some explicit examples of hamiltonian minimal lagrangian submanifolds in complex space forms abstract in this paper we find some new explicit examples of hamiltonian minimal lagrangian submanifolds among the lagrangian isometric immersions of a real space form in a complex space form

reductions of minimal lagrangian submanifolds with symmetries let m be a fano manifold equipped with a kahler form omega in 2 pi c 1 m and k a connected compact lie group acting on m as holomorphic isometries in this paper we show the minimality of a k invariant lagrangian submanifold l in m with respect to a globally conformal kahler metric is equivalent to the minimality of the reduced lagrangian submanifold l 0 l k in a kahler quotient m 0 with respect to the hsiang lawson metric furthermore we give some examples of kahler reductions by using a circle action obtained from a cohomogenenity one action on a kahler einstein manifold of positive ricci curvature applying these results we obtain several examples of minimal lagrangian submanifolds via reductions

large scale multiple kernel learning while classical kernel based learning algorithms are based on a single kernel in practice it is often desirable to use multiple kernels lanckriet et al 2004 considered conic combinations of kernel matrices for classification leading to a convex quadratically constrained quadratic program we show that it can be rewritten as a semi infinite linear program that can be efficiently solved by recycling the standard svm implementations moreover we generalize the formulation and our method to a larger class of problems including regression and one class classification experimental results show that the proposed algorithm works for hundred thousands of examples or hundreds of kernels to be combined and helps for automatic model selection improving the interpretability of the learning result in a second part we discuss general speed up mechanism for svms especially when used with sparse feature maps as appear for string kernels allowing us to train a string kernel svm on a 10 million real world splice data set from computational biology we integrated multiple kernel learning in our machine learning toolbox shogun for which the source code is publicly available at http www fml tuebingen mpg de raetsch projects shogun

a sequential algorithm for sparse support vector classifiers support vector machines svms though accurate are not preferred in applications requiring high classification speed or when deployed in systems of limited computational resources due to the large number of support vectors involved in the model to overcome this problem we have devised a primal svm method with the following properties 1 it solves for the svm representation without the need to invoke the representer theorem 2 forward and backward selections are combined to approach the final globally optimal solution and 3 a criterion is introduced for identification of support vectors leading to a much reduced support vector set in addition to introducing this method the paper analyzes the complexity of the algorithm and presents test results on three public benchmark problems and a human activity recognition application these applications demonstrate the effectiveness and efficiency of the proposed algorithm

sequential testing of sorted and transformed data as an efficient way to implement long glrts it is often required to detect a long weak signal in gaussian noise and frequently the exact form of that signal is parameterized but not known a bank of matched filters provides an appropriate detector however in some practical applications there are very many matched filters and most are quite long the consequent computational needs may render the classical bank of filters approach infeasibly expensive one example and our original motivation is the detection of chirp gravitational waves by an earth based interferometer in this paper we provide a computational approach to this problem via sequential testing since the sequential tests to be used are not for constant signals we develop the theory in terms of average sample number asn for this case specifically we propose two easily calculable expressions for the asn one a bound and the other an approximation the sequential approach does yield moderate computational savings but we find that by preprocessing the data using short medium fast fourier transforms ffts and an appropriate sorting of these fft outputs such that the most informative samples are entered to a sequential test first quite high numerical efficiency can be realized the idea is simple but appears to be quite successful examples are presented in which the computational load is reduced by several orders of magnitude the fft is an example of an energy agglomerating transform but of course there are many others the point here is that the transform need not match the sought signal exactly in the sense that all energy becomes confined to a single sample it is enough that the energy becomes concentrated and the more concentrated the better

on lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres the n dimensional complex hyperquadric is a compact complex algebraic hypersurface defined by the quadratic equation in the n 1 dimensional complex projective space which is isometric to the real grassmann manifold of oriented 2 planes and is a compact hermitian symmetric space of rank 2 in this paper we study geometry of compact lagrangian submanifolds in complex hyperquadrics from the viewpoint of the theory of isoparametric hypersurfaces in spheres from this viewpoint we provide a classification theorem of compact homogeneous lagrangian submanifolds in complex hyperquadrics by using the moment map technique moreover we determine the hamiltonian stability of compact minimal lagrangian submanifolds embedded in complex hyperquadrics which are obtained as gauss images of isoparametric hypersurfaces in spheres with g 1 2 3 distinct principal curvatures

