application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

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

an efficient algorithm for solving integro differential equations system in this paper an application of he s homotopy perturbation hpm method is applied to solve of system of integro differential equations the results reveal that the hpm is very effective and simple

variational iteration method for autonomous ordinary differential systems in this paper a new iteration technique is proposed to solve autonomous ordinary differential systems in this method general lagrange multipliers are introduced to construct correction functionals for the systems the multipliers in the functionals can be identified by the variational theory the initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary initial conditions some examples are given the results reveal that the method is very effective and convenient

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

a new method of feature fusion and its application in image recognition a new method of feature extraction based on feature fusion is proposed in this paper according to the idea of canonical correlation analysis cca at first the theory framework of cca used in pattern recognition and its reasonable description are discussed the process can be explained as follows extract two groups of feature vectors with the same pattern establish the correlation criterion function between the two groups of feature vectors and extract their canonical correlation features to form effective discriminant vector for recognition then the problem of canonical projection vectors is solved when two total scatter matrixes are singular such that it fits for the case of high dimensional space and small sample size in this sense the applicable range of cca is extended at last the inherent essence of this method used in recognition is analyzed further in theory experimental results on concordia university cenparmi database of handwritten arabic numerals and yale face database show that recognition rate is far higher than that of the algorithm adopting single feature or the existing fusion algorithm

adomian decomposition method for solving the volterra integral form of the lane emden equations with initial values and boundary conditions in this paper we use the systematic adomian decomposition method to handle the integral form of the lane emden equations with initial values and boundary conditions the volterra integral form of the lane emden equation overcomes the singular behavior at the origin x 0 we confirm our belief that the adomian decomposition method provides efficient algorithm for analytic approximate solutions of the equation our results are supported by investigating several numerical examples that include initial value problems and boundary value problems as well finally we consider the modified decomposition method of rach adomian and meyers for the volterra integral form

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

adsorption and collapse of self avoiding walks in three dimensions a monte carlo study we consider self avoiding walks on the simple cubic lattice with a unit degree vertex at the origin and confined to the half space in addition the walks interact with the plane z 0 and have a vertex vertex interaction within the walk so that the walk can adsorb at the surface z 0 and also undergo collapse we investigate the interaction between collapse and adsorption using monte carlo methods and explore the form of the phase diagram

a one dimensional analysis for the probability of error of linear classifiers for normally distributed classes computing the probability of error is an important problem in evaluating classifiers when dealing with normally distributed classes this problem becomes intricate due to the fact that there is no closed form expression for integrating the probability density function in this paper we derive lower and upper bounds for the probability of error for a linear classifier where the random vectors representing the underlying classes obey the multivariate normal distribution the expression of the error is derived in the one dimensional space independently of the dimensionality of the original problem based on the two bounds we propose an approximating expression for the error of a generic linear classifier in particular we derive the corresponding bounds and the expression for approximating the error of fisher s classifier our empirical results on synthetic data including up to two hundred dimensional featured samples show that the computations for the error are extremely fast and quite accurate it differs from the actual error in at most e 0 0184340683 the scheme has also been successfully tested on real life data sets drawn from the uci machine learning repository

explicit magnification control of self organizing maps for forbidden data in this paper we examine the scope of validity of the explicit self organizing map som magnification control scheme of bauer 1996 on data for which the theory does not guarantee success namely data that are n dimensional nges2 and whose components in the different dimensions are not statistically independent the bauer algorithm is very attractive for the possibility of faithful representation of the probability density function pdf of a data manifold or for discovery of rare events among other properties since theoretically unsupported data of higher dimensionality and higher complexity would benefit most from the power of explicit magnification control we conduct systematic simulations on forbidden data for the unsupported n 2 cases that we investigate the simulations show that even though the magnification exponent alphaachieved achieved by magnification control is not the same as the desired alphadesired alphaachieved systematically follows alphadesired with a slowly increasing positive offset we show that for simple synthetic higher dimensional data information theoretically optimum pdf matching alphaachieved 1 can be achieved and that negative magnification has the desired effect of improving the detectability of rare classes in addition we further study theoretically unsupported cases with real data

a collapse transition in a directed walk model the authors consider a directed walk model of linear polymers in dilute solution with an energy associated with the number of near neighbour contacts in the walk for this model they can derive an exact expression for the generating function in two variables conjugate to the number of steps and the number of contacts they discuss the analytic structure of this generating function and identify the transition corresponding to collapse

