rigidity and tolerance in point processes gaussian zeros and ginibre eigenvalues let be a translation invariant point process on the complex plane c and let d c be a bounded open set we ask the following what does the point configuration out obtained by taking the points of outside d tell us about the point configuration in of inside d we show that for the ginibre ensemble out determines the number of points in in for the translation invariant zero process of a planar gaussian analytic function we show that out determines the number as well as the center of mass of the points in in further in both models we prove that the outside says nothing more about the inside in the sense that the conditional distribution of the inside points given the outside is mutually absolutely continuous with respect to the lebesgue measure on its supporting submanifold

pairwise sparsity preserving embedding for unsupervised subspace learning and classification two novel unsupervised dimensionality reduction techniques termed sparse distance preserving embedding sdpe and sparse proximity preserving embedding sppe are proposed for feature extraction and classification sdpe and sppe perform in the clean data space recovered by sparse representation and enhanced euclidean distances over noise removed data are employed to measure pairwise similarities of points in extracting informative features sdpe and sppe aim at preserving pairwise similarities between data points in addition to preserving the sparse characteristics this paper calculates the sparsest representation of all vectors jointly by a convex optimization the sparsest codes enable certain local information of data to be preserved and can endow sdpe and sppe a natural discriminating power adaptive neighborhood and robust characteristic against noise and errors in delivering low dimensional embeddings we also mathematically show sdpe and sppe can be effectively extended for discriminant learning in a supervised manner the validity of sdpe and sppe is examined by extensive simulations comparison with other related state of the art unsupervised algorithms show that promising results are delivered by our techniques

least squares twin bounded support vector machines based on l1 norm distance metric for classification abstract in this paper we construct a least squares version of the recently proposed twin bounded support vector machine tbsvm for binary classification as a valid classification tool tbsvm attempts to seek two non parallel planes that can be produced by solving a pair of quadratic programming problems qpps but this is time consuming here we solve two systems of linear equations rather than two qpps to avoid this deficiency furthermore the distance in least squares tbsvm lstbsvm is measured by l2 norm but l1 norm distance is usually regarded as an alternative to l2 norm to improve model robustness in the presence of outliers inspired by the advantages of least squares twin support vector machine lstwsvm tbsvm and l1 norm distance we propose a lstbsvm based on l1 norm distance metric for binary classification termed as l1 lstbsvm which is specially designed for suppressing the negative effect of outliers and improving computational efficiency in large datasets then we design a powerful iterative algorithm to solve the l1 norm optimal problems and it is easy to implement and its convergence to an optimum solution is theoretically ensured finally the feasibility and effectiveness of l1 lstbsvm are validated by extensive experimental results on both uci datasets and artificial datasets

new method for deriving nonlinear integrable systems a new approach is proposed to derive nonlinear integrable systems it is used to obtain several new nonlinear integrable systems the above results are relevant to some problems of hydrodynamics plasma physics solid state physics etc

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

fuzzy regularized generalized eigenvalue classifier with a novel membership function supervised classification of data affected by noise or error with unknown probability distribution is a challenging task to this extend we propose the fuzzy regularized eigenvalue classifier based on a recent technique to classify data in two or more classes we compare the execution time and accuracy of the classifier with other de facto standard methods with the adoption of a novel membership function the classifier is capable to produce more accurate models that well compare with results obtained by other methods and fuzzy weighting functions on benchmark datasets

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

integration of the soliton hierarchy with self consistent sources in contrast with the soliton equations the evolution of the eigenfunctions in the lax representation of soliton equation with self consistent sources sescs possesses singularity we present a general method to treat the singularity to determine the evolution of scattering data the akns hierarchy with self consistent sources the mkdv hierarchy with self consistent sources the nonlinear schrodinger equation hierarchy with self consistent sources the kaup newell hierarchy with self consistent sources and the derivative nonlinear schrodinger equation hierarchy with self consistent sources are integrated directly by using the inverse scattering method the n soliton solutions for some sescs are presented it is shown that the insertion of a source may cause the variation of the velocity of soliton this approach can be applied to all other 1 1 dimensional soliton hierarchies

nonparallel hyperplane support vector machine for binary classification problems in this paper we propose a nonparallel hyperplane support vector machine nhsvm for binary classification problems our proposed nhsvm is formulated by clustering the training points according to the similarity between classes it constructs two nonparallel hyperplanes simultaneously by solving a single quadratic programming problem and is consistent between its predicting and training processes an essential difference that distinguishes it from other nonparallel svms this proposed nhsvm has been analyzed theoretically and implemented experimentally the results of experiments conducted using it on both artificial and publicly available benchmark datasets confirm its feasibility and efficacy especially for cross planes datasets and datasets with heteroscedastic noise