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

a dependent data extension of wald s identity and its application to sequential test performance computation the development of an exponential transformation of measure not restricted to independent identically distributed data is presented for a class of semi markov processes known as markov additive ma process the ma measure transformation is applied to obtain a new form of the wald identity to demonstrate the utility of this extension to ma processes the application of sequential tests with markov data to error probability performance analysis is investigated in particular it is demonstrated how previous work dealing with robust error probability evaluation in the presence of uncertain serial dependency can be applied to sequential tests

learning the kernel with hyperkernels this paper addresses the problem of choosing a kernel suitable for estimation with a support vector machine hence further automating machine learning this goal is achieved by defining a reproducing kernel hilbert space on the space of kernels itself such a formulation leads to a statistical estimation problem similar to the problem of minimizing a regularized risk functional we state the equivalent representer theorem for the choice of kernels and present a semidefinite programming formulation of the resulting optimization problem several recipes for constructing hyperkernels are provided as well as the details of common machine learning problems experimental results for classification regression and novelty detection on uci data show the feasibility of our approach

second variation and stabilities of minimal lagrangian submanifolds in kahler manifolds first we derive a new second variation formula which holds for any minimal lagrangian submanifold in k ihler manifolds using this we prove that any minimal lagrangian submanifold in kfihler manifolds with nonpositive chern class is stable we also prove that in kfihler manifolds with positive chern class any stable minimal lagrangian submanifold l satisfies that h l 0 next we introduce the notion of hamiltonian stability either local or global of minimal lagrangian submanifolds in einstein kfihler manifolds using our second variation formula we find a general criterion for the local hamiltonian stability for minimal lagrangian submanifolds in einstein k ihler manifolds this criterion is satisfied for all real forms which are einstein of irreducible hermitian symmetric spaces e g the cannonical rp c cp it is also satisfied by the clifford torus t c cp

an isoperimetric inequality for hamiltonian stationary lagrangian tori in mathbb c 2 related to oh s conjecture we compute loops integrals on hamiltonian stationary lagrangian tori in mathbb c 2 which are symplectic invariants then we show an isoperimetric inequality involving these invariants and the area finally we show that the flat torus s 1 times s 1 subset mathbb c times mathbb c has least area among hamiltonian stationary lagrangian tori of its isotopy class

comment on optimality of the sequential probability ratio test for nonstationary observations by y liu and s d blostein for original paper see ieee trans inform theory vol 38 p 177 82 1992 liu and blostein 1992 consider sequential tests with varying stopping bounds nsprt for testing simple hypotheses on independent but nonstationary observations they state a considerable generalization of the famous wald wolfowitz theorem 1948 on the simultaneous minimization of the expected sample sizes for given error probabilities liu and blostein theorem 27 unfortunately this statement fails to be true 1 a simple counterexample may be constructed by choosing densities f sub 01 spl ne f sub 1 1 such that 0

an adaptive support vector regression based on a new sequence of unified orthogonal polynomials in practical engineering small scale data sets are usually sparse and contaminated by noise in this paper we propose a new sequence of orthogonal polynomials varying with their coefficient unified chebyshev polynomials ucp which has two important properties namely orthogonality and adaptivity based on these new polynomials a new kernel function the unified chebyshev kernel uck is constructed which has been proven to be a valid svm kernel to find the optimal polynomial coefficient and the optimal kernel we propose an adaptive algorithm based on the evaluation criterion for adaptive ability of uck to evaluate the performance of the new method we applied it to learning some benchmark data sets for regression and compared it with other three algorithms the experiment results show that the proposed adaptive algorithm has excellent generalization performance and prediction accuracy and does not cost more time compared with other svms therefore this method is suitable for practical engineering application

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

the entropy of ordered sequences and order statistics the entropy of a sequence of random variables under order restrictions is examined a theorem that shows the amount of entropy reduction when the sequence is ordered is presented upper and lower bounds to the entropy reduction and conditions under which they are achieved are derived some interesting properties of the entropy of the individual order statistics are also presented it is shown that the difference between the average entropy of the individual order statistics and the entropy of a member of the original independent identically distributed iid population is a constant regardless of the original distribution finally the entropies of the individual order statistics are found to be symmetric about the median when the probability density function pdf of the original iid sequence is symmetric about its mean

irahc instance reduction algorithm using hyperrectangle clustering abstract in instance based classifiers there is a need for storing a large number of samples as training set in this work we propose an instance reduction method based on hyperrectangle clustering called instance reduction algorithm using hyperrectangle clustering irahc irahc removes non border interior instances and keeps border and near border ones this paper presents an instance reduction process based on hyperrectangle clustering a hyperrectangle is an n dimensional rectangle with axes aligned sides which is defined by min and max points and a corresponding distance function the min max points are determined by using the hyperrectangle clustering algorithm instance based learning algorithms are often confronted with the problem of deciding which instances must be stored to be used during an actual test storing too many instances can result in a large memory requirements and a slow execution speed in irahc core of instance reduction process is based on set of hyperrectangles the performance has been evaluated on real world data sets from uci repository by the 10 fold cross validation method the results of the experiments have been compared with state of the art methods which show superiority of the proposed method in terms of classification accuracy and reduction percentage

comparison of the sprt and the sequential linear detector in autoregressive noise corresp the sequential probability ratio test sprt with constant thresholds and the sequential linear detector sld are compared under an autoregressive noise assumption in terms of the average sample number asn when both detectors have the same error probabilities for small asn their performances are evaluated numerically results show that the sld is better when rho the parameter in the autoregressive noise is positive and the sprt is better when rho is negative however their asymptotic efficiencies as the signal approaches zero are found to be the same

