frequency range this functions set is built from trigonometric functions instead of polynomials as classically encountered in the literature it is shown that such a trigonometric set presents all the advantages of a classical hierarchical polynomials set and additional ones which are of interest if very high order functions are intended to be used it is stated that this new trigonometric set can be used at very high orders up to 2048 without taking care of computer round off errors while the polynomials set fail at order 46 because of the limited numerical dynamics of computers this trigonometric set can be easily implemented on a computer it does not require quadruple precision pre computed arrays only a very low number which does not depend on the function order of basic operations is needed when calling such functions moreover it is shown that this trigonometric set presents a better convergence rate than polynomials when predicting high order natural flexural modes of rectangular plates with any boundary conditions

the cobar construction as a hopf algebra we show that the integral cobar construction c x of a 1 reduced simplicial set x has the structure of a homotopy hopf algebra this leads to a rational differential lie algebra x given by a differential d on the free lie algebra l s 1 x the universal enveloping algebra u x is naturally isomorphic to c x let x be a 1 reduced simplicial set and let s 1 x be the desuspension of the reduced chain complex x of x the cobar construction is given by a differential d on the tensor algebra t s 1 x defined over the homology of c x coincides with the homology of the loop space x a formula for d was given by adams ad we show that the cobar construction c x has over the additional natural structure of a homotopy hopf algebra consisting of a coassociative diagonal and a derivation homotopy e explicit formulas for and e are given in 2 9 the result is based on the geometric cobar construction in b using the fundamental theory of anick a we derive from the data c x e a differential lie algebra which is defined by a differential d on the free rational lie algebra l s 1 x the homology of x coincides with the rational homotopy groups of x moreover we describe a cocommutative diagonal together with a derivation homotopy h and a natural iso morphism of differential hopf algebras formulas for h and are obtained by an induction a map f x y between 1 reduced simplicial sets induces the map f l s 1 f l s 1 x l s 1 y between free lie algebras which is compatible with the differential d hence x x yields a canonical functor from 1 reduced simplicial sets to free differential lie algebras this functor induces an isomorphism of rational homotopy categories in fact is up to homotopy naturally equivalent to the functor npg of quillen q which is the composite of four intricate functors we describe in b inductively a sequence of elements 2 3 which determine the differential d and we compute the quadratic part of d a complete formula for d however is highly intricate since it can be considered as a kind of simplicial form of the classical hausdorff formula see 4 9 4 we cannot expect a simple form of the differential d since the homology of x yields the rational homotopy groups of x that is this supplements the result of kan k who gave a combinatorial description of x in terms of the free simplicial group gx hence x requires computations in free groups while the formula for x requires only the computation of the homology of a chain complex of rational vector spaces we point out that x is a chain complex of finite type if x has only finitely many non degenerate simplices hence in this case d yields a finite formula for n x such a formula was not yet achieved in the literature for example using the sullivan method one obtains x only implicitly by computing a minimal model of the de rham algebra a x see bousfield gugenheim bg here a x is defined explicitly in terms of x but is not of finite type if x has only finitely many non degenerate simplices so that a x does not give a finite formula for n x in this case the minimal model m x of a x is of finite type and hence also gives a finite formula for n x there is however no explicit formula for m x in terms of x in the literature and m x is not natural in x on the other hand also the model x of quillen is considerably larger than x above and is only defined as the normalization of a simplicial object see 4 9 4 below

a continuum three dimensional vibration analysis of thick rectangular plates abstract this paper presents a continuum three dimensional ritz formulation for the vibration analysis of homogeneous thick rectangular plates with arbitrary combinations of boundary constraints this model is formulated on the basis of the linear three dimensional small deformation elasticity theory to predict the vibratory responses of these thick rectangular plates the displacement fields in the transverse and in plane directions are expressed by sets of orthogonally generated polynomial functions these shape functions are intrinsically a product of a class of orthogonal polynomial functions and a basic function which are chosen to satisfy the essential geometric boundary conditions at the outset sets of frequency data for plates with various aspect ratios and thickness ratios have been presented these data are used to examine the merits and limitations of the classical plate theory and mindlin plate theory by direct comparisons finally using the three dimensional continuum approach sets of first known deformed mode shapes have been generated thus helping to understand the vibratory motion furthermore these results may also serve as the benchmark to further research into the refined plate theories

