extended nearest neighbor chain induced instance weights for svms prior knowledge plays an important role in increasing the performance of support vector machine svm one way to utilize prior knowledge is to assign different weight to each sample which is called weighted support vector machine wsvm in this paper a novel instance weighted method is proposed for support vector machines the weight is determined by the distances between a sequence of the nearest heterogeneous samples named the extended nearest neighbor chain the samples near the decision plane also locate near the heterogeneous samples thus the samples near the decision plane can be found by the extended nearest neighbor chain before svms training and then assigned higher weights meanwhile the samples far away from the decision plane are assigned lower weights this is consistent with the fact that the samples near the decision plane are more important for svms moreover this strategy can also assign lower weights to the samples which locate in the wrong classes the results of the experiments performed on both artificial synthetic datasets and real world benchmark datasets demonstrate that the proposed instance weighted method can further improve the performance of svms a novel instance weighted strategy is proposed for svms the samples near decision plane are assigned higher weights via the proposed method the sample near decision plane can be found by a chain named extended nearest neighbor chain the proposed method makes svm become more robust for noises

sparse ensembles using weighted combination methods based on linear programming an ensemble of multiple classifiers is widely considered to be an effective technique for improving accuracy and stability of a single classifier this paper proposes a framework of sparse ensembles and deals with new linear weighted combination methods for sparse ensembles sparse ensemble is to sparsely combine the outputs of multiple classifiers by using a sparse weight vector when the continuous outputs of multiple classifiers are provided in our methods the problem of solving sparse weight vector can be formulated as linear programming problems in which the hinge loss or and the 1 norm regularization are exploited both the hinge loss and the 1 norm regularization are techniques inducing sparsity used in machine learning we only ensemble classifiers with nonzero weight coefficients in these lp based methods the ensemble training error is minimized while the weight vector of ensemble learning is controlled which can be thought as implementing the structure risk minimization rule and naturally explains good performance of these methods the promising experimental results over uci data sets and the radar high resolution range profile data are presented

a boundary method for outlier detection based on support vector domain description the support vector domain description svdd is a popular kernel method for outlier detection which tries to fit a class of data with a sphere and uses a few target objects to support its decision boundary the problem is that even with a flexible gaussian kernel function the svdd could sometimes generate such a loose decision boundary that the discrimination ability becomes poor therefore a computationally intensive procedure called kernel whitening is often required to improve the performance in this paper we propose a simple post processing method which tries to modify the svdd boundary in order to achieve a tight data description with no need of kernel whitening with the derivation of the distance between an object and its nearest boundary point in input space the proposed method can efficiently construct a new decision boundary based on the svdd boundary the improvement from the proposed method is demonstrated with synthetic and real world datasets the results show that the proposed decision boundary can fit the shape of synthetic data distribution closely and achieves better or comparable classification performance on real world datasets

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

fractal and nonfractal shapes in two dimensional vesicles abstract ongoing collaborative work on the statistical mechanics of two dimensional vesicles is reviewed with emphasis on the range of fractal and nonfractal shapes exhibited by the bead and tether model of a closed membrane which also embodies an osmotic pressure difference p and a bending rigidity modulus monte carlo simulations and scaling analyses are described flaccid vesicles with p 0 represent closed self avoiding rings their mean area a scales with the mean square size r g 2 their mean shape is close to elliptical inflated p 0 vesicles become circular deflated p branched polymers the vesicle shapes appear to vary continuously with the scaling combination p n 2 where n is the number of monomers beads and 3 4 for p k b t large relative to n 3 a range of characteristic nonfractal shapes or cytotypes appears