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

optimal reduced set vectors for support vector machines with a quadratic kernel to reduce computational cost the discriminant function of a support vector machine svm should be represented using as few vectors as possible this problem has been tackled in different ways in this article we develop an explicit solution in the case of a general quadratic kernel k x x c d xtx 2 for a given number of vectors this solution provides the best possible approximation and can even recover the discriminant function if the number of used vectors is large enough the key idea is to express the inhomogeneous kernel as a homogeneous kernel on a space having one dimension more than the original one and to follow the approach of burges 1996

warped product decompositions of real space forms and hamiltonian stationary lagrangian submanifolds abstract a lagrangian submanifold of a kaehler manifold is said to be hamiltonian stationary or h stationary for short if it is a critical point of the area functional restricted to compactly supported hamiltonian variations in this article we present some simple relationship between warped product decompositions of real space forms and hamiltonian stationary lagrangian submanifolds we completely classify h stationary lagrangian submanifolds in complex space forms arisen from warped product decompositions more precisely we prove that there exist two such families of h stationary lagrangian submanifolds in c n two families in c p n and twenty one families in c h n as immediate by product we obtain many new families of hamiltonian stationary lagrangian submanifolds in complex space forms

hamiltonian stability of the gauss images of homogeneous isoparametric hypersurfaces i the image of the gauss map of any oriented isopara metric hypersurface of the unit standard sphere s n 1 1 is a mini mal lagrangian submanifold in the complex hyperquadric qn c in this paper we determine the hamiltonian stability of all com pact minimal lagrangian submanifolds embedded in complex hy perquadrics which are obtained as the images of the gauss map of homogeneous isoparametric hypersurfaces in the unit spheres

an equivalence between sparse approximation and support vector machines in the first part of this paper we show a similarity between the principle of structural risk minimization principle srm vapnik 1982 and the idea of sparse approximation as defined in chen donoho and saunders 1995 and olshausen and field 1996 then we focus on two specific approximate implementations of srm and sparse approximation which have been used to solve the problem of function approximation for srm we consider the support vector machine technique proposed by v vapnik and his team at at t bell labs and for sparse approximation we consider a modification of the basis pursuit de noising algorithm proposed by chen donoho and saunders 1995 we show that under certain conditions these two techniques are equivalent they give the same solution and they require the solution of the same quadratic programming problem

dynamical analysis of bayesian inference models for the eriksen task the eriksen task is a classical paradigm that explores the effects of competing sensory inputs on response tendencies and the nature of selective attention in controlling these processes in this task conflicting flanker stimuli interfere with the processing of a central target especially on short reaction time trials this task has been modeled by neural networks and more recently by a normative bayesian account here we analyze the dynamics of the bayesian models which are nonlinear coupled discrete time dynamical systems by considering simplified approximate systems that are linear and decoupled analytical solutions of these allow us to describe how posterior probabilities and psychometric functions depend on model parameters we compare our results with numerical simulations of the original models and derive fits to experimental data showing that agreements are rather good we also investigate continuum limits of these simplified dynamical systems and demonstrate that bayesian updating is closely related to a drift diffusion process whose implementation in neural network models has been extensively studied this provides insight into how neural substrates can implement bayesian computations

a novel formulation of orthogonal polynomial kernel functions for svm classifiers the gegenbauer family abstract orthogonal polynomial kernels have been recently introduced to enhance support vector machine classifiers by reducing their number of support vectors previous works have studied these kernels as isolated cases and discussed only particular aspects in this paper a novel formulation of orthogonal polynomial kernels that includes and improves previous proposals legendre chebyshev and hermite is presented two undesired effects that must be avoided in order to use orthogonal polynomial kernels are identified and resolved the annihilation and the explosion effects the proposed formulation is studied by means of introducing a new family of orthogonal polynomial kernels based on gegenbauer polynomials and comparing it against other kernels experimental results reveal that the gegenbauer family competes with the rbf kernel in accuracy while requiring fewer support vectors and overcomes other classical and orthogonal kernels

reducing the number of support vectors of svm classifiers using the smoothed separable case approximation in this brief we propose a new method to reduce the number of support vectors of support vector machine svm classifiers we formulate the approximation of an svm solution as a classification problem that is separable in the feature space due to the separability the hard margin svm can be used to solve it this approach which we call the separable case approximation sca is very similar to the cross training algorithm explained in which is inspired by editing algorithms the norm of the weight vector achieved by sca can however become arbitrarily large for that reason we propose an algorithm called the smoothed sca ssca that additionally upper bounds the weight vector of the pruned solution and for the commonly used kernels reduces the number of support vectors even more the lower the chosen upper bound the larger this extra reduction becomes upper bounding the weight vector is important because it ensures numerical stability reduces the time to find the pruned solution and avoids overfitting during the approximation phase on the examined datasets ssca drastically reduces the number of support vectors

morse theory for lagrangian intersections soit p une variete symplectique compacte et soit l p une sous variete lagrangienne avec 2 p l 0 pour un diffeomorphisme exact de p avec la propriete que l coupe l transversalement on demontre une inegalite de morse reliant l ensemble l l a la cohomologie de l

