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

fuzzy granular gravitational clustering algorithm for multivariate data abstract a new method for finding fuzzy information granules from multivariate data through a gravitational inspired clustering algorithm is proposed in this paper the proposed algorithm incorporates the theory of granular computing which adapts the cluster size with respect to the context of the given data via an inspiration in newton s law of universal gravitation both conditions of clustering similar data and adapting to the size of each granule are achieved this paper compares the fuzzy granular gravitational clustering algorithm fggca against other clustering techniques on two grounds classification accuracy and clustering validity indices e g rand fm davies bouldin dunn homogeneity and separation the fggca is tested with multiple benchmark classification datasets such as iris wine seeds and glass identification

joint distance and similarity measure learning based on triplet based constraints a novel model is proposed to learn combined distance and similarity measure cdsm based on triplet based constraints our cdsm can be kernelized for learning nonlinear measures two effective strategies are suggested to speed up the training and testing of kernelized cdsm extensive experiments validate the superiority of cdsm and kernelized cdsm distance and similarity measures usually are complementary to pattern classification with pairwise constraints several approaches have been proposed to combine distance and similarity measures however it remains less investigated to use triplets of samples for joint learning of distance and similarity measures moreover the kernel extension of triplet based model is also nontrivial and computationally expensive in this paper we propose a novel method to learn a combined distance and similarity measure cdsm by incorporating with the max margin model we suggest a triplet based cdsm learning model with a unified regularizer of the frobenius norm a support vector machine svm based algorithm is then adopted to solve the optimization problem furthermore we extend cdsm for learning nonlinear measures via the kernel trick two effective strategies are adopted to speed up training and testing of kernelized cdsm experiments on the uci handwritten digits and person re identification datasets demonstrate that cdsm and kernelized cdsm outperform several state of the art metric learning methods

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

convergence rates of solutions toward boundary layer solutions for generalized benjamin bona mahony burgers equations in the half space this paper is concerned with the initial boundary value problem of the generalized benjamin bona mahony burgers equation in the half space r

global existence and asymptotic behavior for a coupled hyperbolic system with localized damping abstract in this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system the semi explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality we extend the energy decay result in alabau boussouira f alabau boussouira convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems appl math optim 51 2005 61 105 for a single equation to the coupled hyperbolic system

multi granularity distance metric learning via neighborhood granule margin maximization learning a distance metric from training samples is often a crucial step in machine learning and pattern recognition locality compactness and consistency are considered as the key principles in distance metric learning however the existing metric learning methods just consider one or two of them in this paper we develop a multi granularity distance learning technique first a new index neighborhood granule margin which simultaneously considers locality compactness and consistency of neighborhood is introduced to evaluate a distance metric by maximizing neighborhood granule margin we formulate the distance metric learning problem as a sample pair classification problem which can be solved by standard support vector machine solvers then a set of distance metrics are learned in different granular spaces the weights of the granular spaces are learned through optimizing the margin distribution finally the decisions from different granular spaces are combined with weighted voting experiments on uci datasets gender classification and object categorization tasks show that the proposed method is superior to the state of the art distance metric learning algorithms

sorting shuffled monotone sequences we present a new sorting algorithm that adapts to existing order within an input sequence let k be the smallest integer such that a sequence x of length n can be reduced to the empty sequence by the removal of k monotone increasing or decreasing subsequences the algorithm slabsort sorts x in o n log k time without knowing k beforehand which is optimal in a comparison based model

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

large time behavior for convection diffusion equations in rn abstract we describe the large time behavior of solutions of the convection diffusion equation u t u a u q 1 u in 0 r n with a r n and q 1 1 n n 1 when q 1 1 n we prove that the large time behavior of solutions with initial data in l 1 r n is given by a uniparametric family of self similar solutions the relevant parameter is the mass of the solution that is conserved for all t our result extends to dimensions n 1 well known results on the large time behavior of solutions for viscous burgers equations in one space dimension the proof is based on la salle s invariance principle applied to the equation written in its self similarity variables when q 1 1 n the convection term is too weak and the large time behavior is given by the heat kernel in this case the result is easily proved applying standard estimates of the heat kernel on the integral equation related to the problem