an integrable couplings of g wki equations hierarchy with self consistent sources we present a kind of integrable couplings of soliton equations hierarchy with self consistent sources by using the loop algebra sl 4 as an application a new integrable couplings of the generalized wadati konono ichikawa g wki equations hierarchy with self consistent sources is derived through the enlarged loop algebra sl 4

twin support vector machine for clustering the twin support vector machine twsvm is one of the powerful classification methods in this brief a twsvm type clustering method called twin support vector clustering twsvc is proposed our twsvc includes both linear and nonlinear versions it determines k cluster center planes by solving a series of quadratic programming problems to make twsvc more efficient and stable an initialization algorithm based on the nearest neighbor graph is also suggested the experimental results on several benchmark data sets have shown a comparable performance of our twsvc

capture and confinement of solitons in nonlinear integrable systems the system describing the interaction of a long wave with a short wave packet on thex y plane is considered the solutions are found to describe a soliton that comes from infinity and then is captured into a conditionally periodical oscillatory regime the solutions are also found that describe a soliton coming from infinity and then decaying into two solitons one goes to infinity and the other is captured into a conditionally periodical oscillatory regime the obtained results are relevant to some problems of hydrodynamics plasma physics solid state physics etc

structural regularized projection twin support vector machine for data classification abstract projection twin support vector machine ptsvm seeks two projection directions for two classes by solving two smaller sized quadratic programming problems qpps such that the projected samples of one class are well separated from those of the other one in its respective subspace however it only simply considers the prior class based structural information in the optimization problems in this paper a structural regularized ptsvm srptsvm classifier for binary classification is presented this proposed srptsvm focuses on the cluster based structural information of the corresponding class in each optimization problem which is vital for designing a good classifier in different real world problems this srptsvm is extended to a nonlinear version by the kernel trick experimental results demonstrate that srptsvm is superior in generalization performance to other classifiers

twin support vector machines for pattern classification we propose twin svm a binary svm classifier that determines two nonparallel planes by solving two related svm type problems each of which is smaller than in a conventional svm the twin svm formulation is in the spirit of proximal svms via generalized eigenvalues on several benchmark data sets twin svm is not only fast but shows good generalization twin svm is also useful for automatically discovering two dimensional projections of the data

l1 norm loss based twin support vector machine for data recognition this paper proposes a novel l1 norm loss based twin support vector machine l1ltsvm classifier for binary recognition in this l1ltsvm each optimization problem simultaneously minimizes the l1 norm based losses for the two classes of points which results in a different dual problem compared with twin support vector machine twsvm compared with twsvm the main advantages of this l1ltsvm classifier are first the dual problems of l1ltsvm do not need to inverse the kernel matrices during the learning process indicating l1ltsvm not only has a partly sparse decision function but also can be solved efficiently by some svm type learning algorithms and then is suitable for large scale problems second this l1ltsvm has more perfect and practical geometric interpretation experimental results on several synthetic as well as benchmark datasets indicate the significant advantage of l1ltsvm in the generalization performance

distribution of roots of random polynomials we consider polynomials of high degree with random coefficients which appear in the context of quantum chaotic dynamics and investigate various conditions under which their roots tend to concentrate near the unit circle in the complex plane correlation functions of roots are computed analytically we also investigate a certain class of random polynomials whose roots cover in a uniform way the riemann sphere special emphasis is devoted to the influence of symmmetries

a ga based model selection for smooth twin parametric margin support vector machine the recently proposed twin parametric margin support vector machine denoted by tpmsvm gains good generalization and is suitable for many noise cases however in the tpmsvm it solves two dual quadratic programming problems qpps moreover compared with support vector machine svm tpmsvm has at least four regularization parameters that need regulating which affects its practical applications in this paper we increase the efficiency of tpmsvm from two aspects first by introducing a quadratic function we directly optimize a pair of qpps of tpmsvm in the primal space called stpmsvm for short compared with solving two dual qpps in the tpmsvm stpmsvm can obviously improve the training speed without loss of generalization second a genetic algorithm ga based model selection for stpmsvm in the primal space is suggested the ga based stpmsvm can not only select the parameters efficiently but also provide discriminative feature selection computational results on several synthetic as well as benchmark datasets confirm the great improvements on the training process of our ga based stpmsvm