improvements on cross validation the 632 bootstrap method abstract a training set of data has been used to construct a rule for predicting future responses what is the error rate of this rule this is an important question both for comparing models and for assessing a final selected model the traditional answer to this question is given by cross validation the cross validation estimate of prediction error is nearly unbiased but can be highly variable here we discuss bootstrap estimates of prediction error which can be thought of as smoothed versions of cross validation we show that a particular bootstrap method the 632 rule substantially outperforms cross validation in a catalog of 24 simulation experiments besides providing point estimates we also consider estimating the variability of an error rate estimate all of the results here are nonparametric and apply to any possible prediction rule however we study only classification problems with 0 1 loss in detail our simulations include smooth prediction rules like fisher s linear discriminant fun

hamiltonian stationary tori in the complex projective plane hamiltonian stationary lagrangian surfaces are lagrangian surfaces in a four dimensional kahler manifold which are critical points of the area functional for hamiltonian infinitesimal deformations in this paper we analyze these surfaces in the complex projective plane in a previous work we showed that they correspond locally to solutions to an integrable system formulated as a zero curvature on a twisted loop group here we give an alternative formulation using non twisted loop groups and as an application we show in detail why hamiltonian stationary lagrangian tori are finite type solutions and eventually describe the simplest of them the homogeneous ones

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

connections of berry and hannay type for moving lagrangian submanifolds abstract berry s phase is the holonomy of the natural connection on the canonical circle bundle over projectivized quantum hilbert space given a symplectic manifold p a classical limit of this phase is constructed as the holonomy of a berry connection over a finite codimensional isodrastic foliation defined by constancy of action integrals on the space of lagrangian submanifolds in p equipped with smooth densities of total measure 1 if the densities are determined by a kahler metric compatible with the symplectic structure the curvature of the berry connection at the lagrangian submanifold l is given by a simple formula involving curvature of l in particular the berry connection defines a homotopy invariant for isodrastic loops of minimal lagrangian submanifolds in a simply connected kahler manifold a similar invariant constructed by the author for loops of symplectomorphisms is also a special case of the classical berry phase a classical analogue of berry s phase was discovered by hannay for moving families of completely integrable systems following berry and hannay we interpret hannay s angles as the holonomy of a hannay connection on a bundle of tori over the isodrastic foliation on the space of lagrangian toral layers consisting of lagrangian tori with a flat affine structure and an extension of this structure to the first infinitesimal neighborhood finally we show that the hannay angles are the derivatives with respect to action variables of the classical berry phase

on stable compact minimal submanifolds of riemannian product manifolds abstract in this paper we prove a classification theorem for stable compact minimal submanifolds of a riemannian product of an m 1 dimensional m 1 3 hypersurface m 1 in euclidean space and any riemannian manifold m 2 when the sectional curvature k m 1 of m 1 satisfies 1 m 1 1 k m 1 1 in particular when the ambient space is an m dimensional m 3 compact hypersurface m in euclidean space if the sectional curvature k m of m satisfies 1 m 1 k m 1 then we conclude that there exist no stable compact minimal submanifolds in m

asymptotic efficiencies of truncated sequential tests truncation of a sequential test with constant boundaries is considered for the problem of testing a location hypothesis f x theta 0 versus f x theta 1 a test design procedure is developed by using bounds for the error probabilities under the hypothesis and alternative by viewing the truncated sequential test as a mixture of a sequential probability ratio test and a fixed sample size test its boundaries and truncation point can be obtained once the degree of mixture is specified asymptotically correct approximations for the operating characteristic function and the average sample number function of the resulting test are derived numerical results show that an appropriately designed truncated sequential test performs favorably as compared to both the fixed sample size test and the sequential probability ratio test with the same error probabilities the average sample number function of the truncated test is uniformly smaller than that of the fixed sample size test and the truncated test maintains average sample sizes under the hypothesis and the alternative that are close to those optimum values achieved by wald s sequential probability ratio test moreover the truncated test is more favorable than the sequential probability ratio test in the sense that is has smaller average sample size when the actual location parameter is between theta 0 and theta 1 this behavior becomes more pronounced as the error probabilities become smaller implying that the truncated sequential test becomes more favorable as the error probabilities become smaller

adaptive simplification of solution for support vector machine svm has been receiving increasing interest in areas ranging from its original application in pattern recognition to other applications such as regression estimation due to its remarkable generalization performance unfortunately svm is currently considerably slower in test phase caused by number of the support vectors which has been a serious limitation for some applications to overcome this problem we proposed an adaptive algorithm named feature vectors selection fvs to select the feature vectors from the support vector solutions which is based on the vector correlation principle and greedy algorithm through the adaptive algorithm the sparsity of solution is improved and the time cost in testing is reduced to select the number of the feature vectors adaptively by the requirements the generalization and complexity trade off can be directly controlled the computer simulations on regression estimation and pattern recognition show that fvs is a promising algorithm to simplify the solution for support vector machine

linear and non linear fuzzy regression evolutionary algorithm solutions given some data which consists of pairs of fuzzy numbers our evolutionary algorithm searches our library of fuzzy functions which includes linear polynomial exponential and logarithmic for a fuzzy function which best fits the data tests of our fuzzy regression package are given for each of the four cases linear polynomial exponential and logarithmic for the linear model we also consider multiple independent variables in all cases we use data generated with and without noise we prove that fuzzy polynomial regression can model the extension principle extension of continuous real valued functions