local feature weighting in nearest prototype classification the distance metric is the corner stone of nearest neighbor nn based methods and therefore of nearest prototype np algorithms that is because they classify depending on the similarity of the data when the data is characterized by a set of features which may contribute to the classification task in different levels feature weighting or selection is required sometimes in a local sense however local weighting is typically restricted to nn approaches in this paper we introduce local feature weighting lfw in np classification lfw provides each prototype its own weight vector opposite to typical global weighting methods found in the np literature where all the prototypes share the same one providing each prototype its own weight vector has a novel effect in the borders of the voronoi regions generated they become nonlinear we have integrated lfw with a previously developed evolutionary nearest prototype classifier enpc the experiments performed both in artificial and real data sets demonstrate that the resulting algorithm that we call lfw in nearest prototype classification lfw npc avoids overfitting on training data in domains where the features may have different contribution to the classification task in different areas of the feature space this generalization capability is also reflected in automatically obtaining an accurate and reduced set of prototypes

composite models of polygons a composite polygon is composed of a lattice polygon in the square lattice which contains in its interior an internal structure which may also be a lattice polygon or a lattice tree or a lattice animal or a lattice disc or a collection of these the properties of composite polygons are considered in this manuscript in particular i shall consider the growth constants and generating functions of these models as well as the statistical mechanics of interacting models of composite polygons it is shown that there is an adsorption transition of the internal structure on the containing polygon and a transition which corresponds to the inflation of the containing polygon by the internal structure

a novel hybrid linear nonlinear classifier for two class classification theory algorithm and applications classifier design for a given classification task needs to take into consideration both the complexity of the classifier and the size of the dataset that is available for training the classifier with limited training data as often is the situation in computer aided diagnosis of medical images a classifier with simple structure e g a linear classifier is more robust and therefore preferred we propose a novel two class classifier which we call a hybrid linear nonlinear classifier hlnlc that involves two stages the input features are linearly combined to form a scalar variable in the first stage and then the likelihood ratio of the scalar variable is used as the decision variable for classification we first develop the theory of hlnlc by assuming that the feature data follow normal distributions we show that the commonly used fisher s linear discriminant function is generally not the optimal linear function in the first stage of the hlnlc we formulate an optimization problem to solve for the optimal linear function in the first stage of the hlnlc i e the linear function that maximizes the area under the receiver operating characteristic roc curve of the hlnlc for practical applications we propose a robust implementation of the hlnlc by making a loose assumption that the two class feature data arise from a pair of latent rather than explicit multivariate normal distributions the novel hybrid classifier fills a gap between linear discriminant analysis lda and quadratic discriminant analysis qda in the sense that both its theoretical performance and its complexity lie between those of the lda and those of the qda simulation studies show that the hybrid linear nonlinear classifier performs better than lda without increasing the classifier complexity accordingly with a finite number of training samples the hlnlc can perform better than that of the ideal observer due to its simplicity finally we demonstrate the application of the hlnlc in computer aided diagnosis of breast lesions in ultrasound images

brief paper necessary conditions for hadamard factorizations of hurwitz polynomials a property of hurwitz polynomials is related with the hadamard product garloff and wagner proved that hadamard products of hurwitz polynomials are hurwitz polynomials and garloff and shrinivasan shown that there are hurwitz polynomials of degree 4 which do not have a hadamard factorization into two hurwitz polynomials of the same degree 4 in this paper we give necessary conditions for an even degree hurwitz polynomial to have a hadamard factorization into two even degree hurwitz polynomials such conditions are given in terms of the coefficients of the given polynomial alone furthermore we show that if an odd degree hurwitz polynomial has a hadamard factorization then a system of nonlinear inequalities has at least one solution

study of the θ point by enumeration of self avoiding walks on the triangular lattice the author reports series expansion analyses of self avoiding walks with nearest neighbour bond interactions the estimates 2 nu t 1 07 or 0 05 and phi 0 64 or 0 05 for the correlation and crossover exponents at the theta point were obtained by examining the number of walks and the end to end distance data up to 16 steps on the triangular lattice

the variational iteration method a highly promising method for solving the system of integro differential equations this paper applies he s variational iteration method for solving two systems of volterra integro differential equations the solution process is illustrated and various physically relevant results are obtained comparison of the obtained results with exact solutions shows that the used method is an effective and highly promising method for various classes of both linear and nonlinear integro differential equations