nonlinear knowledge in kernel approximation prior knowledge over arbitrary general sets is incorporated into nonlinear kernel approximation problems in the form of linear constraints in a linear program the key tool in this incorporation is a theorem of the alternative for convex functions that converts nonlinear prior knowledge implications into linear inequalities without the need to kernelize these implications effectiveness of the proposed formulation is demonstrated on two synthetic examples and an important lymph node metastasis prediction problem all these problems exhibit marked improvements upon the introduction of prior knowledge over nonlinear kernel approximation approaches that do not utilize such knowledge

some types of solutions and generalized binary darboux transformation for the mkp equation with self consistent sources in this paper an mkp equation with self consistent sources mkpescss is structured in the framework of the constrained mkp equation based on the conjugate lax pairs we construct the generalized binary darboux transformation and the n times repeated darboux transformation with arbitrary functions at time t for the mkpescss which offers a non auto backlund transformation between two mkpescss with different degrees of sources with the help of these transformations some new solutions for the mkpescss such as soliton solutions rational solutions breather type solutions and exponential solutions are found by taking the special initial solution for auxiliary linear problems and the special functions of t time

improvements on twin support vector machines for classification problems the generalized eigenvalue proximal support vector machine gepsvm and twin support vector machine twsvm are regarded as milestones in the development of the powerful svms as they use the nonparallel hyperplane classifiers in this brief we propose an improved version named twin bounded support vector machines tbsvm based on twsvm the significant advantage of our tbsvm over twsvm is that the structural risk minimization principle is implemented by introducing the regularization term this embodies the marrow of statistical learning theory so this modification can improve the performance of classification in addition the successive overrelaxation technique is used to solve the optimization problems to speed up the training procedure experimental results show the effectiveness of our method in both computation time and classification accuracy and therefore confirm the above conclusion further

bi hamiltonian structure of jm hierarchy with self consistent sources by taking the space variable x as the evolution parameter and introducing the jacobi ostrogradiski coordinates we present t type hamiltonian description of soliton equations with self consistent sources which have not x type hamiltonian formulation when considering t as evolution parameter the t type miura map generates the second hamiltonian structure for these t type hamiltonian systems the two compatible hamiltonian operators are used to construct a hereditary operator and to obtain new hierarchies of infinite dimensional integrable hamiltonian systems the reduction of these equations with sources gives rise to the constrained flows of soliton equations and their bi hamiltonian structure we use the jaulent miodek hierarchy with self consistent sources to illustrate the method c 1999 elsevier science b v all rights reserved

spectral transform and solitons for generalized coupled bloch systems the spectral transform and backlund transformation for a generalization of the coupled bloch system arising in nonlinear optics are studied the equation is related to a singular dispersion relation and is treated as a representative example of a general method for studying such equations the spectral transform is developed through the formalism the backlund transformation is derived in a very general way and solved to obtain the one soliton and breatherlike solutions the nonlinear superposition formula is also constructed

tpmsvm a novel twin parametric margin support vector machine for pattern recognition a novel twin parametric margin support vector machine tpmsvm for classification is proposed in this paper this tpmsvm in the spirit of the twin support vector machine twsvm determines indirectly the separating hyperplane through a pair of nonparallel parametric margin hyperplanes solved by two smaller sized support vector machine svm type problems similar to the parametric margin email protected support vector machine email protected svm this tpmsvm is suitable for many cases especially when the data has heteroscedastic error structure that is the noise strongly depends on the input value but there is an advantage in the learning speed compared with the email protected svm the experimental results on several artificial and benchmark datasets indicate that the tpmsvm not only obtains fast learning speed but also shows good generalization

solution of an initial boundary value problem for coupled nonlinear waves the authors derive and study a hierarchy of nonlinear coupled evolution equations among which is the coupled korteveg de vries schrodinger equation for which they prove that a mixed initial boundary value problem is solvable they give the method of solution together with the backlund transformation and establish the infinite set of conserved densities they finally discuss the applicability of such equations in plasma physics and hydrodynamics

backlund transformations for the kp and mkp hierarchies with self consistent sources using gauge transformations for the corresponding generating pseudo differential operators ln in terms of eigenfunctions and adjoint eigenfunctions we construct several types of auto backlund transformations for the kp hierarchy with self consistent sources kphscs and mkp hierarchy with self consistent sources mkphscs respectively the backlund transformations from kphscs to mkphscs are also constructed in this way