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

weighted mahalanobis distance kernels for support vector machines the support vector machine svm has been demonstrated to be a very effective classifier in many applications but its performance is still limited as the data distribution information is underutilized in determining the decision hyperplane most of the existing kernels employed in nonlinear svms measure the similarity between a pair of pattern images based on the euclidean inner product or the euclidean distance of corresponding input patterns which ignores data distribution tendency and makes the svm essentially a ldquolocalrdquo classifier in this paper we provide a step toward a paradigm of kernels by incorporating data specific knowledge into existing kernels we first find the data structure for each class adaptively in the input space via agglomerative hierarchical clustering ahc and then construct the weighted mahalanobis distance wmd kernels using the detected data distribution information in wmd kernels the similarity between two pattern images is determined not only by the mahalanobis distance md between their corresponding input patterns but also by the sizes of the clusters they reside in although wmd kernels are not guaranteed to be positive definite pd or conditionally positive definite cpd satisfactory classification results can still be achieved because regularizers in svms with wmd kernels are empirically positive in pseudo euclidean pe spaces experimental results on both synthetic and real world data sets show the effectiveness of ldquopluggingrdquo data structure into existing kernels

ssc eke semi supervised classification with extensive knowledge exploitation we introduce a new semi supervised classification method that extensively exploits knowledge the method has three steps first the manifold regularization mechanism adapted from the laplacian support vector machine lapsvm is adopted to mine the manifold structure embedded in all training data especially in numerous label unknown data meanwhile by converting the labels into pairwise constraints the pairwise constraint regularization formula pcrf is designed to compensate for the few but valuable labelled data second by further combining the pcrf with the manifold regularization the precise manifold and pairwise constraint jointly regularized formula mpcjrf is achieved third by incorporating the mpcjrf into the framework of the conventional svm our approach referred to as semi supervised classification with extensive knowledge exploitation ssc eke is developed the significance of our research is fourfold 1 the mpcjrf is an underlying adjustment with respect to the pairwise constraints to the graph laplacian enlisted for approximating the potential data manifold this type of adjustment plays the correction role as an unbiased estimation of the data manifold is difficult to obtain whereas the pairwise constraints converted from the given labels have an overall high confidence level 2 by transforming the values of the two terms in the mpcjrf such that they have the same range with a trade off factor varying within the invariant interval 0 1 the appropriate impact of the pairwise constraints to the graph laplacian can be self adaptively determined 3 the implication regarding extensive knowledge exploitation is embodied in ssc eke that is the labelled examples are used not only to control the empirical risk but also to constitute the mpcjrf moreover all data both labelled and unlabelled are recruited for the model smoothness and manifold regularization 4 the complete framework of ssc eke organically incorporates multiple theories such as joint manifold and pairwise constraint based regularization smoothness in the reproducing kernel hilbert space empirical risk minimization and spectral methods which facilitates the preferable classification accuracy as well as the generalizability of ssc eke

orthogonal laplacianfaces for face recognition following the intuition that the naturally occurring face data may be generated by sampling a probability distribution that has support on or near a submanifold of ambient space we propose an appearance based face recognition method called orthogonal laplacianface our algorithm is based on the locality preserving projection lpp algorithm which aims at finding a linear approximation to the eigenfunctions of the laplace beltrami operator on the face manifold however lpp is nonorthogonal and this makes it difficult to reconstruct the data the orthogonal locality preserving projection olpp method produces orthogonal basis functions and can have more locality preserving power than lpp since the locality preserving power is potentially related to the discriminating power the olpp is expected to have more discriminating power than lpp experimental results on three face databases demonstrate the effectiveness of our proposed algorithm

cosimplicial objects and little n cubes i in this paper we show that if a cosimplicial space has a certain kind of combinatorial structure then its total space has an action of an operad weakly equivalent to the little n cubes operad our results are also valid for cosimplicial spectra

a classification of taylor towers of functors of spaces and spectra abstract we describe new structure on the goodwillie derivatives of a functor and we show how the full taylor tower of the functor can be recovered from this structure this new structure takes the form of a coalgebra over a certain comonad which we construct and whose precise nature depends on the source and target categories of the functor in question the taylor tower can be recovered from standard cosimplicial cobar constructions on the coalgebra formed by the derivatives we get from this an equivalence between the homotopy category of polynomial functors and that of bounded coalgebras over this comonad for functors with values in the category of spectra we give a rather explicit description of the associated comonads and their coalgebras in particular for functors from based spaces to spectra we interpret this new structure as that of a divided power right module over the operad formed by the derivatives of the identity on based spaces