hierarchical mixtures of experts and the em algorithm we present a tree structured architecture for supervised learning the statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models glim s learning is treated as a maximum likelihood problem in particular we present an expectation maximization em algorithm for adjusting the parameters of the architecture we also develop an on line learning algorithm in which the parameters are updated incrementally comparative simulation results are presented in the robot dynamics domain

surface critical exponents for models of polymer collapse and adsorption the universality of the theta and theta points the surface critical exponents are estimated both in ordinary and in special regimes from exact series expansions of up to 28 terms for a model of the theta point they are found to be in agreement with those derived for the theta point confirming the conjecture that the theta and theta points lie in the same universality class some essential features of the phase diagram for a self interacting self avoiding polymer in solution are also calculated to a higher degree of accuracy than previously obtained

adsorption of uniform lattice animals with specified topology the author studies the effects of topology on the free energy of uniform lattice animals interacting with a surface topology is specified by fixing an abstract graph tau and the lattice animals considered are embeddings of tau in the square and simple cubic lattice he proves that such embeddings in the simple cubic lattice and interacting with a plane have the same free energy as self avoiding walks independent of the choice of tau and independent of whether or not the embeddings are restricted to be uniform for embeddings in the square lattice and interacting with a line he proves that the free energy may differ from that for walks depending on whether tau has a cut edge further restricting the embeddings to be uniform forces the free energy to be different from that for walks for all tau except the tau corresponding to walks and we obtain bounds on the free energy which depend on the number of branches cycles and vertices of degree 3 and 4 in the graph

adsorption of self avoiding walks at an impenetrable plane in the expanded phase a monte carlo study we consider self avoiding walks on the simple cubic lattice confined to the half space z0 in addition the walks interact with the plane z 0 and have a vertex vertex interaction the walks can adsorb at the plane z 0 the location of the adsorption phase transition depends in general on the contact interaction we use monte carlo methods to investigate the form of the adsorption phase boundary in the expanded phase region

multiple markov chain monte carlo study of adsorbing self avoiding walks in two and in three dimensions a self avoiding walk adsorbing on a line in the square lattice and on a plane in the cubic lattice is studied numerically as a model of an adsorbing polymer in dilute solution the walk is simulated by a multiple markov chain monte carlo implementation of the pivot algorithm for self avoiding walks vertices in the walk that are visits in the adsorbing line or plane are weighted by e t he critical value of where the walk adsorbs on the adsorbing line or adsorbing plane is determined by considering energy ratios and approximations to the free energy we determine that the critical values of are c 0 565 0 010 in the square lattice 0 288 0 020 in the cubic lattice in addition the value of the crossover exponent is determined 0 501 0 015 in the square lattice 0 5005 0 0036 in the cubic lattice metric quantities including the mean square radius of gyration are also considered as well as rescaling of the specific heat and free energy as the critical point is approached

classification using geometric level sets a variational level set method is developed for the supervised classification problem nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin based loss and a geometric regularization term new to machine learning the surface area of the decision boundary this geometric level set classifier is analyzed in terms of consistency and complexity through the calculation of its e entropy for multicategory classification an efficient scheme is developed using a logarithmic number of decision functions in the number of classes rather than the typical linear number of decision functions geometric level set classification yields performance results on benchmark data sets that are competitive with well established methods

self avoiding walks interacting with a surface discusses two models of polymer adsorption in one model a self avoiding walk on a d dimensional lattice interacts with a d 1 dimensional hyperplane in the other model this walk must also lie in or on one side of this hyperplane both models exhibit non analytic behaviour corresponding to a phase transition but these phase transitions do not occur at the same point the authors give numerical estimates of the locations of these transitions

interacting self avoiding walks and polygons in three dimensions self interacting walks and polygons on the simple cubic lattice undergo a collapse transition at the point we consider self avoiding walks and polygons with an additional interaction between pairs of vertices which are unit distance apart but not joined by an edge of the walk or polygon we prove that these walks and polygons have the same limiting free energy if the interactions between nearest neighbour vertices are repulsive the attractive interaction regime is investigated using monte carlo methods and we find evidence that the limiting free energies are also equal here in particular this means that these models have the same point in the asymptotic limit the dimensions and shapes of walks and polygons are also examined as a function of the interaction strength

collapse of two dimensional linear polymers we study the collapse transition of a two dimensional very long polymer the model we consider is a lattice model where the chain is represented by a self avoiding walk with nearest neighbor attraction by using the transfer matrix technique we calculate exactly the thermal and geometrical properties of the polymer on strips of finite width we then use finite size scaling to determine the values of the tricritical point exponentsv1 0 55 0 01vu 1 15 0 15 1 v1 1 80 0 05 we compare these results to the other values already proposed in the literature