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

a twin hypersphere support vector machine classifier and the fast learning algorithm this paper formulates a twin hypersphere support vector machine thsvm classifier for binary recognition similar to the twin support vector machine twsvm classifier this thsvm determines two hyperspheres by solving two related support vector machine svm type problems each one is smaller than the classical svm which makes the thsvm be more efficient than the classical svm in addition the thsvm avoids the matrix inversions in its two dual quadratic programming problems qpps compared with the twsvm by considering the characteristics of the dual qpps of thsvm an efficient gilbert s algorithm for the thsvm based on the reduced convex hull rch instead of directly optimizing its pair of qpps is further presented computational results on several synthetic as well as benchmark datasets indicate the significant advantages of the thsvm classifier in the computational time and test accuracy

a geometric approach to support vector machine svm classification the geometric framework for the support vector machine svm classification problem provides an intuitive ground for the understanding and the application of geometric optimization algorithms leading to practical solutions of real world classification problems in this work the notion of reduced convex hull is employed and supported by a set of new theoretical results these results allow existing geometric algorithms to be directly and practically applied to solve not only separable but also nonseparable classification problems both accurately and efficiently as a practical application of the new theoretical results a known geometric algorithm has been employed and transformed accordingly to solve nonseparable problems successfully

a biased least squares support vector machine based on mahalanobis distance for pu learning abstract in many domains the presence of both positive and negative examples is not satisfied and only one class of examples is available this special case of binary classification is called as pu positive and unlabeled learning in short at present many classification algorithms have been introduced for pu learning such as blssvm bsvm and so on however all of these classical approaches were measured by euclidean distance which did not take into account the correlative information of each class and the fluctuation of various attributions in order to reflect this information we propose a new mahalanobis distance based least squares support vector machines md blssvm classifier in which two mahalanobis distances are constructed according to the covariance matrices of two class data for optimizing the hyper planes actually md blssvm has a special case of blssvms when the covariance matrices are degenerated to the identity matrix the merits of md blssvm are 1 mahalanobis distance of two classes can measure more suitable distance with certain weights on attributions 2 excellent kernel technique can be introduced in a reproducing kernel hilbert space after making certain linear transformation ingeniously 3 a solution is obtained simply by solving the system of linear equations in all md blssvm is appropriate to many real problems especially for the case that the distribution and correlation of two classes of data are obviously different the experimental results on several artificial and benchmark datasets indicate that md blssvm not only possess faster learning speed but also obtains better generalization than blssvms and other methods

the lp lq estimates of solutions to one dimensional damped wave equations and their application to the compressible flow through porous media we first obtain the lp lq estimates of solutions to the cauchy problem for one dimensional damped wave equation vtt vxx vt 0 v vt t 0 v0 v1 x x t r r corresponding to that for the parabolic equation t xx 0 t 0 v0 v1 x the estimates are shown by v t e t 2v0 t v0 t 2lp ct 121q 1p 1 v0 v1 lq t 1 etc for 1 q p to show the explicit formula of the damped wave equation will be used to apply the estimates to nonlinear problems is the second aim we will treat the system of a compressible flow through porous media the solution is expected to behave as the diffusion wave which is the solution to the porous media equation due to the darcy law when the initial data has the same constant state at a sharp lp convergence rate for p 2 has been recently obtained by nishihara proc roy soc edinburgh sect a 133a 2003 1 20 by choosing a suitably located diffusion wave we will show the l1 convergence applying

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

energy decay rate for a coupled hyperbolic system with nonlinear damping abstract in this paper we investigate the energy decay rate for the solution of a coupled hyperbolic system the explicit energy decay rate is established by using multiplier techniques and constructing a suitable energy functional

large time asymptotics for partially dissipative hyperbolic systems this work is concerned with n component hyperbolic systems of balance laws in m space dimensions first we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t using the fourier transform we examine the role that control theoretical tools such as the classical kalman rank condition play we build lyapunov functionals allowing us to establish explicit decay rates depending on the frequency variable in this way we extend the previous analysis by shizuta and kawashima under the so called algebraic condition sk in particular we show the existence of systems exhibiting more complex behavior than the one that the sk condition allows we also discuss links between this analysis and previous literature in the context of damped wave equations hypoellipticity and hypocoercivity to conclude we analyze the existence of global solutions around constant equilibria for nonlinear systems of balance laws our analysis of the linear case allows proving existence results in situations that the previously existing theory does not cover

