an algorithm for linearly constrained convex nondifferentiable minimization problems abstract a readily implementable algorithm is proposed for minimizing any convex not necessarily differentiable function f of several variables subject to a finite number of linear constraints the algorithm requires only the calculation of f at designated feasible points at each iteration a lower polyhedral approximation to f is constructed from a few previously calculated subgradients and an aggregate subgradient the recursively updated aggregate subgradient accumulates the subgradient information to deal with nondifferentiability of f the polyhedral approximation and the linear constraints generate constraints in the search direction finding subproblem that is a quadratic programming problem then a step length is found by approximate line search it is shown that the algorithm converges to a solution if any

plurality voting based multiple classifier systems statistically independent with respect to dependent classifier sets abstract the simultaneous use of multiple classifiers has been shown to provide performance improvement in classification problems the selection of an optimal set of classifiers is an important part of multiple classifier systems and the independence of classifier outputs is generally considered to be an advantage for obtaining better multiple classifier systems in this paper the need for the classifier independence is interrogated from classification performance point of view the performance achieved with the use of classifiers having independent joint distributions is compared to some other classifiers which are defined to have best and worst joint distributions these distributions are obtained by formulating the combination operation as an optimization problem the analysis revealed several important observations about classifier selection which are then used to analyze the problem of selecting an additional classifier to be used with the available multiple classifier system

analyticity and nonexistence of classical steady hele shaw fingers this paper concerns analyticity of a classical steadily translating nger in a hele shaw cell and nonexistence of solutions when the relative nger width is smaller than 1 it is proven that any classical solution to the nger problem if it exists for sufciently small but nonzero surface tension is close to some saffman taylor zero surface tension solution and satises some algebraic decay conditions at 1 must belong to the analytic function space a0 as dened in section 1 and chosen in a previous study 34 of the existence of nger solutions further it is proven that for any x ed 2 0 1 there can be no classical steadynger solution when surface tension is sufciently small which contradicts a previous conclusion based on numerical simulation c 2002 wiley periodicals inc

a novel approach for the determination of asymptotic expansions of certain oscillatory integrals abstract a standard method for deriving asymptotic expansion consists of applying integration by parts to standard integral representation in this paper we consider cases in which this method is ineffective to deal with these we derive alternative integral representations which are amenable to this and other standard methods

a new algorithm for distorted fingerprints matching based on normalized fuzzy similarity measure coping with nonlinear distortions in fingerprint matching is a challenging task this paper proposes a novel algorithm normalized fuzzy similarity measure nfsm to deal with the nonlinear distortions the proposed algorithm has two main steps first the template and input fingerprints were aligned in this process the local topological structure matching was introduced to improve the robustness of global alignment second the method nfsm was introduced to compute the similarity between the template and input fingerprints the proposed algorithm was evaluated on fingerprints databases of fvc2004 experimental results confirm that nfsm is a reliable and effective algorithm for fingerprint matching with nonliner distortions the algorithm gives considerably higher matching scores compared to conventional matching algorithms for the deformed fingerprints

on the impact of fusion strategies on classification errors for large ensembles of classifiers the growing availability of sensor networks brings practical situations where a large number of classifiers can be used for building a classifier ensemble in the most general case involving sensor networks the classifiers are fed with multiple inputs collected at different locations however classifier fusion is often studied within an idealized formulation where each classifier is fed with the same point in the feature space and estimate the posterior class probability given this input we first expand this formulation to situations where classifiers are fed with multiple inputs demonstrating the relevance of the formulation to situations involving sensor networks and a large number of classifiers following that we determine the rate of convergence of the classification error of a classifier ensemble for three fusion strategies average median and maximum when the number of classifiers becomes large as the size of the ensemble increases the best strategy is defined as the one that results in fastest convergence of the classification error to zero the best strategy is analytically shown to depend on the distribution of the individual classification errors average is the best for normal distributions maximum is the best for uniform distributions and median is the best for cauchy distributions the general effect of heavy tailedness is also analytically investigated for the average and median strategies the median strategy is shown to be robust to heavy tailedness while performance of the average strategy is shown to degrade as heavy tailedness becomes more pronounced the combined effects of bimodality and heavy tailedness are also investigated when the number of classifiers become large

a note on asymptotic evaluation of some hankel transforms asymptotic behavior of the integral if w ejo wx f x2 xdx is investigated where jo x is the bessel function of the first kind and w is a large positive parameter it is shown that 1f w decays exponentially like ewy2 y 0 when f z is an entire function subject to a suitable growth condition a complete asymptotic expansion is obtained when f z is a meromorphic function satisfying the same growth condition similar results are given when f z has some specific branch point singularities