face recognition based on the uncorrelated discriminant transformation abstract the extraction of discriminant features is the most fundamental and important problem in face recognition this paper presents a method to extract optimal discriminant features for face images by using the uncorrelated discriminant transformation and kl expansion experiments on the orl database and the nust603 database have been performed experimental results show that the uncorrelated discriminant transformation is superior to the foley sammon discriminant transformation and the new method to extract uncorrelated discriminant features for face images is very effective an error rate of 2 5 is obtained with the experiments on the orl database an average error rate of 1 2 is obtained with the experiments on the nust603 database experiments show that by extracting uncorrelated discriminant features face recognition could be performed with higher accuracy on lower than 16 16 resolution mosaic images it is suggested that for the uncorrelated discriminant transformation the optimal face image resolution can be regarded as the resolution m n which makes the dimensionality n mn of the original image vector space be larger and closer to the number of known face classes

propagation and stability of waves of electrical activity in the cerebral cortex nonlinear equations are introduced to model the behavior of the waves of cortical electrical activity that are responsible for signals observed in electroencephalography these equations incorporate nonlinearities axonal and dendritic lags excitatory and inhibitory neuronal populations and the two dimensional nature of the cortex while rendering nonlinear features far more tractable than previous formulations both analytically and numerically the model equations are first used to calculate steady state levels of cortical activity for various levels of stimulation dispersion equations for linear waves are then derived analytically and an analytic expression is found for the linear stability boundary beyond which a seizure will occur the effects of boundary conditions in determining global eigenmodes are also studied in various geometries and the corresponding eigenfrequencies are found numerical results confirm the analytic ones which are also found to reproduce existing results in the relevant limits thereby elucidating the limits of validity of previous approximations

examination of the theta point from exact enumeration of self avoiding walks self avoiding walks on the square lattice with nearest neighbour attractive interactions are investigated as a model for the two dimensional version of a polymer in dilute solution temperature dependences of the exponent nu and the free energy of the chain are estimated from the exact enumeration data for up to 20 steps the value of nu at the theta point disagrees with the mean field theory the end distance distribution function at the theta point is also examined

collapsing and adsorbing polygons the adsorption transition in the phase diagram of a self interacting lattice polygon is examined the polygon has a nearest neighbour contact fugacity and the interaction between the polygon and an impenetrable wall is modelled by a visit fugacity which is conjugate to the number of vertices of the polygon incident with the wall the partition function of this model is z c y z d p v cp c v c y v z c where p c v c is the number of polygons with c nearest neighbour contacts v visits to the wall and n edges and counted up to translations parallel to the wall the limiting free energy of this model is f c y z d limn 1 1 logz c y z and it is known to be a non analytic function of y for each z 1 for all z2 0 1

a novel method for fisher discriminant analysis abstract a novel model for fisher discriminant analysis is developed in this paper in the new model maximal fisher criterion values of discriminant vectors and minimal statistical correlation between feature components extracted by discriminant vectors are simultaneously required then the model is transformed into an extreme value problem in the form of an evaluation function based on the evaluation function optimal discriminant vectors are worked out experiments show that the method presented in this paper is comparative to the winner between fslda and ulda

prime discriminant simplicial complex the structure representation of data distribution plays an important role in understanding the underlying mechanism of generating data in this paper we propose the prime discriminant simplicial complex pdsc by utilizing persistent homology to capture such structures assuming that each class is represented with a prime simplicial complex we classify unlabeled samples based on the nearest projection distances from the samples to the simplicial complexes we also extend the extrapolation ability of these complexes with a projection constraint term experiments in simulated and practical datasets indicate that compared with several published algorithms the proposed pdsc approaches achieve promising performance without losing structure representation

novelty detection using level set methods this paper presents a level set boundary description lsbd approach for novelty detection that treats the nonlinear boundary directly in the input space the proposed approach consists of level set function lsf construction boundary evolution and termination of the training process it employs kernel density estimation to construct the lsf of the initial boundary for the training data set then a sign of the lsf based algorithm is proposed to evolve the boundary and make it fit more tightly in the data distribution the training process terminates when an expected fraction of rejected normal data is reached the evolution process utilizes the signs of the lsf values at all training data points to decide whether to expand or shrink the boundary extensive experiments are conducted on benchmark data sets to evaluate the proposed lsbd method and compare it against four representative novelty detection methods the experimental results demonstrate that the novelty detector modeled with the proposed lsbd can effectively detect anomalies