on compressing permutations and adaptive sorting we prove that given a permutation p over 1 n formed of nruns sorted blocks of sizes given by the vector r there exists a compressed data structure encoding p in n 1 h r n i 1 n r u n sr ilog 2nr i

global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy we consider the cauchy problem for a general one dimensional n n hyperbolic symmetrizable system of balance laws it is well known that in many physical examples for instance for the isentropic euler system with damping the dissipation due to the source term may prevent the shock formation at least for smooth and small initial data our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions and possibly to investigate their asymptotic behavior for systems which are entropy dissipative a quite natural generalization of the kawashima condition for hyperbolic parabolic systems can be given in this paper we first propose a general framework for this kind of problem by using the so called entropy variables then we go on to prove some general statements about the global existence of smooth solutions under different sets of conditions in particular the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension our main tools will be some refined energy estimates and the use of a suitable version of the kawashima condition

dissipative structure and entropy for hyperbolic systems of balance laws in this paper we introduce an entropy condition for hyperbolic systems of balance laws under this condition we use the chapman enskog expansion to derive the corresponding viscous conservation laws further structural conditions are discussed in order to develop local and global existence theories for the balance laws and viscous conservation laws

a robust minimax approach to classification when constructing a classifier the probability of correct classification of future data points should be maximized we consider a binary classification problem where the mean and covariance matrix of each class are assumed to be known no further assumptions are made with respect to the class conditional distributions misclassification probabilities are then controlled in a worst case setting that is under all possible choices of class conditional densities with given mean and covariance matrix we minimize the worst case maximum probability of misclassification of future data points for a linear decision boundary this desideratum is translated in a very direct way into a convex second order cone optimization problem with complexity similar to a support vector machine problem the minimax problem can be interpreted geometrically as minimizing the maximum of the mahalanobis distances to the two classes we address the issue of robustness with respect to estimation errors in the means and covariances of the classes via a simple modification of the input data we also show how to exploit mercer kernels in this setting to obtain nonlinear decision boundaries yielding a classifier which proves to be competitive with current methods including support vector machines an important feature of this method is that a worst case bound on the probability of misclassification of future data is always obtained explicitly

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

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

optimal lower bounds for rank and select indexes we develop a new lower bound technique for data structures we show an optimal omega n lg lg n lg n space lower bounds for storing an index that allows to implement rank and select queries on a bit vector b provided that b is stored explicitly these results improve upon miltersen soda 05 we show omega m t lg t lower bounds for storing rank select index in the case where b has m 1 bits in it e g low 0 th entropy and the algorithm is allowed to probe t bits of b we simplify the select index given in raman et al soda 02 and show how to implement both rank and select queries with an index of size 1 o 1 n lg lg n lg n o n lg n i e we give an explicit constant for storage in the ram model with word size lg n

nonlinear kernel based statistical pattern analysis the eigenstructure of the second order statistics of a multivariate random population can be inferred from the matrix of pairwise combinations of inner products of the samples therefore it can be also efficiently obtained in the implicit high dimensional feature spaces defined by kernel functions we elaborate on this property to obtain general expressions for immediate derivation of nonlinear counterparts of a number of standard pattern analysis algorithms including principal component analysis data compression and denoising and fisher s discriminant the connection between kernel methods and nonparametric density estimation is also illustrated using these results we introduce the kernel version of mahalanobis distance which originates nonparametric models with unexpected and interesting properties and also propose a kernel version of the minimum squared error mse linear discriminant function this learning machine is particularly simple and includes a number of generalized linear models such as the potential functions method or the radial basis function rbf network our results shed some light on the relative merit of feature spaces and inductive bias in the remarkable generalization properties of the support vector machine svm although in most situations the svm obtains the lowest error rates exhaustive experiments with synthetic and natural data show that simple kernel machines based on pseudoinversion are competitive in problems with appreciable class overlapping