local classifier weighting by quadratic programming it has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers however how to combine multiple classifiers with various potentially conflicting decisions is still an open problem a rich collection of classifier combination procedures many of which are heuristic in nature have been developed for this goal in this brief we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space to this end we use local classifier accuracy estimates to weight classifier outputs specifically we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors and then use these estimates to find the best weights of classifiers to label the query the problem is formulated as a convex quadratic optimization problem which returns optimal nonnegative classifier weights with respect to the chosen objective function and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes particularly on problems with complex decision boundaries hence the results indicate that local classification accuracy based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space

iterative boolean combination of classifiers in the roc space an application to anomaly detection with hmms hidden markov models hmms have been shown to provide a high level performance for detecting anomalies in sequences of system calls to the operating system kernel using boolean conjunction and disjunction functions to combine the responses of multiple hmms in the roc space may significantly improve performance over a single best hmm however these techniques assume that the classifiers are conditional independent and their of roc curves are convex these assumptions are violated in most real world applications especially when classifiers are designed using limited and imbalanced training data in this paper the iterative boolean combination ibc technique is proposed for efficient fusion of the responses from multiple classifiers in the roc space it applies all boolean functions to combine the roc curves corresponding to multiple classifiers requires no prior assumptions and its time complexity is linear with the number of classifiers the results of computer simulations conducted on both synthetic and real world host based intrusion detection data indicate that the ibc of responses from multiple hmms can achieve a significantly higher level of performance than the boolean conjunction and disjunction combinations especially when training data are limited and imbalanced the proposed ibc is general in that it can be employed to combine diverse responses of any crisp or soft one or two class classifiers and for wide range of application domains

exponential asymptotics and boundary value problems keeping both sides happy at all orders we introduce templates for exponential asymptotic expansions that in contrast to matched asymptotic approaches enable the simultaneous satisfaction of both boundary values in classes of linear and nonlinear equations that are singularly perturbed with an asymptotic parameter graphic 1 and have a single boundary layer at one end of the interval for linear equations the template is a transseries that takes the form of a sliding ladder of exponential scales for nonlinear equations the transseries template is a two dimensional array of exponential scales that tilts and realigns asymptotic balances as the interval is traversed an exponential asymptotic approach also reveals how boundary value problems force the surprising presence of transseries in the linear case and negative powers of terms in the series beyond all orders in the nonlinear case we also demonstrate how these transseries can be resummed to generate multiple scales type approximations that can generate uniformly better approximations to the exact solution out to larger values of the perturbation parameter finally we show for a specific example how a reordering of the terms in the exponential asymptotics can lead to an acceleration of the accuracy of a truncated expansion 1 embed inline graphic 1 gif

fusion of local normalization and gabor entropy weighted features for face identification face recognition is one of the most extensively studied topics in image analysis because of its wide range of possible applications such as in surveillance access control content based video search human computer interaction electronic advertisement and more face identification is a one to n matching problem where a captured face is compared to n samples in a database in this work we propose two new methods for face identification the first one combines entropy like weighted gabor features with the local normalization of gabor features the second fuses the entropy like weighted gabor features at the score level with the local binary pattern lbp applied to the magnitude lgbp and phase lgxp components of the gabor features we used the feret ar and frgc 2 0 databases to test and compare our results with those previously published results on these databases show significant improvement relative to previously published results reaching the best performance on the feret and ar databases our methods also showed significant robustness to slight pose variations we tested the proposed methods assuming noisy eye detection to check their robustness to inexact face alignment results show that the proposed methods are robust to errors of up to 3 pixels in eye detection highlightswe propose an entropy weighted strategy over selected gabor features we fuse local normalization with gabor features to improve face identification fusion of different features improve face identification relative to cases with no fusion our results are compared advantageously on several international face databases we tested our methods with variable illumination gesticulation pose and occlusion

learn mf a random subspace approach for the missing feature problem we introduce learn mf an ensemble of classifiers based algorithm that employs random subspace selection to address the missing feature problem in supervised classification unlike most established approaches learn mf does not replace missing values with estimated ones and hence does not need specific assumptions on the underlying data distribution instead it trains an ensemble of classifiers each on a random subset of the available features instances with missing values are classified by the majority voting of those classifiers whose training data did not include the missing features we show that learn mf can accommodate substantial amount of missing data and with only gradual decline in performance as the amount of missing data increases we also analyze the effect of the cardinality of the random feature subsets and the ensemble size on algorithm performance finally we discuss the conditions under which the proposed approach is most effective