brief paper smooth trivial vector bundle structure of the space of hurwitz polynomials due to the importance of the robustness of stable systems the properties of the set of hurwitz real polynomials are interesting to study among these properties is that the set is an open and not a convex set and recently it was proved that the set of hurwitz polynomials of degree n with positive coefficients h n is contractible now we will prove that the set h n is a smooth trivial vector bundle over h n k of rank k

adsorption and collapse of self avoiding walks at a defect plane we consider self avoiding walks and polygons on the simple cubic lattice with a vertex vertex interaction i e a contact interaction which also interact with a defect plane z 0 the walks or polygons can undergo a collapse transition and can also adsorb at the defect plane for the polygon case we prove that the limiting free energy exists and show that there is an adsorption transition for each finite value of the vertex vertex interaction we use monte carlo methods to investigate the form of the phase diagram for the walk problem

what s wrong with fisher criterion in this paper a seemingly contradictory experimental result concerning fisher criterion is first exhibited then we analyze this result from the statistical correlation point of view and give a reasonable explanation more importantly we emphasize that fisher criterion is not an absolute criterion and it should be associated with the statistical correlation together to assess the discrimination of a set of discriminant vectors

theory analysis on fslda and ulda abstract it is first revealed that the fisher criterion ratio of each fslda discriminant vector must not be less than that of corresponding ulda discriminant vector so the phenomenon in yang et al pattern recognition 35 2002 2665 is not strange but certain and must be available in all experiments in addition it is also first illustrated that in fact ulda discriminant vectors are the s t orthogonal eigenvectors of a generalized eigenequation as a result the algorithms to obtain s t orthogonal eigenvectors of the generalized eigenequation are equivalent to the ulda algorithm consequently it is possible to work out ulda discriminant vectors more efficiently

a fast kernel based nonlinear discriminant analysis for multi class problems nonlinear discriminant analysis may be transformed into the form of kernel based discriminant analysis thus the corresponding discriminant direction can be solved by linear equations from the view of feature space the nonlinear discriminant analysis is still a linear method and it is provable that in feature space the method is equivalent to fisher discriminant analysis we consider that one linear combination of parts of training samples called significant nodes can replace the total training samples to express the corresponding discriminant vector in feature space to some extent in this paper an efficient algorithm is proposed to determine significant nodes one by one the principle of determining significant nodes is simple and reasonable and the consequent algorithm can be carried out with acceptable computation cost depending on the kernel functions between test samples and all significant nodes classification can be implemented the proposed method is called fast kernel based nonlinear method fknm it is noticeable that the number of significant nodes may be much smaller than that of the total training samples as a result for two class classification problems the fknm will be much more efficient than the naive kernel based nonlinear method nknm the fknm can be also applied to multi class via two approaches one against the rest and one against one although there is a view that one against one is superior to one against the rest in classification efficiency it seems that for the fknm one against the rest is more efficient than one against one experiments on benchmark and real datasets illustrate that for two class and multi class classifications the fknm is effective feasible and much efficient

adsorbing and collapsing trees self interacting branched polymers interacting with a wall can be modelled by lattice trees in a half space with a nearest neighbour contact fugacity and a visit fugacity conjugate to the number of visits the tree makes to the wall which is the boundary of the half space we show that there is a limiting free energy in this model and that it is a non analytic function of the visit fugacity for every finite and fixed value of the contact fugacity this implies the existence of an adsorption transition in this model and there is a critical curve in the phase diagram which separates the phase of desorbed trees from a phase of adsorbed trees moreover we show that for all finite values of the contact fugacity and the adsorption transition occurs at a strictly attractive value of the interaction between the tree and the wall

supervised dimensionality reduction via sequential semidefinite programming many dimensionality reduction problems end up with a trace quotient formulation since it is difficult to directly solve the trace quotient problem traditionally the trace quotient cost function is replaced by an approximation such that the generalized eigenvalue decomposition can be applied in contrast we directly optimize the trace quotient in this work it is reformulated as a quasi linear semidefinite optimization problem which can be solved globally and efficiently using standard off the shelf semidefinite programming solvers also this optimization strategy allows one to enforce additional constraints for example sparseness constraints on the projection matrix we apply this optimization framework to a novel dimensionality reduction algorithm the performance of the proposed algorithm is demonstrated in experiments by several uci machine learning benchmark examples usps handwritten digits as well as orl and yale face data