a nonparallel support vector machine for a classification problem with universum learning universum samples defined as samples not belonging to any class for a classification problem of interest have been useful in supervised learning here we design a new nonparallel support vector machine u nsvm that can exploit prior knowledge embedded in the universum to construct a more robust classifier for training to this end u nsvm maximizes the two margins associated with the two closest neighboring classes which is combined by two nonparallel hyperplanes therefore u nsvm has better flexibility and can yield a more reasonable classifier in most cases in addition our method includes fewer parameters than u svm so is easier to implement experiments demonstrate that u nsvm outperforms the traditional svm and u svm

a twin hyperspheres support vector machine with automatic variable weights for data classification abstract this paper proposes a novel twin hyperspheres support vector machine thsvm classifier for binary classification called the automatic variable weighted thsvm vthsvm classifier by solving a single optimization problem this classifier not only finds a pair of hyperspheres for classification but also automatically constructs a weight vector for each class in order to describe the dissimilarity of different classes this vthsvm is extended to the kernel case by the fact that a kernel can be written as a sum of one s evaluated on each variable separately the main advantage of this method is that it allows the use of adaptive distance which is suitable to find an as compact as possible hypersphere for each class experiments with synthetic and benchmark datasets indicate vthsvm obtains better performance than some other classifiers

finding the samples near the decision plane for support vector learning abstract the decision plane of support vector machine svm is decided by a few support vectors svs in the training set if there exist overlapping regions among different classes svs mainly locate in the overlap regions a number of approaches have been proposed to find the samples in overlapping regions to condense the training set however the performance of these approaches would degrade if there is no overlapping region in the training set in this paper the extended nearest neighbor chain is proposed to find samples near the decision plane to avoid degrading performance in the cases of no overlapping region between different classes experimental results demonstrate that the proposed method performs better than the previous ones on artificial synthetic datasets as well as benchmark datasets additionally the proposed method can obtain a higher compression ratio than previous ones

some new integrable systems constructed from the bi hamiltonian systems with pure differential hamiltonian operators abstract when both hamiltonian operators of a bi hamiltonian system are pure differential operators we show that the generalized kupershmidt deformation gkd developed from the kupershmidt deformation in 10 offers an useful way to construct new integrable system starting from the bi hamiltonian system we construct some new integrable systems by means of the generalized kupershmidt deformation in the cases of harry dym hierarchy classical boussinesq hierarchy and coupled kdv hierarchy we show that the gkd of harry dym equation gkd of classical boussinesq equation and gkd of coupled kdv equation are equivalent to the new integrable rosochatius deformations of these soliton equations with self consistent sources we present the lax pair for these new systems therefore the generalized kupershmidt deformation provides a new way to construct new integrable systems from bi hamiltonian systems and also offers a new approach to obtain the rosochatius deformation of soliton equation with self consistent sources

building sparse twin support vector machine classifiers in primal space abstract twin support vector machines tsvm obtain faster training speeds than classical support vector machines svm however tsvm augmented vectors lose sparsity in this paper a rapid sparse twin support vector machine stsvm classifier in primal space is proposed to improve the sparsity and robustness of tsvm based on a simple back fitting strategy the stsvm iteratively builds each nonparallel hyperplanes by adding one support vector sv from the corresponding class at one time this process is terminated using an adaptive and stable stopping criterion stsvm learning is implemented by linear equation computing systems through introducing a quadratic function to approximate the empirical risk the computational results on several synthetic and benchmark datasets indicate that the stsvm obtains a sparse separating hyperplane at a low cost without sacrificing its generalization performance

exact statistical properties of the zeros of complex random polynomials the zeros of complex gaussian random polynomials with coefficients such that the density in the underlying complex space is uniform are known to have the same statistical properties as the zeros of the coherent state representation of one dimensional chaotic quantum systems we extend the interpretation of these polynomials by showing that they also arise as the wavefunction for a quantum particle in a magnetic field constructed from a random superposition of states in the lowest landau level a study of the statistical properties of the zeros is undertaken using exact formulae for the one and two point distribution functions attention is focused on the moments of the two point correlation in the bulk the variance of a linear statistic and the asymptotic form of the two point correlation at the boundary a comparison is made with the same quantities for the eigenvalues of complex gaussian random matrices