nonlinear eigenvalue problems this paper begins with a review of earlier work on extending the notion of an eigenvalue problem for a linear differential equation to an eigenvalue problem for a nonlinear differential equation in previous work it was argued that in the nonlinear context a separatrix plays the role of an eigenfunction and the initial conditions that spawn the separatrix play the role of an eigenvalue previously discussed nonlinear differential equations that have discrete eigenvalue structure include the first order equation y cos xy and the painleve transcendents p i and p ii in new work it is shown here that the concept of a nonlinear eigenvalue problem extends to huge classes of nonlinear differential equations numerical and analytical results on the eigenvalue behavior for some of these new differential equations are presented

decision combination in multiple classifier systems a multiple classifier system is a powerful solution to difficult pattern recognition problems involving large class sets and noisy input because it allows simultaneous use of arbitrary feature descriptors and classification procedures decisions by the classifiers can be represented as rankings of classifiers and different instances of a problem the rankings can be combined by methods that either reduce or rerank a given set of classes an intersection method and union method are proposed for class set reduction three methods based on the highest rank the borda count and logistic regression are proposed for class set reranking these methods have been tested in applications of degraded machine printed characters and works from large lexicons resulting in substantial improvement in overall correctness

analysis of decision boundaries in linearly combined neural classifiers combining or integrating the outputs of several pattern classifiers has led to improved performance in a multitude of applications this paper provides an analytical framework to quantify the improvements in classification results due to combining we show that combining networks linearly in output space reduces the variance of the actual decision region boundaries around the optimum boundary this result is valid under the assumption that the a posteriori probability distributions for each class are locally monotonic around the bayes optimum boundary in the absence of classifier bias the error is shown to be proportional to the boundary variance resulting in a simple expression for error rate improvements in the presence of bias the error reduction expressed in terms of a bias reduction factor is shown to be less than or equal to the reduction obtained in the absence of bias the analysis presented here facilitates the understanding of the relationships among error rates classifier boundary distributions and combining in output space

asymptotic expansions of mellin convolutions by means of analytic continuation we present a method for deriving asymptotic expansions of integrals of the form 0 f t h xt dt for small x based on analytic continuation the expansion is given in terms of two asymptotic sequences the coefficients of both sequences being mellin transforms of h and f many known and unknown asymptotic expansions of important integral transforms are derived trivially from the approach presented here this paper reconsiders earlier work of mcclure and wong explicit error terms for asymptotic expansions of stieltjes transforms j inst math appl 22 1978 129 145 exact remainders for asymptotic expansions of fractional integrals j inst math appl 24 1979 139 147 and asymptotic approximations of integrals academic press new york 1989 chaps 5 where elements of distribution theory are used and wong explicit error terms for asymptotic expansions of mellin convolutions j math anal appl 72 2 1979 740 756 where as in the present paper the asymptotic expansions are obtained without the use of distributions in this paper we re derive the expansions given in wong explicit error terms for asymptotic expansions of mellin convolutions j math anal appl 72 2 1979 740 756 by using a different approach and we obtain new results which are not present in wong explicit error terms for asymptotic expansions of mellin convolutions j math anal appl 72 2 1979 740 756 a proof of the asymptotic character of the expansions and accurate error bounds

exactification of the asymptotics for bessel and hankel functions exactification is the process of showing how a complete asymptotic expansion can be evaluated to yield exact values of the original function it represents because the process does not involve neglecting the remainders of truncated component asymptotic series within a complete asymptotic expansion techniques for evaluating divergent series are required one such technique is borel summation but in many instances it can be computationally slow and consequently lacking in precision another is the numerical technique of mellin barnes regularization which is capable of evaluating divergent series with great precision far more rapidly than borel summation here both techniques are presented in the evaluation of exact values for bessel and hankel functions from their complete asymptotic expansions

a statistical unified framework for rank based multiple classifier decision combination abstract this study presents a theoretical investigation of the rank based multiple classifier decision combination problem with the aim of providing a unified framework to understand a variety of such systems the combination of the decisions of more than one classifiers with the aim of improving overall system performance is a concept of general interest in pattern recognition as a viable alternative to designing a single sophisticated classifier the problem of combining the classifier decisions in the raw form of candidate class rankings is formulated as a discrete optimization problem the objective function to be maximized is selected as the overall probability of correct decision this formulation introduces a set of observation statistics about the joint behavior of the classifiers which are to be estimated by observing the classifiers operated on a cross validation test set the resulting binary programming problem is shown to have a simple and global optimum solution but which also necessitates a prohibitive number of observation statistics from the objective function expansion the problem observation space is defined and a method based on partitioning is introduced to reduce its prohibitive dimensionality within this partitioning formalism called as the partitioned observation space pos theory the number of behavior observation statistics can be reduced to levels which are feasible to estimate from the available cross validation test data it is shown by examples that such specific partitionings can be defined when reasonable assumptions or prior knowledge about the classifiers are incorporated into the problem domain it is also demonstrated that certain specific partitionings of the classifier observation space effectively lead to the highest rank borda count and logistic regression rank based decision combination methods from the literature the analysis presented is general and promises to lead to a class of algorithms for rank based decision combination the potential of the theory and practical issues in implementation are illustrated by applying it in a real life phonetic discrimination problem from speech pattern classification with encouraging results