rapid and brief communiction possibilistic support vector machines we propose new support vector machines svms that incorporate the geometric distribution of an input data set by associating each data point with a possibilistic membership which measures the relative strength of the self class membership by using a possibilistic distance measure based on the possibilistic membership we reformulate conventional svms in three ways the proposed methods are shown to have better classification performance than conventional svms in various tests

a reduced support vector machine approach for interval regression analysis the support vector machine svm has been shown to be an efficient approach for a variety of classification problems it has also been widely used in pattern recognition regression and distribution estimation for separable data however there are two problems with using the svm model 1 large scale when dealing with large scale data sets the solution may be difficult to find when using svm with nonlinear kernels 2 unbalance the number of samples from one class is much larger than the number of samples from the other classes it causes the excursion of separation margin under these circumstances developing an efficient method is necessary recently the use of the reduced support vector machine rsvm was proposed as an alternative to the standard svm it has been proven more efficient than the traditional svm in processing large scaled data in this paper we introduce the principle of rsvm to evaluate interval regression analysis the main idea of the proposed method is to reduce the number of support vectors by randomly selecting a subset of samples

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

image reconstruction from continuous gaussian hermite moments implemented by discrete algorithm the problem of image reconstruction from its statistical moments is particularly interesting to researchers in the domain of image processing and pattern recognition compared to geometric moments the orthogonal moments offer the ability to recover much more easily the image due to their orthogonality which allows reducing greatly the complexity of computation in the phase of reconstruction since the 1980s various orthogonal moments such as legendre moments zernike moments and discrete tchebichef moments have been introduced early or late to image reconstruction in this paper another set of orthonormal moments the gaussian hermite moments based on hermite polynomials modulated by a gaussian envelope is proposed to be used for image reconstruction especially the paper s focus is on the determination of the optimal scale parameter and the improvement of the reconstruction result by a post processing which make gaussian hermite moments be useful and comparable with other moments for image reconstruction the algorithms for computing the values of the basis functions moment computation and image reconstruction are also given in the paper as well as a brief discussion on the computational complexity the experimental results and error analysis by comparison with other moments show a good performance of this new approach

bayesian classification with gaussian processes we consider the problem of assigning an input vector to one of m classes by predicting p c x for c 1 m for a two class problem the probability of class one given x is estimated by spl sigma y x where spl sigma y 1 1 e sup y a gaussian process prior is placed on y x and is combined with the training data to obtain predictions for new x points we provide a bayesian treatment integrating over uncertainty in y and in the parameters that control the gaussian process prior the necessary integration over y is carried out using laplace s approximation the method is generalized to multiclass problems m 2 using the softmax function we demonstrate the effectiveness of the method on a number of datasets

second variation of superminimal surfaces into self dual einstein four manifolds the index of a compact orientable superminimal surface of a selfdual einstein four manifold m with positive scalar curvature is computed in terms of its genus and area also a lower bound of its nullity is obtained applications to the cases m 4 and m cip2 are given characterizing the standard veronese immersions and their twistor deformations as those with lowest index

hamiltonian minimal submanifolds in complex hyperbolic space with so n symmetry in this paper we construct complete hamiltonian minimal submanifolds in complex hyperbolic space with so n symmetry which are not minimal in the usual sense

hamiltonian stationary lagrangian surfaces of constant curvature e in complex space form m2 4e abstract a lagrangian surface in a kaehler manifold is called hamiltonian stationary if it is a critical point of the area functional restricted to compactly supported hamiltonian variations in the first part of this article we study the traveling wave solutions of an over determined pde system arising from a study of hamiltonian stationary lagrangian surfaces of constant curvature e in a complex space form m 2 4 e then by applying the traveling wave solutions we construct families of type ii hamiltonian stationary lagrangian surfaces of constant curvature e in complex space forms m 2 4 e via an effective method of b y chen f dillen l verstraelen and l vrancken lagrangian isometric immersions of a real space form m n c into a complex space form m n 4 c math proc cambridge philo soc 124 1998 107 125 in the second part we are able to completely solve the over determined pde system for the case e 0 and to determine their corresponding hamiltonian stationary lagrangian surfaces as an immediate by product some interesting new families of hamiltonian stationary lagrangian surfaces of constant curvature are obtained

on the existence of hamiltonian stationary lagrangian submanifolds in symplectic manifolds let m omega be a compact symplectic 2n manifold and g a riemannian metric on m compatible with omega for instance g could be k ahler with k ahler form omega consider compact lagrangian submanifolds l of m we call l it hamiltonian stationary or it h minimal if it is a critical point of the volume functional mathop rm vol nolimits g under hamiltonian deformations computing mathop rm vol nolimits g l using g vert l it is called it hamiltonian stable if in addition the second variation of mathop rm vol nolimits g under hamiltonian deformations is nonnegative our main result is that if l is a compact hamiltonian stationary lagrangian in mathbin bbb c n which is it hamiltonian rigid then for any m omega g as above there exist compact hamiltonian stationary lagrangians l in m contained in a small ball about some p in m and locally modelled on t l for small t0 identifying m near p with mathbin bbb c n near 0 if l is hamiltonian stable we can take l to be hamiltonian stable applying this to known examples l in mathbin bbb c n shows that there exist families of hamiltonian stable hamiltonian stationary lagrangians diffeomorphic to t n and to cal s 1 times cal s n 1 mathbin bbb z 2 and with other topologies in every compact symplectic 2n manifold m omega with compatible metric g