recursive concave convex fisher linear discriminant with applications to face handwritten digit and terrain recognition in classification previous studies have shown that an eigenvalue based technique can be cast as an related svm type problem and that by solving this svm type problem the performance can be improved significantly in this paper we develop a recursive concave convex fisher linear discriminant dr rpfld for dimension reduction technique of high dimensional data to extract as many meaningful features as possible which incorporates the fundamental idea behind fisher linear discriminant and casts the fisher linear discriminant as a concave convex programming problem based on the hinge loss the solution of our method follows from solving the related svm type optimization problems iteratively which means the proposed method can be viewed as the combination of multiple related svm type problems the special formulation of our method provides convenience for constructing sparse multi class fisher linear discriminant directly due to use of a recursive procedure the number of features available from rpfld is independent of the number of classes meaning that in contrast to the original fisher linear discriminant the number of features available from our method has no upper bound we evaluate our algorithm on the yale and orl face image databases handwritten digit database and terrain image dataset experimental results show that rpfld outperforms other fisher linear discriminant algorithms

active set support vector regression this paper presents active set support vector regression asvr a new active set strategy to solve a straightforward reformulation of the standard support vector regression problem this new algorithm is based on the successful asvm algorithm for classification problems and consists of solving a finite number of linear equations with a typically large dimensionality equal to the number of points to be approximated however by making use of the sherman morrison woodbury formula a much smaller matrix of the order of the original input space is inverted at each step the algorithm requires no specialized quadratic or linear programming code but merely a linear equation solver which is publicly available asvr is extremely fast produces comparable generalization error to other popular algorithms and is available on the web for download

the deduction of the lax representation for constrained flows from the adjoint representation for x and tn finite dimensional hamiltonian systems obtained from the decompositions of zero curvature equations it is shown that their lax representations can be deduced directly from the adjoint representations of the auxiliary linear problems as a consequence the zero curvature representation for soliton hierarchy with source is presented

the periodic solutions of the discrete modified kdv equation with a self consistent source abstract this work is devoted to the application of inverse spectral problem for integration of the periodic solutions of the discrete modified kdv equation with a self consistent source the effective method of solution of the inverse spectral problem for the discrete linear ablowitz ladik equation is presented

on the general variable coefficient kp equation with self consistent sources a new general variable coefficient kp equation with self consistent sources and its grammian solutions is obtained by using the source generation procedure moreover by applying the pfaffianization procedure a new coupled variable coefficient kp equation is constructed its wronski type pfaffian solution and gramm type pfaffian solution are given at last a new integrable system of the general variable coefficient kp equation with self consistent sources is established

robust neighborhood preserving projection by nuclear l2 1 norm regularization for image feature extraction we propose two nuclear and l2 1 norm regularized 2d neighborhood preserving projection 2dnpp methods for extracting representative 2d image features 2dnpp extracts neighborhood preserving features by minimizing a frobenius norm based reconstruction error that is very sensitive noise and outliers in given data to make the distance metric more reliable and robust and encode the neighborhood reconstruction error more accurately we minimize the nuclear and l2 1 norm based reconstruction error respectively and measure it over each image technically we propose two enhanced variants of 2dnpp nuclear norm based 2dnpp and sparse reconstruction based 2dnpp besides to optimize the projection for more promising feature extraction we also add the nuclear and sparse l2 1 norm constraints on it accordingly where l2 1 norm ensures the projection to be sparse in rows so that discriminative features are learnt in the latent subspace and the nuclear norm ensures the low rank property of features by projecting data into their respective subspaces by fully considering the neighborhood preserving power using more reliable and robust distance metric and imposing the low rank or sparse constraints on projections at the same time our methods can outperform related state of the arts in a variety of simulation settings

a generalized information criterion for generalized minor component extraction generalized minor component analysis gmca is an essential technique in data classification and signal processing in this paper we propose an information criterion for gmca and derive a fast gmca algorithm for extracting the first generalized minor component gmc by using quasi newton method to this information criterion in order to extract multiple gmcs through the weighed matrix method this information criterion is extended into a weighted one which has a unique global maximum attained if and only if its state matrices converge to the gmcs of the matrix pencil composed of the autocorrelation matrices of two stochastic processes a gradient algorithm is also derived based on this weighted information criterion theoretical analysis shows that the gradient algorithm has self stabilizing property and does not need the normalization operation required in other algorithms the global convergence analysis of the proposed algorithm is accomplished through the lyapunov method numerical simulations and real application are carried out to further demonstrate the accuracy and speed advantages of the proposed algorithms