exactification of the method of steepest descents the bessel functions of large order and argument the hadamard expansion procedure applied to laplace type integrals taken along contours in the complex plane enables an exact description of the method of steepest descents this mode of expansion is illustrated by the evaluation of the bessel functions j v x and y v v x of large order and argument when x is bounded away from unity the limit x 1 corresponding to the coalescence of the active saddles in the integral representations of the bessel functions translates into a progressive loss of exponential separation between the different levels of the hadamard expansion which renders computation in this limit more difficult it is shown how a simple modification to this procedure can be employed to deal with the coalescence of the active saddles when x 1

two new asymptotic expansions of the ratio of two gamma functions formal expansions giving as particular cases semiasymptotic expansions of the ratio of two gamma functions are obtained

radiating solitary waves of a model evolution equation in fluids of finite depth abstract the evolution equation proposed by kubota et al j hydronautics 12 1978 157 165 and joseph j phys a 10 1977 225 227 for long waves in stratified fluids of finite depth is considered under a small third order derivative dispersive perturbation solitary wave solutions to this model equation become weakly nonlocal they develop oscillatory tails of infinite extent and exponentially small amplitude here these tails are calculated asymptotically following a perturbation procedure in the wavenumber domain

classifier combination based on confidence transformation this paper investigates the effects of confidence transformation in combining multiple classifiers using various combination rules the combination methods were tested in handwritten digit recognition by combining varying classifier sets the classifier outputs are transformed to confidence measures by combining three scaling functions global normalization gaussian density modeling and logistic regression and three confidence types linear sigmoid and evidence the combination rules include fixed rules sum rule product rule median rule etc and trained rules linear discriminants and weighted combination with various parameter estimation techniques the experimental results justify that confidence transformation benefits the combination performance of either fixed rules or trained rules trained rules mostly outperform fixed rules especially when the classifier set contains weak classifiers among the trained rules the support vector machine with linear kernel linear svm performs best while the weighted combination with optimized weights performs comparably well i have also attempted the joint optimization of confidence parameters and combination weights but its performance was inferior to that of cascaded confidence transformation combination this justifies that the cascaded strategy is a right way of multiple classifier combination

asymptotic expansions of mellin convolution integrals an oscillatory case in a recent paper j l lopez asymptotic expansions of mellin convolution integrals siam rev 50 2 2008 275 293 we have presented a new very general and simple method for deriving asymptotic expansions of 0 f t h xt dt for small x it contains watson s lemma and other classical methods mellin transform techniques mcclure and wong s distributional approach and the method of analytic continuation used in this approach as particular cases in this paper we generalize that idea to the case of oscillatory kernels that is to integrals of the form 0 e i c tf t h xt dt with c r and we give a method as simple as the one given in the above cited reference for the case c 0 we show that mcclure and wong s distributional approach for oscillatory kernels and the summability method for oscillatory integrals are particular cases of this method some examples are given as illustration

the evaluation of bessel functions via exp arc integrals a standard method for computing values of bessel functions has been to use the well known ascending series for small argument and to use an asymptotic series for large argument with the choice of the series changing at some appropriate argument magnitude depending on the number of digits required in a recent paper d borwein j borwein and r crandall 1 derived a series for an exp arc integral which gave rise to an absolutely convergent series for the j and i bessel functions with integral order such series can be rapidly evaluated via recursion and elementary operations and provide a viable alternative to the conventional ascending asymptotic switching in the present work we extend the method to deal with bessel functions of general non integral order as well as to deal with the y and k bessel functions

nonparametric discriminant analysis for face recognition in this paper we develop a new framework for face recognition based on nonparametric discriminant analysis nda and multi classifier integration traditional lda based methods suffer a fundamental limitation originating from the parametric nature of scatter matrices which are based on the gaussian distribution assumption the performance of these methods notably degrades when the actual distribution is non gaussian to address this problem we propose a new formulation of scatter matrices to extend the two class nonparametric discriminant analysis to multi class cases then we develop two more improved multi class nda based algorithms nsa and nfa with each one having two complementary methods based on the principal space and the null space of the intra class scatter matrix respectively comparing to the nsa the nfa is more effective in the utilization of the classification boundary information in order to exploit the complementary nature of the two kinds of nfa pnfa and nnfa we finally develop a dual nfa based multi classifier fusion framework by employing the over complete gabor representation to boost the recognition performance we show the improvements of the developed new algorithms over the traditional subspace methods through comparative experiments on two challenging face databases purdue ar database and xm2vts database