robust truncated hinge loss support vector machines the support vector machine svm has been widely applied for classification problems in both machine learning and statistics despite its popularity however svm has some drawbacks in certain situations in particular the svm classifier can be very sensitive to outliers in the training sample moreover the number of support vectors svs can be very large in many applications to circumvent these drawbacks we propose the robust truncated hinge loss svm rsvm which uses a truncated hinge loss the rsvm is shown to be more robust to outliers and to deliver more accurate classifiers using a smaller set of svs than the standard svm our theoretical results show that the rsvm is fisher consistent even when there is no dominating class a scenario that is particularly challenging for multicategory classification similar results are obtained for a class of margin based classifiers

identification of damping in mdof systems using time scale decomposition abstract a method of damping identification in multi degree of freedom systems is presented the method is based on the time scale decomposition of the system impulse response the continuous wavelet transform is used to decompose the impulse response into the time scale domain three techniques based on the wavelet tranform are used to estimate damping these are the wavelet transform cross section procedure the impulse response recovery procedure based on wavelet domain filtering and the wavelet ridge detection procedure the methods are applied to simulated multi degree of freedom systems

chern simons perturbation theory ii we study the perturbation theory for three dimensional chern simons quantum field theory on a general compact three manifold without boundary we show that after a simple change of variables the action obtained by brs gauge fixing in the lorentz gauge has a superspace formulation the basic properties of the propagator and the feynman rules are written in a precise manner in the language of differential forms using the explicit description of the propagator singularities we prove that the theory is finite finally the anomalous metric dependence of the 2 loop partition function on the riemannian metric which was introduced to define the gauge fixing can be cancelled by a local counterterm as in the 1 loop case in fact the counterterm is equal to the chern simons action of the metric connection normalized precisely as one would expect based on the framing dependence of witten s exact solution invited talk at the xxth conference on differential geometric methods in physics new york june 1991

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

a least squares approach to direct importance estimation we address the problem of estimating the ratio of two probability density functions which is often referred to as the importance the importance values can be used for various succeeding tasks such as covariate shift adaptation or outlier detection in this paper we propose a new importance estimation method that has a closed form solution the leave one out cross validation score can also be computed analytically therefore the proposed method is computationally highly efficient and simple to implement we also elucidate theoretical properties of the proposed method such as the convergence rate and approximation error bounds numerical experiments show that the proposed method is comparable to the best existing method in accuracy while it is computationally more efficient than competing approaches

modules and morita theorem for operads associative rings a b are called morita equivalent when the categories of left modules over them are equivalent we call two classical linear operads p q morita equivalent if the categories of algebras over them are equivalent we transport a part of morita theory to the operadic context by studying modules over operads as an application of this philosophy we consider an operadic version of the sheaf of linear differential operators on a super manifold m and give a comparison theorem between algebras over this sheaf on m and m red

minimum class variance support vector machines in this paper a modified class of support vector machines svms inspired from the optimization of fisher s discriminant ratio is presented the so called minimum class variance svms mcvsvms the mcvsvms optimization problem is solved in cases in which the training set contains less samples that the dimensionality of the training vectors using dimensionality reduction through principal component analysis pca afterward the mcvsvms are extended in order to find nonlinear decision surfaces by solving the optimization problem in arbitrary hilbert spaces defined by mercer s kernels in that case it is shown that under kernel pca the nonlinear optimization problem is transformed into an equivalent linear mcvsvms problem the effectiveness of the proposed approach is demonstrated by comparing it with the standard svms and other classifiers like kernel fisher discriminant analysis in facial image characterization problems like gender determination eyeglass and neutral facial expression detection

training v support vector regression theory and algorithms we discuss the relation between e support vector regression e svr and support vector regression svr in particular we focus on properties that are different from those of c support vector classification c svc and support vector classification svc we then discuss some issues that do not occur in the case of classification the possible range of e and the scaling of target values a practical decomposition method for svr is implemented and computational experiments are conducted we show some interesting numerical observations specific to regression