the pencil se a and controllability observability for generalized linear systems a geometric approach in the first part of the paper we study the pencil se a by using some geometric concepts given by bernhard siam j control optim 20 1982 pp 612 6331 and some new ones which are introduced here such concepts are then used to obtain an alternative characterization for the finite and infinite zero structure of the pencil and to construct a polynomial basis for ker se a necessary and sufficient conditions for the rows or and the columns of the pencil to be linearly independent over the ring of the polynomials are also given the main geometric properties of a regular pencil are presented including the identification of the subspace in which the impulsive response of the autonomous generalized linear system e dot x ax takes place in the second part we consider the generalized linear system e dot x ax bu y cx and we give necessary and sufficient conditions for the infinite zeros of the regular pencil se a to be controllable and observable

moments of inertia and the shapes of brownian paths we compute the joint probability law of the principal moments of inertia of brownian paths open or closed using constrained path integrals and random matrix theory the case of two dimensional paths is discussed in detail in particular we show that the ratio of the average values of the largest and smallest moments is equal to 4 99 open paths and 3 07 closed paths we also present results of numerical simulations which include investigation of the relationships between the moments of inertia and the arithmetic area enclosed by a path

shapes and sizes of arbitrary random walks at o 1 d3 ii asphericity and prolateness parameters abstract for arbitrary random walks in any d dimensional space expansions in powers of 1 d of asphericity and prolateness parameters and moments of the inverse size ratio have been developed which at o 1 d 3 yield very good approximations to exact values of the parameters for chains rings dumbbells and 3 and 5 arm regular stars the 1 d expansions have also been used to obtain an estimate of these shape asymmetry parameters for 3d edwards chains rings dumbbells and 3 arm stars and to give a mathematical proof that infinitely large random nets such as bethe lattice or starburst and mckay s net exhibit spherical symmetry for arbitrary random walks at d it is proved that these parameters coincide with their corresponding factors while for an end looped self avoiding walk it is found that its shape asymmetry is even larger than that of an open saw an 1 f expansion of the parameters for f arm regular stars has also been obtained and a comparison of the dimensionality dependence of the parameters with that of the corresponding factors has been made for the four types of random walks

on the application of geometric probability theory to polymer networks and suspensions ii the theory of stochastic processes and integral geometry is applied to polymer networks and suspensions averaged monomer density is calculated for adsorbed and depleted layers of single chain polymers modelled as brownian paths near plane and spherical surfaces and exact solutions are given for an adsorbed layer with a force field asymptotic expressions are deduced for the available space fraction for a small solute in such layers a measure of the typical asymmetry of a single chain polymer modelled as a brownian path is obtained by calculating the averaged integral of the mean curvature surface area and volume of its convex hull the averaged integral of the mean curvature and surface area also give the first two terms of an asymptotic expression for the depletion near a smooth slightly curved surface and an upper bound on the averaged capacitance these quantities are also calculated for model polymer aggregates brownian rings and brownian paths with drift from the latter we deduce averages of powers of the end to end distance of a brownian path weighted by the integral of the mean curvature and surface area of its convex hull the depletion due to a lamina with a smooth slightly curved boundary in a solution of single chain polymers is calculated and the result is interpreted in terms of averaged geometrical properties of brownian paths

geometrical properties of aggregates with tunable fractal dimension we have computed geometrical characteristics of large clusters up to 32 768 particles obtained by a hierarchical cluster cluster aggregation computer model in three dimensions the off lattice variable d model using a box counting method we have calculated the fractal dimensions of the surface and the perimeter of their two dimensional projections as a function of their fractal dimension d by diagonalizing the radius of gyration tensor we have obtained numerical estimates for the intrinsic anisotropy coefficients ratios of the eigenvalues and we have proposed analytical expressions to describe their behaviour as a function of the fractal dimension

the aspherity of random walks the asphericity a of a random walk is defined and calculated for non self avoiding walks the definition of a generalises to self avoiding walks percolating clusters and other fractal objects and thus provides a generalised quantitative measure of the departure from spherical symmetry of the gross shape of these objects