on visualization and aggregation of nearest neighbor classifiers nearest neighbor classification is one of the simplest and most popular methods for statistical pattern recognition a major issue in k nearest neighbor classification is how to find an optimal value of the neighborhood parameter k in practice this value is generally estimated by the method of cross validation however the ideal value of k in a classification problem not only depends on the entire data set but also on the specific observation to be classified instead of using any single value of k this paper studies results for a finite sequence of classifiers indexed by k along with the usual posterior probability estimates a new measure called the bayesian measure of strength is proposed and investigated in this paper as a measure of evidence for different classes the results of these classifiers and their corresponding estimated misclassification probabilities are visually displayed using shaded strips these plots provide an effective visualization of the evidence in favor of different classes when a given data point is to be classified we also propose a simple weighted averaging technique that aggregates the results of different nearest neighbor classifiers to arrive at the final decision based on the analysis of several benchmark data sets the proposed method is found to be better than using a single value of k

on the use of hadamard expansions in hyperasymptotic evaluation differential equations of hypergeometric type we describe how a modication of a common technique for developing asymptotic expansions of solutions of linear di erential equations can be used to derive hadamard expansions of solutions of di erential equations hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions particularly that of having exponentially small remainders when truncated and as a consequence provide a useful computational tool for evaluating special functions the methods we discuss can be applied to linear di erential equations of hypergeometric type and may have wider applicability

a novel combining classifier method based on variational inference in this paper we propose a combining classifier method based on the bayesian inference framework specifically the outputs of base classifiers called level1 data or meta data are utilized in a combiner to produce the final classification in our ensemble system each class in the training set induces a distribution on the level1 data which is modeled by a multivariate gaussian distribution traditionally the parameters of the gaussian are estimated using a maximum likelihood approach however maximum likelihood estimation cannot be applied since the covariance matrix of level1 data of each class is not full rank instead we propose to estimate the multivariate gaussian distribution of level1 data of each class by using the variational inference method experiments conducted on eighteen uci machine learning repository datasets and a selected 10 class clef2009 medical imaging database demonstrated the advantage of our method compared with several well known ensemble methods we proposed a variational inference method for multivariate gaussian distribution estimation we proposed a novel combining classifier method by employing variational inference on base classifiers outputs the proposed method is highly competitive to many state of the arts ensemble classifier methods

regression and ordered categorical variables read before the royal statistical society by professor r l plackett on behalf of the late professor anderson at a meeting organized by the research section on wednesday october 5th 1983 professor j b copas in the chair summary a general approach to regression modelling for ordered categorical response variables y is given which is equally applicable to ordered and unordered y the regressor variables xt xi x may be continuous or categorical the method is based on the logistic family which contains a hierarchy of regression models ranging from ordered to unordered models ordered properties of the former the stereotype model are established the choice between models is made empirically on the basis of model fit this is particularly important for assessed ordered categorical response variables where it is not obvious a priori whether or not the ordering is relevant to the regression relationship model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x the models are fitted iteratively using the method of maximum likelihood examples are given

optical uniform estimates and rigorous asymptotics beyond all orders for a class of ordinary differential equations for first order differential equations of the form y9 p p x y p and second order homogeneous linear differential equations y a x y9 b x y 0 with locally integrable coefficients having asymptotic possibly divergent power series when x oo on a ray arg x const under some further assumptions it is shown that on the given ray there is a one to one correspondence between true solutions and complete formal solutions the correspondence is based on asymptotic inequalities which are required to be uniform in x and optimal with respect to certain weights

on the use of hadamard expansions in hyperasymptotic evaluation of laplace type integrals ii complex variable we review and discuss the application of hadamard expansions to the hyperasymptotic evaluation of laplace integrals c ex p t f t dt x where for simplicity in this paper x is restricted to be a positive real variable the integration path c can be taken over both finite and semi infinite intervals in the complex plane in general these expansions take the form of compound expansions each associated with a different exponential level and involve absolutely convergent series containing the incomplete gamma function as a smoothing factor the early terms in each convergent expansion possess a rapid asymptotic like decay when the variable x is large with late terms that can be transformed into a rapid decay comparable with that of the early terms the hadamard expansion of the above integral when the phase function p t is linear is shown to depend significantly on the singularity structure of the amplitude function f t the application of the theory to laplace type integrals with quadratic cubic and nonpolynomial phase functions is considered in addition to the amplitude function the location of the saddle points satisfying p t 0 also plays a role in the detailed structure of the different exponential levels in the resulting hadamard expansion numerical examples are given to illustrate the accuracy that can be achieved with this new procedure