a locality correlation preserving support vector machine abstract this paper proposes a locality correlation preserving based support vector machine lcpsvm by combining the idea of margin maximization between classes and local correlation preservation of class data it is a support vector machine svm like algorithm which explicitly considers the locality correlation within each class in the margin and the penalty term of the optimization function canonical correlation analysis cca is used to reveal the hidden correlations between two datasets and a variant of correlation analysis model which implements locality preserving has been proposed by integrating local information into the objective function of cca inspired by the idea used in canonical correlation analysis we propose a locality correlation preserving within class scatter matrix to replace the within class scatter matrix in minimum class variance support machine mcvsvm this substitution has the property of keeping the locality correlation of data and inherits the properties of svm and other similar modified class of support vector machines lcpsvm is discussed under linearly separable small sample size and nonlinearly separable conditions and experimental results on benchmark datasets demonstrate its effectiveness

support vector machinery for infinite ensemble learning ensemble learning algorithms such as boosting can achieve better performance by averaging over the predictions of some base hypotheses nevertheless most existing algorithms are limited to combining only a finite number of hypotheses and the generated ensemble is usually sparse thus it is not clear whether we should construct an ensemble classifier with a larger or even an infinite number of hypotheses in addition constructing an infinite ensemble itself is a challenging task in this paper we formulate an infinite ensemble learning framework based on the support vector machine svm the framework can output an infinite and nonsparse ensemble through embedding infinitely many hypotheses into an svm kernel we use the framework to derive two novel kernels the stump kernel and the perceptron kernel the stump kernel embodies infinitely many decision stumps and the perceptron kernel embodies infinitely many perceptrons we also show that the laplacian radial basis function kernel embodies infinitely many decision trees and can thus be explained through infinite ensemble learning experimental results show that svm with these kernels is superior to boosting with the same base hypothesis set in addition svm with the stump kernel or the perceptron kernel performs similarly to svm with the gaussian radial basis function kernel but enjoys the benefit of faster parameter selection these properties make the novel kernels favorable choices in practice

derived koszul duality and tq homology completion of structured ring spectra abstract working in the context of symmetric spectra we consider algebraic structures that can be described as algebras over an operad o topological quillen homology or tq homology is the spectral algebra analog of quillen homology and stabilization working in a framework for homotopical descent the associated tq homology completion map appears as the unit map of an adjunction comparing the homotopy categories of o algebra spectra with coalgebra spectra over the associated comonad via tq homology we prove that this adjunction between homotopy categories can be turned into an equivalence by replacing o algebras with the full subcategory of 0 connected o algebras we also construct the spectral algebra analog of the unstable adams spectral sequence that starts from the tq homology groups tq x of an o algebra x and prove that it converges strongly to x when x is 0 connected

a formal analysis of stopping criteria of decomposition methods for support vector machines in a previous paper the author 2001 proved the convergence of a commonly used decomposition method for support vector machines svms however there is no theoretical justification about its stopping criterion which is based on the gap of the violation of the optimality condition it is essential to have the gap asymptotically approach zero so we are sure that existing implementations stop in a finite number of iterations after reaching a specified tolerance here we prove this result and illustrate it by two extensions spl nu svm and a multiclass svm by crammer and singer 2001 a further result shows that in final iterations of the decomposition method only a particular set of variables are still being modified this supports the use of the shrinking and caching techniques in some existing implementations finally we prove the asymptotic convergence of a decomposition method for this multiclass svm discussions on the difference between this convergence proof and the one in another paper by lin are also included

input space versus feature space in kernel based methods this paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector sv kernel functions we first discuss the geometry of feature space in particular we review what is known about the shape of the image of input space under the feature space map and how this influences the capacity of sv methods following this we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel using the example of the class of inhomogeneous polynomial kernels which are often used in sv pattern recognition we then discuss the connection between feature space and input space by dealing with the question of how one can given some vector in feature space find a preimage exact or approximate in input space we describe algorithms to tackle this issue and show their utility in two applications of kernel methods first we use it to reduce the computational complexity of sv decision functions second we combine it with the kernel pca algorithm thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real world data

orthogonal neighborhood preserving projections a projection based dimensionality reduction technique this paper considers the problem of dimensionality reduction by orthogonal projection techniques the main feature of the proposed techniques is that they attempt to preserve both the intrinsic neighborhood geometry of the data samples and the global geometry in particular we propose a method named orthogonal neighborhood preserving projections which works by first building an affinity graph for the data in a way that is similar to the method of locally linear embedding lle however in contrast with the standard lle where the mapping between the input and the reduced spaces is implicit onpp employs an explicit linear mapping between the two as a result handling new data samples becomes straightforward as this amounts to a simple linear transformation we show how we can define kernel variants of onpp as well as how we can apply the method in a supervised setting numerical experiments are reported to illustrate the performance of onpp and to compare it with a few competing methods