quantitative analysis of nonlinear embedding a lot of nonlinear embedding techniques have been developed to recover the intrinsic low dimensional manifolds embedded in the high dimensional space however the quantitative evaluation criteria are less studied in literature the embedding quality is usually evaluated by visualization which is subjective and qualitative the few existing evaluation methods to estimate the embedding quality neighboring preservation rate for example are not widely applicable in this paper we propose several novel criteria for quantitative evaluation by considering the global smoothness and co directional consistence of the nonlinear embedding algorithms the proposed criteria are geometrically intuitive simple and easy to implement with a low computational cost experiments show that our criteria capture some new geometrical properties of the nonlinear embedding algorithms and can be used as a guidance to deal with the embedding of the out of samples

extract minimum positive and maximum negative features for imbalanced binary classification in an imbalanced dataset the positive and negative classes can be quite different in both size and distribution this degrades the performance of many feature extraction methods and classifiers this paper proposes a method for extracting minimum positive and maximum negative features in terms of absolute value for imbalanced binary classification this paper develops two models to yield the feature extractors model 1 first generates a set of candidate extractors that can minimize the positive features to be zero and then chooses the ones among these candidates that can maximize the negative features model 2 first generates a set of candidate extractors that can maximize the negative features and then chooses the ones that can minimize the positive features compared with the traditional feature extraction methods and classifiers the proposed models are less likely affected by the imbalance of the dataset experimental results show that these models can perform well when the positive class and negative class are imbalanced in both size and distribution

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

geometric mean for subspace selection subspace selection approaches are powerful tools in pattern classification and data visualization one of the most important subspace approaches is the linear dimensionality reduction step in the fisher s linear discriminant analysis flda which has been successfully employed in many fields such as biometrics bioinformatics and multimedia information management however the linear dimensionality reduction step in flda has a critical drawback for a classification task with c classes if the dimension of the projected subspace is strictly lower than c 1 the projection to a subspace tends to merge those classes which are close together in the original feature space if separate classes are sampled from gaussian distributions all with identical covariance matrices then the linear dimensionality reduction step in flda maximizes the mean value of the kullback leibler kl divergences between different classes based on this viewpoint the geometric mean for subspace selection is studied in this paper three criteria are analyzed 1 maximization of the geometric mean of the kl divergences 2 maximization of the geometric mean of the normalized kl divergences and 3 the combination of 1 and 2 preliminary experimental results based on synthetic data uci machine learning repository and handwriting digits show that the third criterion is a potential discriminative subspace selection method which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in flda and its several representative extensions

a higher order finite difference method for solving a system of integro differential equations abstract a finite difference method and gauss method of numerical integration are used to approximate the integro differential system of eq 1 with the global error z h o h4 the resulting system of algebraic equations is solved by efficient implicit iterations a mathematica module is designed for the purpose of testing and using the method an example of an integral differential equation with the green s function as the kernel is solved

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

a theorem on the uncorrelated optimal discriminant vectors this paper proposes a theorem on the uncorrelated optimal discriminant vectors uodvs it is proved that the classical optimal discriminant vectors are equivalent to uodv which can be used to extract l 1 uncorrelated discriminant features for l class problems without losing any discriminant information in the meaning of fisher discriminant criterion function experiments on concordia university cenparmi handwritten numeral database indicate that uodvs are much more powerful than the foley sammon optimal discriminant vectors it is believed that when the number of training samples is large the conjugate orthogonal set of discriminant vectors can be much more powerful than the orthogonal set of discriminant vectors

growing a hypercubical output space in a self organizing feature map neural maps project data from an input space onto a neuron position in a often lower dimensional output space grid in a neighborhood preserving way with neighboring neurons in the output space responding to neighboring data points in the input space a map learning algorithm can achieve an optimal neighborhood preservation only if the output space topology roughly matches the effective structure of the data in the input space we here present a growth algorithm called the gsom or growing self organizing map which enhances a widespread map self organization process kohonen s self organizing feature map sofm by an adaptation of the output space grid during learning the gsom restricts the output space structure to the shape of a general hypercubical shape with the overall dimensionality of the grid and its extensions along the different directions being subject of the adaptation this constraint meets the demands of many larger information processing systems of which the neural map can be a part we apply our gsom algorithm to three examples two of which involve real world data using recently developed methods for measuring the degree of neighborhood preservation in neural maps we find the gsom algorithm to produce maps which preserve neighborhoods in a nearly optimal fashion