a ν twin support vector machine ν tsvm classifier and its geometric algorithms in this paper a n twin support vector machine n tsvm is presented improving upon the recently proposed twin support vector machine tsvm this n tsvm introduces a pair of parameters n to control the bounds of the fractions of the support vectors and the error margins the theoretical analysis shows that this n tsvm can be interpreted as a pair of minimum generalized mahalanobis norm problems on two reduced convex hulls rchs based on the well known gilbert s algorithm a geometric algorithm for tsvm ga tsvm and its probabilistic speed up version named pga tsvm are presented computational results on several synthetic as well as benchmark datasets demonstrate the significant advantages of the proposed algorithms in terms of both computation complexity and classification accuracy

density and uniqueness in percolation two results on site percolation on thed dimensional lattice d 1 arbitrary are presented in the first theorem we show that for stationary underlying probability measures each infinite cluster has a well defined density with probability one the second theorem states that if in addition the probability measure satisfies the finite energy condition of newman and schulman then there can be at most one infinite cluster with probability one the simple arguments extend to a broad class of finite dimensional models including bond percolation and regular lattices

continuum percolation for gaussian zeroes and ginibre eigenvalues we study continuum percolation on certain negatively dependent point processes on r 2 specifically we study the ginibre ensemble and the planar gaussian zero process which are the two main natural models of translation invariant point processes on the plane exhibiting local repulsion for the ginibre ensemble we establish the uniqueness of infinite cluster in the supercritical phase for the gaussian zero process we establish that a non trivial critical radius exists and we prove the uniqueness of infinite cluster in the supercritical regime

squared eigenfunctions for the sasa satsuma equation squared eigenfunctions are quadratic combinations of jost functions and adjoint jost functions which satisfy the linearized equation of an integrable equation they are needed for various studies related to integrable equations such as the development of its soliton perturbation theory in this article squared eigenfunctions are derived for the sasa satsuma equation whose spectral operator is a 3 3 system while its linearized operator is a 2 2 system it is shown that these squared eigenfunctions are sums of two terms where each term is a product of a jost function and an adjoint jost function the procedure of this derivation consists of two steps first is to calculate the variations of the potentials via variations of the scattering data by the riemann hilbert method the second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations while this procedure has been used before on other integrable equations it is shown here for

on the two dimensional leznov lattice equation with self consistent sources a two dimensional leznov lattice equation with self consistent sources leznovescs is presented through the source generation procedure starting from the casoratian determinant solution of the two dimensional leznov lattice equation as a result the casoratian determinant solution of the leznovescs is obtained besides we also give the grammian determinant solution of the coupled system in addition the bilinear backlund transformation bt for the leznovescs is given

on the pfaffianized kp equation with self consistent sources abstract a new procedure called source generation is applied to the pfaffianized kp equation as a result the pfaffianized kp equation with self consistent sources escs is obtained this coupled system cannot only be reduced to the pfaffianized kp equation but also reduced to the kp equation with self consistent sources kpescs so the pfaffianized kp escs can be viewed as a pfaffian version of the kpescs which indicates the commutativity of the source generation procedure and pfaffianization

pair v svr a novel and efficient pairing nu support vector regression algorithm this paper proposes a novel and efficient pairing nu support vector regression pair v svr algorithm that combines successfully the superior advantages of twin support vector regression tsvr and classical varepsilon svr algorithms in spirit of tsvr the proposed pair v svr solves two quadratic programming problems qpps of smaller size rather than a single larger qpp and thus has faster learning speed than classical varepsilon svr the significant advantage of our pair v svr over tsvr is the improvement in the prediction speed and generalization ability by introducing the concepts of the insensitive zone and the regularization term that embodies the essence of statistical learning theory moreover pair v svr has additional advantage of using parameter v for controlling the bounds on fractions of svs and errors furthermore the upper bound and lower bound functions of the regression model estimated by pair v svr capture well the characteristics of data distributions thus facilitating automatic estimation of the conditional mean and predictive variance simultaneously this may be useful in many cases especially when the noise is heteroscedastic and depends strongly on the input values the experimental results validate the superiority of our pair v svr in both training prediction speed and generalization ability

constructing hierarchy of sinh gordon type equations from soliton hierarchy with self consistent source abstract a method for constructing hierarchy of sinh gordon shg type equations from soliton hierarchy with self consistent source is proposed the lax representation for the shg type equation is naturally deduced from that for soliton equation with self consistent sources several new hierarchies of shg type equations are presented

on the non isospectral kadomtsev petviashvili equation with self consistent sources abstract a new procedure called source generation is applied to construct non isospectral soliton equations with self consistent sources as results the non isospectral kadomtsev petviashvili equation with self consistent sources kpescs and its gramm type determinant solutions are obtained furthermore the non isospectral pfaffianized kp equation with self consistent sources is constructed this coupled system can not only be reduced to the non isospectral pfaffianized kp equation but also reduced to the non isospectral kpescs