robust fuzzy regression analysis in this paper we propose a robust fuzzy linear regression model based on the least median squares weighted least squares lms wls estimation procedure the proposed model is general enough to deal with data contaminated by outliers due to measurement errors or extracted from highly skewed or heavy tailed distributions we also define suitable goodness of fit indices useful to evaluate the performances of the proposed model the effectiveness of our model in reducing the outliers influence is shown by using applicative examples based both on simulated and real data and by a simulation study

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

optimal reduction of solutions for support vector machines being a universal learning machine a support vector machine svm suffers from expensive computational cost in the test phase due to the large number of support vectors and greatly impacts its practical use to address this problem we proposed an adaptive genetic algorithm to optimally reduce the solutions for an svm by selecting vectors from the trained support vector solutions such that the selected vectors best approximate the original discriminant function our method can be applied to svms using any general kernel the size of the reduced set can be used adaptively based on the requirement of the tasks as such the generalization complexity trade off can be controlled directly the lower bound of the number of selected vectors required to recover the original discriminant function can also be determined

multihypothesis sequential probability ratio tests ii accurate asymptotic expansions for the expected sample size for pt i see ibid vol 45 p 2448 61 1999 we proved in pt i that two specific constructions of multihypothesis sequential tests which we refer to as multihypothesis sequential probability ratio tests msprts are asymptotically optimal as the decision risks or error probabilities go to zero the msprts asymptotically minimize not only the expected sample size but also any positive moment of the stopping time distribution under very general statistical models for the observations in this paper based on nonlinear renewal theory we find accurate asymptotic approximations up to a vanishing term for the expected sample size that take into account the overshoot over the boundaries of decision statistics the approximations are derived for the scenario where the hypotheses are simple the observations are independent and identically distributed i i d according to one of the underlying distributions and the decision risks go to zero simulation results for practical examples show that these approximations are fairly accurate not only for large but also for moderate sample sizes the asymptotic results given here complete the analysis initiated by baum and veeravalli 1994 where first order asymptotics were obtained for the expected sample size under a specific restriction on the kullback leibler distances between the hypotheses

on the regularity of hamiltonian stationary lagrangian submanifolds abstract we prove a morrey type theorem for hamiltonian stationary lagrangian submanifolds of c n if a c 1 lagrangian submanifold is a critical point of the volume functional under hamiltonian variations then it must be real analytic locally a hamiltonian stationary lagrangian submanifold is determined geometrically by harmonicity of its lagrangian phase function or variationally by a nonlinear fourth order elliptic equation of the potential function whose gradient graph defines the hamiltonian stationary lagrangian submanifolds locally our result shows that morrey s theorem for minimal submanifolds admits a complete fourth order analogue we establish full regularity and removability of singular sets of capacity zero for weak solutions to the fourth order equation with c 1 1 norm below a dimensional constant and to c 1 1 potential functions under certain convexity conditions whose lagrangian phase functions are weakly harmonic

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

fuzzy regression methods a comparative assessment abstract the fundamental differences between fuzzy regression and ordinary regression are identified in this paper fuzzy regression can be used to fit fuzzy data and crisp data into a regression model whereas ordinary regression can only fit crisp data through a comprehensive literature review three approaches of fuzzy regression are summarized the first approach of fuzzy regression is based on minimizing fuzziness as an optimal criterion the second approach uses least squares of errors as a fitting criterion and two methods are summarized in this paper the third approach can be described as an interval regression analysis for each fuzzy regression method numerical examples and graphical presentations are used to evaluate their characteristic and differences with ordinary least squares regression based on the comparative assessment the fundamental differences between ordinary least squares regression and conventional fuzzy regression are concluded that is ordinary least squares regression modeling data with randomness type of uncertainty and conventional fuzzy regression modeling data with fuzziness type of uncertainty in order to integrate both randomness and fuzziness types of uncertainty into one regression model the concept of hybrid fuzzy least squares regression analysis is proposed in this paper and the details of its method are derived in the accompanying paper

metric and isoperimetric problems in symplectic geometry introduction 411 1 some basic results in symplectic topology 413 2 capacity and symplectic reduction 414 3 volume estimates for lagrange submanifolds 416 3 1 the case of r 417 3 2 deformations of the zero section in cotangent bundles 419 3 3 generalization to the case of cp 422 4 an application to billiards 423 5 geometry of convex sets and periodic orbits 425 6 compensated compactness and closure of the symplectic group 426 appendix a a summary of symplectic geometry through generating functions 427 appendix b john s ellipsoid 428 references 430