optimizing the data dependent kernel under a unified kernel optimization framework the kernel functions play a central role in kernel methods accordingly over the years the optimization of kernel functions has been a promising research area ideally fisher discriminant criteria can be used as an objective function to optimize the kernel function to augment the margin between different classes unfortunately fisher criteria are optimal only in the case that all the classes are generated from underlying multivariate normal distributions of common covariance matrix but different means and each class is expressed by a single cluster due to the assumptions fisher criteria obviously are not a suitable choice as a kernel optimization rule in some applications such as the multimodally distributed data in order to solve this problem recently many improved discriminant criteria dc have been also developed therefore to apply these discriminant criteria to kernel optimization in this paper based on a data dependent kernel function we propose a unified kernel optimization framework which can use any discriminant criteria formulated in a pairwise manner as the objective functions under the kernel optimization framework to employ different discriminant criteria one has to only change the corresponding affinity matrices without having to resort to any complex derivations in feature space experimental results based on some benchmark data demonstrate the efficiency of our method

confidence bands for least squares support vector machine classifiers a regression approach this paper presents bias corrected 100 email protected simultaneous confidence bands for least squares support vector machine classifiers based on a regression framework the bias which is inherently present in every nonparametric method is estimated using double smoothing in order to obtain simultaneous confidence bands we make use of the volume of tube formula we also provide extensions of this formula in higher dimensions and show that the width of the bands are expanding with increasing dimensionality simulations and data analysis support its usefulness in practical real life classification problems

an algebraic condition for controllability at infinity abstract a necessary and sufficient algebraic condition is given for a generalized state space system to be controllable at infinity a dual condition is given for observability at infinity

a simple dynamical model of two dimensional vesicles two dimensional vesicles are modelled as pressurized self intersecting rings the fluctuating motion of the bounding walls of the vesicle when it is subjected to the random collisions of fluid molecules is treated along the lines suggested by rouse 1953 in his study of dilute polymer solutions within the model exact solutions of the dynamical equation governing the probability distribution of shapes when expressed in an appropriate set of normal coordinates is obtained numerical simulations of the dynamical evolution of the distribution of the principal components of the square of the radius of gyration are also presented

study of the shape of random walks a comprehensive study of the shape of discrete random walks considering the general case of arbitrary length and any space dimension is presented the probability distributions for several magnitudes such as the principal inertia moments the asphericity and the angle between the principal axis of inertia and the end to end vector are evaluated numerically in most cases and especially in low dimensional spaces these probability distributions spread widely and possess a non zero skewness this implies that any description of the shapes of random walks which is based only on mean values of related magnitudes is incomplete this situation does nor vary when random walks of large lengths are considered since the relative fluctuations ratio between the standard deviation and the mean value do not go to zero in that limit on the other hand when the space dimension grows the distributions become more peaked reaching the expected asymptotic limit for infinite dimension the present study also indicates that the probability distributions for the principal inertia moments have approximately the form of chi squared distributions analysing the probability distribution for the asphericity it is shown that the distributions for the different moments are not completely independent

rapid and brief communication improving support vector data description using local density degree we propose a new support vector data description svdd incorporating the local density of a training data set by introducing a local density degree for each data point by using a density induced distance measure based on the degree we reformulate a conventional svdd experiments with various real data sets show that the proposed method more accurately describes training data sets than the conventional svdd in all tested cases

the shapes and sizes of two dimensional pressurized self intersecting rings as models for two dimensional vesicles two dimensional vesicles are modelled as pressurized unrestricted closed random walks the model though suffering from undesirable physical characteristics has the decided advantage of yielding exact analytical statistical analysis of the size and shapes of these objects closed form expressions for the average of the square of the radius of gyration and the asphericity are derived in addition exact expressions for the full probability distribution are also obtained numerical computations of the probability function for several pressures are presented the authors arrive at a new exact formula for the distribution function p r12 r22 of the principal components of the square of the radius of gyration for two dimensional rings