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

long time behavior of solutions to a nonlinear hyperbolic relaxation system abstract we study the large time behavior of solutions of a one dimensional hyperbolic relaxation system that may be written as a nonlinear damped wave equation first we prove the global existence of a unique solution and their decay properties for sufficiently small initial data we also show that for some large initial data solutions blow up in finite time for quadratic nonlinearities we prove that the large time behavior of solutions is given by the fundamental solution of the viscous burgers equation in some other cases the convection term is too weak and the large time behavior is given by the linear heat kernel

existence and nonexistence of time global solutions to damped wave equation on half line on the half line r 0 infinity the initial boundary value problems with null dirichlet boundary for both the semilinear heat equation and damped wave equation are considered the critical exponent p c n k of semilinear term for the existence and nonexistence about the semilinear heat equation on the halved space d n d k r k rn k is given by p c n k 1 2 n k j appl math phys 39 1988 135 149 arch rational mech anal 109 1990 63 71 since the damped wave equation is expected to be close to the heat equation j differential equations 191 2003 445 469 math z 244 2003 631 649 the critical exponent for the semilinear damped wave equation is expected to be same as that of the semilinear heat equation however there is no blow up result on the halved space for the damped wave equation in this paper the exponent pc l 1 2 is shown to be critical for the existence and nonexistence of time global solution to both the semilinear heat equation and damped wave equation on the half line r together with the derivation of the blow up time for the proof the explicit formulas of solutions are used in a similar fashion to those in li and zhou discrete continuous dynamic systems 1 1995 503 520 c 2005 elsevier ltd all rights reserved

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

maxi min margin machine learning large margin classifiers locally and globally in this paper we propose a novel large margin classifier called the maxi min margin machine m4 this model learns the decision boundary both locally and globally in comparison other large margin classifiers construct separating hyperplanes only either locally or globally for example a state of the art large margin classifier the support vector machine svm considers data only locally while another significant model the minimax probability machine mpm focuses on building the decision hyperplane exclusively based on the global information as a major contribution we show that svm yields the same solution as m4 when data satisfy certain conditions and mpm can be regarded as a relaxation model of m4 moreover based on our proposed local and global view of data another popular model the linear discriminant analysis can easily be interpreted and extended as well we describe the m4 model definition provide a geometrical interpretation present theoretical justifications and propose a practical sequential conic programming method to solve the optimization problem we also show how to exploit mercer kernels to extend m4 for nonlinear classifications furthermore we perform a series of evaluations on both synthetic data sets and real world benchmark data sets comparison with svm and mpm demonstrates the advantages of our new model

the minimum error minimax probability machine we construct a distribution free bayes optimal classifier called the minimum error minimax probability machine mempm in a worst case setting i e under all possible choices of class conditional densities with a given mean and covariance matrix by assuming no specific distributions for the data our model is thus distinguished from traditional bayes optimal approaches where an assumption on the data distribution is a must this model is extended from the minimax probability machine mpm a recently proposed novel classifier and is demonstrated to be the general case of mpm moreover it includes another special case named the biased minimax probability machine which is appropriate for handling biased classification one appealing feature of mempm is that it contains an explicit performance indicator i e a lower bound on the worst case accuracy which is shown to be tighter than that of mpm we provide conditions under which the worst case bayes optimal classifier converges to the bayes optimal classifier we demonstrate how to apply a more general statistical framework to estimate model input parameters robustly we also show how to extend our model to nonlinear classification by exploiting kernelization techniques a series of experiments on both synthetic data sets and real world benchmark data sets validates our proposition and demonstrates the effectiveness of our model

a study on smo type decomposition methods for support vector machines decomposition methods are currently one of the major methods for training support vector machines they vary mainly according to different working set selections existing implementations and analysis usually consider some specific selection rules this paper studies sequential minimal optimization type decomposition methods under a general and flexible way of choosing the two element working set the main results include 1 a simple asymptotic convergence proof 2 a general explanation of the shrinking and caching techniques and 3 the linear convergence of the methods extensions to some support vector machine variants are also discussed

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

lrm trees compressed indices adaptive sorting and compressed permutations lrm trees are an elegant way to partition a sequence of values into sorted consecutive blocks they have been used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them we describe how they yield many other convenient results in a variety of areas compressed indices for range minimum queries on partially sorted arrays a new adaptive sorting algorithm and a compressed data structure for permutations supporting direct and inverse application in time inversely proportional to the compressibility of the permutation