best fitting hyperplanes for classification in this paper we propose novel methods that are more suitable than classical large margin classifiers for open set recognition and object detection tasks the proposed methods use the best fitting hyperplanes approach and the main idea is to find the best fitting hyperplanes such that each hyperplane is close to the samples of one of the classes and is as far as possible from the other class samples to this end we propose two different classifiers the first classifier solves a convex quadratic optimization problem but negative samples can lie on one side of the best fitting hyperplane the second classifier however allows the negative samples to lie on both sides of the fitting hyperplane by using concave convex procedure both methods are extended to the nonlinear case by using the kernel trick in contrast to the existing hyperplane fitting classifiers in the literature our proposed methods are suitable for large scale problems and they return sparse solutions the experiments on several databases show that the proposed methods typically outperform other hyperplane fitting classifiers and they work as good as the svm classifier in classical recognition tasks however the proposed methods significantly outperform svm in open set recognition and object detection tasks

a non isospectral integrable couplings of volterra lattice hierarchy with self consistent sources a kind of non isospectral integrable couplings of discrete soliton equations hierarchy with self consistent sources associated with email protected 4 y f zhang e g fan characteristic numbers of matrix lie algebras commun theor phys china 49 2008 845 is presented as an application example the hierarchy of non isospectral cubic volterra lattice hierarchy with self consistent sources is derived furthermore we construct a non isospectral integrable couplings of cubic volterra lattice hierarchy with self consistent sources by using the loop algebra email protected 4

multisurface proximal support vector machine classification via generalized eigenvalues a new approach to support vector machine svm classification is proposed wherein each of two data sets are proximal to one of two distinct planes that are not parallel to each other each plane is generated such that it is closest to one of the two data sets and as far as possible from the other data set each of the two nonparallel proximal planes is obtained by a single matlab command as the eigenvector corresponding to a smallest eigenvalue of a generalized eigenvalue problem classification by proximity to two distinct nonlinear surfaces generated by a nonlinear kernel also leads to two simple generalized eigenvalue problems the effectiveness of the proposed method is demonstrated by tests on simple examples as well as on a number of public data sets these examples show the advantages of the proposed approach in both computation time and test set correctness

new factorization of the kaup newell hierarchy abstract the new factorizations of each equation in the kaup newell kn hierarchy into two commuting x and t n finite dimensional integrable hamiltonian systems fdihs via the higher order potential eigenfunction constraints are presented the integrability commutativity and lax representation for these fdihss are deduced from the adjoint representations of the auxiliary linear problems for the kn hierarchy this approach provides a natural way to study soliton hierarchies with source the zero curvature representation and darboux transformation for the kn hierarchy with source related to eigenfunctions are found

a modified kdv equation with self consistent sources in non uniform media and soliton dynamics two non isospectral modified kdv equations with self consistent sources are derived which correspond to the time dependent spectral parameter satisfying t and t 3 respectively gauge transformation between the first non isospectral equation corresponding to t and its isospectral counterpart is given from which exact solutions and conservation laws for the non isospectral one are easily listed besides solutions to the two nonisospectral modified kdv equations with self consistent sources are derived by means of the hirota method and the wronskian technique respectively nonisospectral dynamics and source effects including one soliton characteristics in non uniform media two solitons scattering and special behaviours related to sources for example the ghost solitons in the degenerate two soliton case are investigated analytically

an integrable couplings of dirac soliton hierarchy with self consistent sources abstract a kind of the integrable couplings of soliton equations hierarchy with self consistent sources associated with sl 4 is presented as an application example we construct a new integrable couplings of the dirac soliton hierarchy with self consistent sources by using of loop algebra sl 4