on the self linking of knots this note describes a subcomplex f of the de rham complex of parametrized knot space which is combinatorial over a number of universal anomaly integrals the self linking integrals of guadaguini martellini and mintchev perturbative aspects of chern simons field theory phys lett b 227 111 1989 and bar natan perturbative aspects of the chern simons topological quantum field theory ph d thesis princeton university 1991 also on the vassiliev knot invariants to appear in topology are seen to represent the first nontrivial element in h0 f occurring at level 4 and are anomaly free however already at the next level an anomalous term is possible

twin mahalanobis distance based support vector machines for pattern recognition twin support vector machines tsvms achieve fast training speed and good performance for data classification however tsvms do not take full advantage of the statistical information in data such as the covariance of each class of data this paper proposes a new twin mahalanobis distance based support vector machine tmsvm classifier in which two mahalanobis distance based kernels are constructed according to the covariance matrices of two classes of data for optimizing the nonparallel hyperplanes tmsvms have a special case of tsvms when the covariance matrices in a reproducing kernel hilbert space are degenerated to the identity ones tmsvms are suitable for many real problems especially for the case that the covariance matrices of two classes of data are obviously different the experimental results on several artificial and benchmark datasets indicate that tmsvms not only possess fast learning speed but also obtain better generalization than tsvms and other methods

formulations of support vector machines a note from an optimization point of view in this article we discuss issues about formulations of support vector machines svm from an optimization point of view first svms map training data into a higher maybe infinite dimensional space currently primal and dual formulations of svm are derived in the finite dimensional space and readily extend to the infinite dimensional space we rigorously discuss the primal dual relation in the infinite dimensional spaces second svm formulations contain penalty terms which are different from unconstrained penalty functions in optimization traditionally unconstrained penalty functions approximate a constrained problem as the penalty parameter increases we are interested in similar properties for svm formulations for two of the most popular svm formulations we show that one enjoys properties of exact penalty functions but the other is only like traditional penalty functions which converge when the penalty parameter goes to infinity

core vector machines fast svm training on very large data sets standard svm training has o m3 time and o m2 space complexities where m is the training set size it is thus computationally infeasible on very large data sets by observing that practical svm implementations only approximate the optimal solution by an iterative strategy we scale up kernel methods by exploiting such approximateness in this paper we first show that many kernel methods can be equivalently formulated as minimum enclosing ball meb problems in computational geometry then by adopting an efficient approximate meb algorithm we obtain provably approximately optimal solutions with the idea of core sets our proposed core vector machine cvm algorithm can be used with nonlinear kernels and has a time complexity that is linear in m and a space complexity that is independent of m experiments on large toy and real world data sets demonstrate that the cvm is as accurate as existing svm implementations but is much faster and can handle much larger data sets than existing scale up methods for example cvm with the gaussian kernel produces superior results on the kddcup 99 intrusion detection data which has about five million training patterns in only 1 4 seconds on a 3 2ghz pentium 4 pc

domain adaptation via transfer component analysis domain adaptation allows knowledge from a source domain to be transferred to a different but related target domain intuitively discovering a good feature representation across domains is crucial in this paper we first propose to find such a representation through a new learning method transfer component analysis tca for domain adaptation tca tries to learn some transfer components across domains in a reproducing kernel hilbert space using maximum mean miscrepancy in the subspace spanned by these transfer components data properties are preserved and data distributions in different domains are close to each other as a result with the new representations in this subspace we can apply standard machine learning methods to train classifiers or regression models in the source domain for use in the target domain furthermore in order to uncover the knowledge hidden in the relations between the data labels from the source and target domains we extend tca in a semisupervised learning setting which encodes label information into transfer components learning we call this extension semisupervised tca the main contribution of our work is that we propose a novel dimensionality reduction framework for reducing the distance between domains in a latent space for domain adaptation we propose both unsupervised and semisupervised feature extraction approaches which can dramatically reduce the distance between domain distributions by projecting data onto the learned transfer components finally our approach can handle large datasets and naturally lead to out of sample generalization the effectiveness and efficiency of our approach are verified by experiments on five toy datasets and two real world applications cross domain indoor wifi localization and cross domain text classification