high precision evaluation of the bessel functions via hadamard series we present a method of high precision calculation of the bessel functions using hadamard series such series are absolutely convergent expansions involving the normalised incomplete gamma function p a z email protected a z c a and possess early terms that behave like those in an asymptotic expansion in the case of real variables the function p a z acts as a smoothing factor on the terms of the series we show how these series representing the bessel functions of complex argument can be chosen so as to produce rapidly convergent series that possess terms decaying at the geometric rate q k where 0 q 1 and k is the ordinal number of the series we give numerical examples with q 12 13 and 14 the theory is extended to cover the confluent hypergeometric functions f11 a b z and u a b z thereby dealing with many of the special functions arising in mathematical physics

rootfinding through global newton iteration and chebyshev polynomials for the amplitude of an electronic oscillator the amplitude z and oscillator gain k of a balanced oscillator are connected by the transcendental equation f z k 0 where f z k 2 z 0 1tanh zsin email protected sin email protected dt 1 k where the email protected 1 and email protected 0 it is trivial to find k z through numerical quadrature but the inverse function z k is a non trivial exercise in rootfinding first we derive a power series for small k and an asymptotic expansion for large k by blending these we obtain an analytic approximation to initialize newton s iteration it is found that the iteration converges to full machine precision within at most four iterations over the entire parameter range however the newton method is rather slow because each iteration requires two numerical quadratures because the integrands are periodic these can be done by the rectangle rule with an accuracy that increases exponentially with the number of quadrature points n but n must be large when z is large a faster method is to apply the newton quadrature algorithm to generate z k at a few selected points and apply chebyshev interpolation twice each chebyshev expansion is to choose the mimic the corresponding power series or asymptotic series so that singularities are avoided just 15 terms of each series plus an asymptotic approximation for very large k are sufficient to approximate z k to within about eight decimal places over the entire parameter range

handwritten numerical recognition based on multiple algorithms abstract in this paper the authors combine two algorithms for application to the recognition of unconstrained isolated handwritten numerals the first algorithm employs a modified quadratic discriminant function utilizing direction sensitive spatial features of the numeral image the second algorithm utilizes features derived from the profile of the character in a structural configuration to recognize the numerals while both algorithms yield very low error rates the authors combine the two algorithms in different ways to study the best polling strategy and realize very low error rates 0 2 or less and rejection rates below 4

on traveling wave solutions of the kuramoto sivashinsky equation abstract previous numerical results indicate that the kuramoto sivashinsky equation admits three classes of non periodic traveling wave solutions namely regular shocks oscillatory shocks and solitary waves however it has been shown that regular monotonic shocks cease to exist in the weak shock limit due to the radiation of oscillatory waves of exponentially small with respect to the shock strength but growing in space amplitude here oscillatory shocks and solitary waves are constructed by asymptotic analysis it thus transpires that in the weak shock limit oscillatory shocks can only be antisymmetric otherwise oscillatory and monotonic waves of exponentially small but growing in space amplitude would inevitably be excited under certain conditions however the growing waves can link a nearly antisymmetric oscillatory shock with a radiating regular shock to form a solitary wave the predictions of the asymptotic theory are supported by numerical results

exponential asymptotics and stokes lines in nonlinear ordinary differential equations a technique for calculating exponentially small terms beyond all orders in singularly perturbed ordinary differential equations is presented the approach is based on the application of a wkbj type ansatz to the late terms in the naive asymptotic expansion and the identification of stokes lines and is closely related to the well known stokes line smoothing phenomenon in linear ordinary differential equations the method is illustrated by application to examples

combinations of weak classifiers to obtain classification systems with both good generalization performance and efficiency in space and time we propose a learning method based on combinations of weak classifiers where weak classifiers are linear classifiers perceptrons which can do a little better than making random guesses a randomized algorithm is proposed to find the weak classifiers they are then combined through a majority vote as demonstrated through systematic experiments the method developed is able to obtain combinations of weak classifiers with good generalization performance and a fast training time on a variety of test problems and real applications theoretical analysis on one of the test problems investigated in our experiments provides insights on when and why the proposed method works in particular when the strength of weak classifiers is properly chosen combinations of weak classifiers can achieve a good generalization performance with polynomial space and time complexity