asymmetric principal component and discriminant analyses for pattern classification this paper studies the roles of the principal component and discriminant analyses in the pattern classification and explores their problems with the asymmetric classes and or the unbalanced training data an asymmetric principal component analysis apca is proposed to remove the unreliable dimensions more effectively than the conventional pca targeted at the two class problem an asymmetric discriminant analysis in the apca subspace is proposed to regularize the eigenvalue that is in general a biased estimate of the variance in the corresponding dimension these efforts facilitate a reliable and discriminative feature extraction for the asymmetric classes and or the unbalanced training data the proposed approach is validated in the experiments by comparing it with the related methods it consistently achieves the highest classification accuracy among all tested methods in the experiments

copolymers at selective interfaces new bounds on the phase diagram we investigate the phase diagram of disordered copolymers at the interface between two selective solvents and in particular its weak coupling behavior encoded in the slope mc of the critical line at the origin we focus on the directed walk case which has turned out to be in spite of the apparent simplicity extremely challenging in mathematical terms the partition function of such a model does not depend on all the details of the markov chain that models the polymer but only on the time elapsed between successive returns to zero and on whether the walk is in the upper or lower half plane between such returns this observation leads to a natural generalization of the model in terms of arbitrary laws of return times the most interesting case being the one of return times with power law tails with exponent 1 1 2 in the case of the symmetric random walk the main results we present here are

complete large margin linear discriminant analysis using mathematical programming approach in this paper we develop a novel dimensionality reduction dr framework coined complete large margin linear discriminant analysis clmlda inspired by several recently proposed dr methods clmlda constructs two mathematical programming models by maximizing the minimum distance between each class center and the total class center respectively in the null space of within class scatter matrix and its orthogonal complementary space in this way clmlda not only makes full use of the discriminative information contained in the whole feature space but also overcome the weakness of linear discriminant analysis lda in dealing with the class separation problem the solutions of clmlda follow from solving two nonconvex optimization problems each of which is transformed to a series of convex quadratic programming problems by using the constrained concave convex procedure first and then solved by off the shelf optimization toolbox experiments on both toy and several publicly available databases demonstrate its feasibility and effectiveness

collapse transition of self avoiding walks on a square lattice in the bulk and near a linear wall the universality classes of the θ and θ points using the scanning method we study by extensive simulations the theta transition of self avoiding walks with nearest neighbor attractions in the bulk and near a linear wall on a square lattice consistent results for the two models are obtained for the radius of gyration but not for the end to end distance our results for the exponents nu and gamma agree with those derived by duplantier and saleur phys rev lett 59 539 1987 for the theta prime model however our results for the crossover exponent phi which constitute upper bounds for the correct value are significantly larger than the value of phi theta prime at the ordinary point our result for gamma sub 1 is larger even though not much than the value suggested by vanderzande stella and seno phys rev lett 67 2757 1991 for the theta prime model

self organizing nets for optimization given some optimization problem and a series of typically expensive trials of solution candidates sampled from a search space how can we efficiently select the next candidate we address this fundamental problem by embedding simple optimization strategies in learning algorithms inspired by kohonen s self organizing maps and neural gas networks our adaptive nets or grids are used to identify and exploit search space regions that maximize the probability of generating points closer to the optima net nodes are attracted by candidates that lead to improved evaluations thus quickly biasing the active data selection process toward promising regions without loss of ability to escape from local optima on standard benchmark functions our techniques perform more reliably than the widely used covariance matrix adaptation evolution strategy the proposed algorithm is also applied to the problem of drag reduction in a flow past an actively controlled circular cylinder leading to unprecedented drag reduction

on image analysis by moments research has been performed investigating the use of moments for pattern recognition in recent years the basic problem of the influence of discretization and noise on moment accuracy as object descriptors has been barely investigated in this paper the detailed error analysis involved in the moment method is discussed several new techniques to increase the accuracy and efficiency of moment descriptor are proposed we utilize these results for the problem of image reconstruction from the orthogonal legendre moments computed from discrete and noisy data the automatic selection of an optimal number of moments is also discussed

rapid and brief communication uncorrelated heteroscedastic lda based on the weighted pairwise chernoff criterion we propose an uncorrelated heteroscedastic lda uhlda technique which extends the uncorrelated lda ulda technique by integrating the weighted pairwise chernoff criterion the uhlda can extract discriminatory information present in both the differences between per class means and the differences between per class covariance matrices meanwhile the extracted feature components are statistically uncorrelated the maximum number of which exceeds the limitation of the ulda experimental results demonstrate the promising performance of our proposed technique compared with the ulda