the shapes of open and closed random walks a 1 d expansion a new technique for calculating the shapes of random walks is presented the method is used to derive an exact analytical expression for the asphericity of an unrestricted closed or ring walk embedded in d spatial dimensions a graphical procedure is developed to systematise a 1 d series expansion for the individual principal radii of gyration and their respective probability distribution functions p r2i 1 or i or d the average principal radii of gyration are calculated to o 1 d2 for both open and closed walks and selected terms in the 1 d expansion are summed to all orders in 1 d in the determination of p r2i this leads to an explicit analytical form for p r2i for open walks the distribution of the largest eigenvalue is compared with a distribution obtained from numerical simulations of walks in three dimensions the agreement between the two is extremely good other predictions for various parameters that characterise the average shape of open and closed walks in three dimensions are also found to agree remarkably well with the results of simulations the error being of the order of 5

fisher regularized support vector machine this paper proposes fisher regularized support vector machine fishersvm fishersvm is a graph based supervised learning method fishersvm has two regularization terms maximum margin and fisher regularizations fishersvm aims to maximize the margin and minimize the within class scatter support vector machine svm and fisher discriminant analysis fda are two commonly used methods in machine learning and pattern recognition a combined method of the linear svm and fda called svm lda linear discriminant analysis has been proposed only for the linear case this paper generalizes this combined method to the nonlinear case from the view of regularization a fisher regularization is defined and incorporated into svm to obtain a fisher regularized support vector machine fishersvm in fishersvm there are two regularization terms the maximum margin regularization and fisher regularization which allow fishersvm to maximize the classification margin and minimize the within class scatter roughly speaking fishersvm can approximatively fulfill the fisher criterion and obtain good statistical separability this paper also discusses the connections of fishersvm to graph based regularization methods and the mathematical programming method to kernel fisher discriminant analysis kfda it shows that fishersvm can be thought of as a graph based supervised learning method or a robust kfda experimental results on artificial and real world data show that fishersvm has a promising generalization performance

density induced margin support vector machines this paper proposes a new classifier called density induced margin support vector machines dmsvms dmsvms belong to a family of svm like classifiers thus dmsvms inherit good properties from support vector machines svms e g unique and global solution and sparse representation for the decision function for a given data set dmsvms require to extract relative density degrees for all training data points these density degrees can be taken as relative margins of corresponding training data points moreover we propose a method for estimating relative density degrees by using the k nearest neighbor method we also show the upper bound on the leave out one error of dmsvms for a binary classification problem and prove it promising results are obtained on toy as well as real world data sets

the shapes of high dimensional random walks the individual principal radii of gyration are computed for unrestricted random walks in a large number of spatial dimensions a low order expansion in one over the dimensionality yields useful information regarding the distribution and average of these measures of the extent and spatial anisotropy of high dimensional random walks such an expansion may well prove useful in the study of the shapes of other random fractal objects

a measure of the symmetry of random walks we derive the probability density for a simple measure of the asymmetry of a one dimensional random walk namely the ratio of the minimum of the two maximum displacements in the positive and negative directions to the maximum we show that in the diffusion limit the asymmetry is independent of time these results are shown to apply to random walks in which individual steps have a stable law distribution as well as to multidimensional random walks

study of the shape of random walks ii inertia moment ratios and the two dimensional asphericity a study of some features of the quantities used to describe the shape of random walks focusing on the probability distribution of the asphericity of discrete random walks in two dimensions is presented a connection is established between the asphericity distribution and the probability distribution corresponding to the ratio of the principal inertia moments the probability distributions of arbitrary inertia moment ratios are analysed for varying spatial dimension and an analytic expression for them is found which presents excellent agreement with monte carlo data in all the cases considered this function is then used to obtain the corresponding two dimensional asphericity distribution which also proved to be a very good approximation to the true distribution obtained from an independent monte carlo simulation

shapes of random walks at order 1 d2 the authors calculate various parameters which characterize the size and shape of random walks utilizing a recently developed 1 d expansion technique where d is the spatial dimension in which the random walk takes place a new procedure for extracting the averages of the principal radii of gyration is presented and the calculation is carried out to order 1 d2 which is one order higher than previous work comparison with the results of numerical simulations provides new insights regarding the accuracy of the 1 d expansion procedure