a constraint linearization method for nondifferentiable convex minimization this paper presents a readily implementable algorithm for solving constrained minimization problems involving possibly nonsmooth convex functions the constraints are handled as in the successive quadratic approximations methods for smooth problems an exact penalty function is employed for stepsize selection a scheme for automatic limitation of penalty growth is given global convergence of the algorithm is established as well as finite termination for piecewise linear problems numerical experience is reported

dispersive hyperasymptotics and the anharmonic oscillator hyperasymptotic summation of steepest descent asymptotic expansions of integrals is extended to functions that satisfy a dispersion relation we apply the method to energy eigenvalues of the anharmonic oscillator for which there is no known integral representation but for which there is a dispersion relation hyperasymptotic summation exploits the rich analytic structure underlying the asymptotics and is a practical alternative to borel summation of the rayleigh schrodinger perturbation series

on the use of hadamard expansions in hyperasymptotic evaluation of laplace type integrals iii clusters of saddle points it is shown how the recently developed hadamard expansion procedure can be applied to the hyperasymptotic evaluation of laplace type integrals containing a large variable when the phase function has a cluster of close lying saddle points the modification to this procedure that is required when the saddles in the cluster coalesce to form a single higher order saddle is discussed an example is also considered in which there is both a coalescence of saddles and a stokes phenomenon as the phase of the large variable is allowed to vary numerical examples are given to illustrate the accuracy that can be obtained with this new procedure

exactification of the poincare asymptotic expansion of the hankel integral spectacularly accurate asymptotic expansions and non asymptotic scales we obtain an exactification of the poincare asymptotic expansion pae of the hankel integral as using the distributional approach of mcclure wong we find that for half integer orders of the bessel function the exactified asymptotic series terminates so that it gives an exact finite sum representation of the hankel integral for other orders the asymptotic series does not terminate and is generally divergent but is amenable to superasymptotic summation i e by optimal truncation for specific examples we compare the accuracy of the optimally truncated asymptotic series owing to the mcclure wong distributional method with owing to the mellin barnes integral method we find that the former is spectacularly more accurate than the latter by in some cases more than 70 orders of magnitude for the same moderate value of b moreover the exactification can lead to a resummation of the pae when it is exact with the resummed poincare series exhibiting again the same spectacular accuracy more importantly the distributional method may yield meaningful resummations that involve scales that are not asymptotic sequences

hyperasymptotics and the linear boundary layer problem why asymptotic series diverge the simplest problem with boundary layers epsilon 2 u xx u f x is used to illustrate i why the perturbation series in powers of epsilon is asymptotic but divergent ii why the optimally truncated expansion is superasymptotic in the sense that that error is proportional to exp mbox constant epsilon and iii how to obtain an improved hyperasymptotic approximation

mellin barnes regularization borel summation and the bender wu asymptotics for the anharmonic oscillator we introduce the numerical technique of mellin barnes integral regularization which can be used to evaluate both convergent and divergent series the technique is shown to be numerically equivalent to the corresponding results obtained by borel summation both techniques are then applied to the bender wu formula which represents an asymptotic expansion for the energy levels of the anharmonic oscillator we find that this formula is unable to give accurate values for the ground state energy particularly when the coupling is greater than 0 1 as a consequence the inability of the bender wu formula to yield exact values for the energy level of the anharmonic oscillator cannot be attributed to its asymptotic nature

on nonlinear boundary value problems ghosts parasites and discretizations ghosts are a new class of approximate solutions to nonlinear boundary value problems bvps they are bounded away from true solutions but solve an initial value problem ivp for the differential equations exactly and approximate boundary and internal matching conditions with exponentially decaying error as a control parameter approaches infinity ghosts are characteristic of singularly perturbed differential equations in which solutions are localized and the ivp depends sensitively on initial data they correspond to shifted localized solutions and they can be observed in imperfect physical experiments and be approximated by convergent discretization schemes the latter property suggests that the concept of the numerically irrelevant solution introduced for discretized second order bvps should be re examined

asymptotics beyond all orders asymptotology and borel summation asymptotics superasymptotics hyperasymptotics m berry the geometric model of crystal growth numerical analysis of the geometric model of crystal growth j m hammersley dendritic crystal growth an experimental assessment of continuum models of dendritic growth j p gollub directional solidification of solids directional growth of dilute mixtures and lamellar eutectics k kassner et al flow in a hele shaw cell viscous displacement in a hele shaw cell s tanveer the rapidly forced pendulum exponentially small estimate for separatrix splittings j scheurle et al ordinary differential equations singular perturbations of solitons y pomeau solitary water waves in the presence of small surface tension solitary waves with ripples beyond all orders j t beale problems in optics potpourri 23 additional articles index