a set of new chebyshev kernel functions for support vector machine pattern classification in this study we introduce a set of new kernel functions derived from the generalized chebyshev polynomials the proposed generalized chebyshev polynomials allow us to derive different kernel functions by using these polynomial functions we generalize recently introduced chebyshev kernel function for vector inputs and as a result we obtain a robust set of kernel functions for support vector machine svm classification thus in this study besides clarifying how to apply the chebyshev kernel functions on vector inputs we also increase the generalization capability of the previously proposed chebyshev kernels and show how to derive new kernel functions by using the generalized chebyshev polynomials the proposed set of kernel functions provides competitive performance when compared to all other common kernel functions on average for the simulation datasets the results indicate that they can be used as a good alternative to other common kernel functions for svm classification in order to obtain better accuracy moreover test results show that the generalized chebyshev kernel approaches to the minimum support vector number for classification in general

exact simplification of support vector solutions this paper demonstrates that standard algorithms for training support vector machines generally produce solutions with a greater number of support vectors than are strictly necessary an algorithm is presented that allows unnecessary support vectors to be recognized and eliminated while leaving the solution otherwise unchanged the algorithm is applied to a variety of benchmark data sets for both classification and regression and in most cases the procedure leads to a reduction in the number of support vectors in some cases the reduction is substantial

legendre polynomials based feature extraction for online signature verification consistency analysis of feature combinations in this paper feature combinations associated with the most commonly used time functions related to the signing process are analyzed in order to provide some insight on their actual discriminative power for online signature verification a consistency factor is defined to quantify the discriminative power of these different feature combinations a fixed length representation of the time functions associated with the signatures based on legendre polynomials series expansions is proposed the expansion coefficients in these series are used as features to model the signatures two different signature styles namely western and chinese from a publicly available signature database are considered to evaluate the performance of the verification system two state of the art classifiers namely support vector machines and random forests are used in the verification experiments error rates comparable to the ones reported over the same signature datasets in a recent signature verification competition show the potential of the proposed approach the experimental results also show that there is a good correlation between the consistency factor and the verification errors suggesting that consistency values could be used to select the optimal feature combination highlightsa feature extraction approach based on legendre series representation of the time functions associated with the signatures is proposed a consistency factor is proposed to quantify the discriminative power of different combinations of the time functions the correlation between the proposed consistency factor and the verification performance of a feature combination is analyzed a recent signature database containing western and chinese signatures is used the verification performance is quantified based on log likelihood ratios

fuzzy phoneme recognition abstract first a scheme for pattern recognition is given in a learning step a relation between acoustic characteristics and the corresponding phoneme is computed using an inference rule next the phonemes are recognised as result of a fuzzy relation equation then the recognition quality is analysed by means of uncertainty measures specially sugeno s and possibility measures

spin c geometry of kahler manifolds and the hodge laplacian on minimal lagrangian submanifolds from the existence of parallel spinor fields on calabi yau hyper kahler or complex flat manifolds we deduce the existence of harmonic differential forms of different degrees on their minimal lagrangian submanifolds in particular when the submanifolds are compact we obtain sharp estimates on their betti numbers which generalize those obtained by smoczyk in 49 when the ambient manifold is kahler einstein with positive scalar curvature and especially if it is a complex contact manifold or the complex projective space we prove the existence of kahlerian killing spinor fields for some particular spin c structures using these fields we construct eigenforms for the hodge laplacian on certain minimal lagrangian submanifolds and give some estimates for their spectra these results also generalize some theorems by smoczyk in 50 finally applications on the morse index of minimal lagrangian submanifolds are obtained

the geometric complexity of special lagrangian t2 cones we prove a number of results on the geometric complexity of special lagrangian slg t2 cones in 3 every slg t2 cone has a fundamental integer invariant its spectral curve genus we prove that the spectral curve genus of an slg t2 cone gives a lower bound for its geometric complexity i e the area the stability index and the legendrian index of any slg t2 cone are all bounded below by explicit linearly growing functions of the spectral curve genus we prove that the cone on the clifford torus which has spectral curve genus zero in s5 is the unique slg t2 cone with the smallest possible legendrian index and hence that it is the unique stable slg t2 cone this leads to a classification of all rigid index 1 slg cone types in dimension three for cones with spectral curve genus two we give refined lower bounds for the area the legendrian index and the stability index one consequence of these bounds is that there exist s1 invariant slg torus cones of arbitrarily large area legendrian and stability indices we explain some consequences of our results for the programme due to joyce to understand the most common three dimensional isolated singularities of generic families of slg submanifolds in almost calabi yau manifolds

self shrinkers for the mean curvature flow in arbitrary codimension in this paper we generalize colding minicozzi s recent results about codimension 1 self shrinkers for the mean curvature flow to higher codimension in particular we prove that the sphere bf s n sqrt 2n is the only complete embedded connected f stable self shrinker in mathbf r n k with mathbf h ne 0 polynomial volume growth flat normal bundle and bounded geometry we also discuss some properties of symplectic self shrinkers proving that any complete symplectic self shrinker in mathbf r 4 with polynomial volume growth and bounded second fundamental form is a plane as a corollary we show that there is no finite time type i singularity for symplectic mean curvature flow which has been proved by chen li using different method we also study lagrangian self shrinkers and prove that for lagrangian mean curvature flow the blow up limit of the singularity may be not f stable