one class proximal support vector machines recently in dufrenois 1 a new fisher type contrast measure has been proposed to extract a target population in a dataset contaminated by outliers although mathematically sound this work presents some further shortcomings in both the formalism and the field of use first we propose to re express this problem from the formalism of proximal support vector machines as introduced in mangasarian and wild 2 this change is far from harmless since it introduces a suited writing for solving the problem another limiting factor of the method is that its performance relies on the assumption that the density between the target and outliers are different this consideration can easily prove to be over optimistic for real world datasets making the method unreliable at least directly the computation of the decision boundary is a time consuming part of the algorithm since it is based on solving a generalized eigenvalue problem gep this method is therefore limited to medium sized data sets in this paper we propose appropriate strategies to unlock all these shortcomings and fully benefit from the interest of the approach firstly we show under some conditions that generating appropriate artificial outliers allows to stay within the constraints of the method and thus enlarges the conditions of use secondly we show that the gep can be advantageously replaced by a conjugate gradient solution cg significantly decreasing the computational cost lastly the proposed algorithm is compared with recent novelty detectors on synthetic and real datasets highlightswe study the extraction of a target population from a dataset contaminated by outliers to this end we propose a new fisher type contrast measure we reconsider this problem from the formalism of proximal support vector machines an approximation of the contrast measure is done using a conjugate gradient method no matrix inversion is needed which lowers the computational complexity

robust twin support vector machine for pattern classification in this paper we proposed a new robust twin support vector machine called r twsvm via second order cone programming formulations for classification which can deal with data with measurement noise efficiently preliminary experiments confirm the robustness of the proposed method and its superiority to the traditional robust svm in both computation time and classification accuracy remarkably since there are only inner products about inputs in our dual problems this makes us apply kernel trick directly for nonlinear cases simultaneously we does not need to solve the extra inverse of matrices which is totally different with existing twsvms in addition we also show that the twsvms are the special case of our robust model and simultaneously give a new dual form of twsvm by degenerating r twsvm which successfully overcomes the existing shortcomings of twsvm

a spatially constrained fuzzy hyper prototype clustering algorithm we present in this paper a fuzzy clustering algorithm which can handle spatially constraint problems often encountered in pattern recognition the proposed method is based on the notions of hyperplanes the fuzzy c means and spatial constraints by adding a spatial regularizer into the fuzzy hyperplane based objective function the proposed method can take into account additionally important information of inherently spatial data experimental results have demonstrated that the proposed algorithm achieves superior results to some other popular fuzzy clustering models and has potential for cluster analysis in spatial domain

an efficient weighted lagrangian twin support vector machine for imbalanced data classification abstract in this paper we propose an efficient weighted lagrangian twin support vector machine wltsvm for the imbalanced data classification based on using different training points for constructing the two proximal hyperplanes the main contributions of our wltsvm are 1 a graph based under sampling strategy is introduced to keep the proximity information which is robustness to outliers 2 the weight biases are embedded in the lagrangian twsvm formulations which overcomes the bias phenomenon in the original twsvm for the imbalanced data classification 3 the convergence of the training procedure of lagrangian functions is proven and 4 it is tested and compared with some other twsvms on synthetic and real datasets to show its feasibility and efficiency for the imbalanced data classification

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

multiconlitron a general piecewise linear classifier based on the convexly separable concept we present a solid geometric theory and a new general framework to design piecewise linear classifiers for two arbitrarily complicated nonintersecting classes by using a multiconlitron which is a union of multiple conlitrons that comprise a set of hyperplanes or linear functions surrounding a convex region for separating two convexly separable datasets we propose a new iterative algorithm called the cross distance minimization algorithm cdma to compute hard margin non kernel support vector machines svms via the nearest point pair between two convex polytopes using cdma we derive two new algorithms i e the support conlitron algorithm sca and the support multiconlitron algorithm sma to construct support conlitrons and support multiconlitrons respectively which are unique and can separate two classes by a maximum margin as in an svm comparative experiments show that sma can outperform linear svm on many of the selected databases and provide similar results to radial basis function svm on some of them while sca performs better than linear svm on three out of four applicable databases other experiments show that sma and sca may be further improved to draw more potential in the new research direction of piecewise linear learning

discriminatively regularized least squares classification over the past decades regularization theory is widely applied in various areas of machine learning to derive a large family of novel algorithms traditionally regularization focuses on smoothing only and does not fully utilize the underlying discriminative knowledge which is vital for classification in this paper we propose a novel regularization algorithm in the least squares sense called discriminatively regularized least squares classification drlsc method which is specifically designed for classification inspired by several new geometrically motivated methods drlsc directly embeds the discriminative information as well as the local geometry of the samples into the regularization term so that it can explore as much underlying knowledge inside the samples as possible and aim to maximize the margins between the samples of different classes in each local area furthermore by embedding equality type constraints in the formulation the solutions of drlsc can follow from solving a set of linear equations and the framework naturally contains multi class problems experiments on both toy and real world problems demonstrate that drlsc is often superior in classification performance to the classical regularization algorithms including regularization networks support vector machines and some of the recent studied manifold regularization techniques