new approaches to shapes of arbitrary random walks abstract the problem of the shape of a random object such as a flexible polymer chain was first tackled by kuhn nearly thirty years after the answer to the probability distribution of its size was publicly sought for by pearson in 1905 since then significant progress in the field has been made but the important task of evaluatin both analytically and accurately averaged individual principal components of the shape or inertia tensor for a walk of a certain architectural type remains unfinished we have recently developed a new and general formalism for both exact and approximate calculations of these and other averages such as asphericity and prolateness parameters which is illustrated here for an end looped random walk and a self avoiding or edwards chain we find that this combined open and closed random walks has surprisingly larger shape asymmetry than a simply open walk despite its smaller size

the two dimensional shapes of simple three and four junction ideal comb polymers we redesign and apply a scheme originally proposed by wei 1995 2 3 to produce numerical shape parameters with high precision for arbitrary tree branched polymers based on their kirchhoff matrix eigenvalue spectrum this algorithm and a monte carlo growth method on square and triangular lattices are employed to investigate the shapes of ideal three and four junction two dimensional comb polymers we find that the extrapolated values obtained by all of these methods are in excellent agreement with each other and the available theory we confirm that polymers with a complete set of interior branches display a more circular shape

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

polymers as self avoiding walks a brief overview is presented of the relation of the properties of real polymers to the problem of self avoiding random walks the self consistent field method is discussed wherein the non markovian continuous self avoiding polymer is replaced by a self consistent markovian approximation an outline is presented of the method of solution of the resultant nonlinear integrodifferential equations a description is also presented of the scaling theories which provide a means for deducing some exponents in the asymptotic dependence of walk properties on the length of the walk in the limit of infinite length walks

the shape of self avoiding walks an exhaustive analysis of the shape properties of discrete self avoiding random walks is presented the dependence of the main parameters of the probability distributions from the length of the walk and the differences between these distributions for conventional and self avoiding walks are studied by means of high precision monte carlo simulations it is shown that the characteristics of the shape of self avoiding random walks when regarded as a function of the walk length present the expected asymptotic behaviour the differences with conventional random walks depend upon the observable considered the probability distributions of the principal inertia eigenvalues of self avoiding walks spread around the most probable value more widely than the corresponding distributions for unrestricted walks while in the cases of the asphericity or ratios of inertia eigenvalues the distributions for self avoiding walks are somewhat more peaked than their counterparts for conventional random walks analytical expressions for the probability distributions of inertia moment ratios and the two dimensional asphericity are given for common random walks there is an excellent agreement between these analytical distributions and the monte carlo data in this work it is established that this concordance is maintained if the same analytical distributions are applied to the self avoiding case this means that within the precision of the simulations the functional form of the mentioned distributions does not vary when passing from conventional to self avoiding walks

universal shape ratios for open and closed random walks exact results for all d the mean asphericities ad of open and closed gaussian polymer chains are computed exactly and analytically up to simple quadratures for arbitrary space dimensions d excellent agreement is found with existing simulation data for d 2 3 and 4 the authors technique can also be used to compute other averages of ratios of fluctuating variables as well as extended to include the effects of self avoiding walk interactions

statistical properties of the set of sites visited by the two dimensional random walk we study the support i e the set of visited sites of a t step random walk on a two dimensional square lattice in the large t limit a broad class of global properties m t of the support is considered including for example the number s t of its sites the length of its boundary the number of islands of unvisited sites that it encloses the number of such islands of given shape size and orientation and the number of occurrences in space of specific local patterns of visited and unvisited sites on a finite lattice we determine the scaling functions that describe the averages on appropriate lattice size dependent time scales on an infinite lattice we first observe that the all increase with t as where k is an m dependent positive integer we then consider the class of random processes constituted by the fluctuations around average we show that to leading order as t gets large these fluctuations are all proportional to a single universal random process normalized to for the probability law of tends to that of varadhan s renormalized local time of self intersections an implication is that in the long time limit all are proportional to