classification of hamiltonian stationary lagrangian submanifolds of constant curvature in cp3 with positive relative nullity abstract a lagrangian submanifold in a kaehler manifold is said to be hamiltonian stationary if it is a critical point of the area functional restricted to compactly supported hamiltonian variations in this paper we classify hamiltonian stationary lagrangian submanifolds of constant curvature in cp 3 with positive relative nullity as an immediate by product several explicit new families of hamiltonian stationary lagrangian submanifolds in cp 3 are obtained

stratified symplectic spaces and reduction let m w be a hamiltonian g space with proper momentum map j m g it is well known that if zero is a regular value of j and g acts freely on the level set j 0 then the reduced space mo j 0 g is a symplectic manifold we show that if the regularity assumptions are dropped the space mo is a union of symplectic manifolds i e it is a stratified symplectic space arms et al 2 proved that mo possesses a natural poisson bracket using their result we study hamiltonian dynamics on the reduced space in particular we show that hamiltonian flows are strata preserving and give a recipe for lifting a reduced hamiltonian flow to the level set j 0 finally we give a detailed description of the stratification of mo and prove the existence of a connected

sequential detection of almost harmonic signals to detect a purely harmonic signal it is difficult to beat a fast fourier transform fft however when the signal is very long and weak parker and white 1999 have shown that a sequential probability ratio test sprt operating on magnitude square fft data is far more efficient indeed both from a numerical error perspective and in terms of robustness against a deviation from a precisely tonal signal the block fft sprt idea is very appealing here the approach is extended to the case that the frequency is unknown and expressions are developed for performance both in terms of detection and of sample number the approach is applicable to a large number of practical problems but particular attention is paid to the continuous gravitational wave gw example the computational savings as compared with a fixed test vary as a function of signal strength block length bandwidth and operating point however gains of a factor of two are easy that these gains are not more exciting relates mostly to the underlying fft structure although many sprts end early it is difficult to take advantage of that with an efficient fft algorithm however the progressive reduction of the number of working sprts implies a substantial reduction of the ensemble of the candidate frequencies with time which is an appealing feature particularly in the gw case

multihypothesis sequential probability ratio tests i asymptotic optimality the problem of sequential testing of multiple hypotheses is considered and two candidate sequential test procedures are studied both tests are multihypothesis versions of the binary sequential probability ratio test sprt and are referred to as msprts the first test is motivated by bayesian optimality arguments while the second corresponds to a generalized likelihood ratio test it is shown that both msprts are asymptotically optimal relative not only to the expected sample size but also to any positive moment of the stopping time distribution when the error probabilities or more generally risks associated with incorrect decisions are small the results are first derived for the discrete time case of independent and identically distributed i i d observations and simple hypotheses they are then extended to general possibly continuous time statistical models that may include correlated and nonhomogeneous observation processes it also demonstrated that the results can be extended to hypothesis testing problems with nuisance parameters where the composite hypotheses due to nuisance parameters can be reduced to simple ones by using the principle of invariance these results provide a complete generalization of the results given by veeravalli and baum see ibid vol 41 p 1994 97 1995 where it was shown that the quasi bayesian msprt is asymptotically efficient with respect to the expected sample size for i i d observations

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

learning the kernel matrix with semidefinite programming kernel based learning algorithms work by embedding the data into a euclidean space and then searching for linear relations among the embedded data points the embedding is performed implicitly by specifying the inner products between each pair of points in the embedding space this information is contained in the so called kernel matrix a symmetric and positive semidefinite matrix that encodes the relative positions of all points specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space classical model selection problems in machine learning in this paper we show how the kernel matrix can be learned from data via semidefinite programming sdp techniques when applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm using the labeled part of the data one can learn an embedding also for the unlabeled part the similarity between test points is inferred from training points and their labels importantly these learning problems are convex so we obtain a method for learning both the model class and the function without local minima furthermore this approach leads directly to a convex method for learning the 2 norm soft margin parameter in support vector machines solving an important open problem

multi variable regression methods using modified chebyshev polynomials of class 2 abstract so far many regression works have been implemented by using linear regression methods although more accurate predictions results could be obtained polynomial regression is not used as much as compared to linear regression in real applications due to occurrence of coefficient explosion to overcome this problem two regression algorithms using chebyshev polynomials of class 2 based on cascade regression and feature selection are proposed in this paper in the experimental part three separate experiments including function interpolation and real case regression were conducted on three datasets to test the proposed algorithms as shown by the experimental results the proposed algorithms performed better than other regression methods in terms of both accuracy and processing time

hamiltonian minimal lagrangian submanifolds in kaehler manifolds with symmetries abstract by making use of the symplectic reduction and the cohomogeneity method we give a general method for constructing hamiltonian minimal lagrangian submanifolds in kaehler manifolds with symmetries as applications we construct infinitely many nontrivial complete hamiltonian minimal lagrangian submanifolds in c p n and c n