a simple algorithm for exact solutions of systems of linear and nonlinear integro differential equations a simple algorithm is used to achieve exact solutions of systems of linear and nonlinear integro differential equations arising in many scientific and engineering applications the algorithm does not need to find the adomain polynomials to overcome the nonlinear terms in adomain decomposition method adm it does not need to create a homotopy with an embedding parameter as in homotopy perturbation method hpm and optimal homotopy asymptotic method oham unlike vim it does not need to find lagrange multiplier in this manuscript no restrictive assumptions are taken for nonlinear terms the applied algorithm consists of a single series in which the unknown constants are determined by the simple means described in the manuscript the outcomes gained by this algorithm are in excellent concurrence with the exact solution and hence proved that this algorithm is effective and easy four systems of linear and nonlinear integro differential equations are solved to prove the above claims and the outcomes are compared with the exact solutions as well as with the outcomes gained by already existing methods

adsorption and collapse of self avoiding walks and polygons in three dimensions we consider self avoiding walks and polygons on the simple cubic lattice confined to the half space and interacting with the plane z 0 in addition there is a short range vertex vertex interaction in the walk or polygon which can lead to a collapse transition we explore the interaction between collapse and adsorption in these systems and discuss the form of the phase diagram key results include a proof of the existence of an adsorption transition for polygons for every value of the vertex vertex interaction a corresponding proof for walks when the vertex vertex interaction term is repulsive and a proof that if polygons exhibit a collapse transition then the phase boundary between the expanded and desorbed phase and the collapsed and desorbed phase must be a straight line

single site localization via maximum discrimination multipath fingerprinting a novel approach to single site localization based on maximum discrimination multipath fingerprinting is presented in contrast to the existing approach which extracts each fingerprint only from the data of that location the new approach uses also the data of all the other locations in the database and leverages it to extract a fingerprint that is as different as possible from the other fingerprints in the database the performance of this approach validated with both simulated and real data is superior to the existing approach demonstrating single site localization accuracy of 1 m in typical indoor environments the new approach has also a lower computational complexity

decision manifolds a supervised learning algorithm based on self organization in this paper we present a neural classifier algorithm that locally approximates the decision surface of labeled data by a patchwork of separating hyperplanes which are arranged under certain topological constraints similar to those of self organizing maps soms we take advantage of the fact that these boundaries can often be represented by linear ones connected by a low dimensional nonlinear manifold thus influencing the placement of the separators the resulting classifier allows for a voting scheme that averages over the classification results of neighboring hyper planes our algorithm is computationally efficient both in terms of training and classification further we present a model selection method to estimate the topology of the classification boundary we demonstrate the algorithm s usefulness on several artificial and real world data sets and compare it to the state of the art supervised learning algorithms

imbalanced data classification using second order cone programming support vector machines learning from imbalanced data sets is an important machine learning challenge especially in support vector machines svm where the assumption of equal cost of errors is made and each object is treated independently second order cone programming svm socp svm studies each class separately instead providing quite an interesting formulation for the imbalanced classification task this work presents a novel second order cone programming socp formulation based on the lp svm formulation principle the bound of the vc dimension is loosened properly using the l norm and the margin is directly maximized using two margin variables associated with each class a regularization parameter c is considered in order to control the trade off between the maximization of these two margin variables the proposed method has the following advantages it provides better results since it is specially designed for imbalanced classification and it reduces computational complexity since one conic restriction is eliminated experiments on benchmark imbalanced data sets demonstrate that our approach accomplishes the best classification performance compared with the traditional socp svm formulation and with cost sensitive formulations for linear svm

solving linear integro differential equations system by using rationalized haar functions method in this paper we use rationalized haar functions to estimate the solution of linear integro differential equations system properties of rationalized haar functions are first presented and the operational matrix of the product of two rationalized haar functions vector is utilized to reduce the computation of linear integro differential equations system to some algebraic equations by using numerical examples we show our estimation have a good degree of accuracy

free energy of self interacting uniform stars we consider uniform star polymers on a variety of lattices with an additional contact interaction between pairs of vertices which are unit distance apart and are not joined by an edge of the star we present some rigorous results and other evidence which indicate that these systems have the same limiting free energy as self interacting self avoiding walks we discuss the extension of these results to other homeomorphism types and to systems with an additional surface interaction term