two class support vector data description support vector data description svdd is a data description method that can give the target data set a spherically shaped description and be used to outlier detection or classification in real life the target data set often contains more than one class of objects and each class of objects need to be described and distinguished simultaneously in this case traditional svdd can only give a description for the target data set regardless of the differences between different target classes in the target data set or give a description for each class of objects in the target data set in this paper an improved support vector data description method named two class support vector data description tc svdd is presented the proposed method can give each class of objects in the target data set a hypersphere shaped description simultaneously if the target data set contains two classes of objects the characteristics of the improved support vector data descriptions are discussed the results of the proposed approach on artificial and actual data show that the proposed method works quite well on the 3 class classification problem with one object class being undersampled severely

universal features of the shapes of percolation clusters and lattice animals the shapes of percolation clusters and lattice animals are investigated the universal quantities delta d and sd which were introduced to measure the average asymmetry and degree of prolate or oblateness respectively of long chain polymers are here computed in an in expansion for percolation clusters and for lattice animals delta d is computed to o in while sd is computed to o 1 the clusters are shown to be on average anisotropic and prolate but less so than polymers percolation clusters and lattice animals have identical shapes above eight dimensions below d 8 animals are slightly more anisotropic than percolation clusters

on the asymmetry of a random walk in the presence of a field any ensemble of random walks with symmetric transition probabilities will have symmetric properties however any single realization of such a random walk may be asymmetric in an earlier paper weiss and weissman developed a measure of asymmetry and applied it to random walks in the absence of a field showing that the degree of asymmetry in the diffusion limit is independent of time and that the most probable degree of asymmetry corresponds to the maximum possible we show in the present paper how the presence of a symmetric field can change this result both in making the degree of asymmetry depend on time and driving the random walk toward a more symmetric state

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

the shapes of ideal five junction comb polymers in two and three dimensions abstract this work investigates a variety of properties of eleven and fourteen branch five junction comb polymers in the ideal regime in two and three dimensions a method based on the kirchhoff matrix eigenvalue spectrum for arbitrary tree branched polymers is used to compute shape properties and a scheme originally proposed by benhamous 2004 is used to produce an exact equation for the form factor of the fourteen branch comb polymers a monte carlo growth algorithm is also employed to compute the same properties it is found that the values obtained by all of these methods are in fine agreement with each other and available theory

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

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

density induced support vector data description the purpose of data description is to give a compact description of the target data that represents most of its characteristics in a support vector data description svdd the compact description of target data is given in a hyperspherical model which is determined by a small portion of data called support vectors despite the usefulness of the conventional svdd however it may not identify the optimal solution of target description especially when the support vectors do not have the overall characteristics of the target data to address the issue in svdd methodology we propose a new svdd by introducing new distance measurements based on the notion of a relative density degree for each data point in order to reflect the distribution of a given data set moreover for a real application we extend the proposed method for the protein localization prediction problem which is a multiclass and multilabel problem experiments with various real data sets show promising results

face recognition using total margin based adaptive fuzzy support vector machines this paper presents a new classifier called total margin based adaptive fuzzy support vector machines taf svm that deals with several problems that may occur in support vector machines svms when applied to the face recognition the proposed taf svm not only solves the overfitting problem resulted from the outlier with the approach of fuzzification of the penalty but also corrects the skew of the optimal separating hyperplane due to the very imbalanced data sets by using different cost algorithm in addition by introducing the total margin algorithm to replace the conventional soft margin algorithm a lower generalization error bound can be obtained those three functions are embodied into the traditional svm so that the taf svm is proposed and reformulated in both linear and nonlinear cases by using two databases the chung yuan christian university cycu multiview and the facial recognition technology feret face databases and using the kernel fisher s discriminant analysis kfda algorithm to extract discriminating face features experimental results show that the proposed taf svm is superior to svm in terms of the face recognition accuracy the results also indicate that the proposed taf svm can achieve smaller error variances than svm over a number of tests such that better recognition stability can be obtained