uniform asymptotic expansions of integrals a selection of problems abstract on the occasion of the conference we mention examples of stieltjes work on asymptotics of special functions the remaining part of the paper gives a selection of asymptotic methods for integrals in particular on uniform approximations we discuss several standard problems and examples in which known special functions error functions airy functions bessel functions etc are needed to construct uniform approximations finally we discuss the recent interest and new insights in the stokes phenomenon an extensive bibliography on uniform asymptotic methods for integrals is given together with references to recent papers on the stokes phenomenon for integrals and related topics

selected tree classifier combination based on both accuracy and error diversity this paper proposes a method for combining multiple tree classifiers based on both classifier ensemble bagging and dynamic classifier selection schemes dcs the proposed method is composed of the following procedures 1 building individual tree classifiers based on bootstrap samples 2 calculating the distance between all possible two trees 3 clustering the trees based on single linkage clustering 4 selecting two clusters by local region in terms of accuracy and error diversity and 5 voting the results of tree classifiers selected in the two clusters empirical evaluation using publicly available data sets confirms the superiority of our proposed approach over other classifier combining methods

on the use of hadamard expansions in hyperasymptotic evaluation of laplace type integrals iv poles this paper is one of a series considering the application of hadamard expansions in the hyperasymptotic evaluation of laplace type integrals of the form cexp email protected t f t dt for large values of z it is shown how the procedure can be employed to deal with the case when the amplitude function f t possesses poles which may coalesce with a saddle point of the integrand or approach the integration path c a novel feature introduced here is the reverse expansion procedure this results in contributions at each exponential level after the first of the expansion in the form of rapidly convergent series thereby enabling the high precision evaluation of the above integral in coalescence problems numerical examples are given to illustrate the procedure

an analysis of ensemble pruning techniques based on ordered aggregation several pruning strategies that can be used to reduce the size and increase the accuracy of bagging ensembles are analyzed these heuristics select subsets of complementary classifiers that when combined can perform better than the whole ensemble the pruning methods investigated are based on modifying the order of aggregation of classifiers in the ensemble in the original bagging algorithm the order of aggregation is left unspecified when this order is random the generalization error typically decreases as the number of classifiers in the ensemble increases if an appropriate ordering for the aggregation process is devised the generalization error reaches a minimum at intermediate numbers of classifiers this minimum lies below the asymptotic error of bagging pruned ensembles are obtained by retaining a fraction of the classifiers in the ordered ensemble the performance of these pruned ensembles is evaluated in several benchmark classification tasks under different training conditions the results of this empirical investigation show that ordered aggregation can be used for the efficient generation of pruned ensembles that are competitive in terms of performance and robustness of classification with computationally more costly methods that directly select optimal or near optimal subensembles

pseudospectral delves freeman computations of the radiation coefficient for weakly nonlocal solitary waves of the third order nonlinear schroedinger equation and their relation to hyperasymptotic perturbation theory we revive a strategy of delves to precondition a spectral calculation using an almost diagonal galerkin matrix we also show that hyperasymptotic singular perturbation theory is a specialization of the delves freeman iteration to a single step with a diagonal galerkin matrix we calculate the first three orders in the hyperasymptotic expansion of the radiation coefficient of the weakly nonlocal envelope solitary waves of the third order nonlinear schroedinger tnls equation which is important in fiber optics telecommunications and water waves in a long appendix it was necessary to develop some non numerical but numerically essential additions to the theory of the tnls equation good numerics often requires a much deeper understanding of a problem than the generation of a string of power series coefficients

an algorithm for calculating one subgradient of a convex function of two variables we present an algorithm which enables us to calculate one particular subgradient of a convex functionf 2 at a given point such a calculation is required in many existing numerical methods for convex nondifferentiable optimization the novelty of our approach lies in the assumption that only the values off are computable and no analytical formula for the subdifferential is known we include some numerical examples

harmonic moment dynamics in laplacian growth harmonic moments are integrals of integer powers of z x iy over a domain here the domain is an exterior of a bubble of air growing in an oil layer between two horizontal closely spaced plates harmonic moments are a natural basis for such laplacian growth phenomena because unlike other representations these moments linearize the zero surface tension problem s richardson j fluid mech 56 609 1972 so that all moments except the lowest one the area of the bubble are conserved in time in our experiments we directly determine the harmonic moments and show that for nonzero surface tension all moments except the lowest one decay in time rather than exhibiting the divergences of other representations further we derive an expression that relates the derivative of the k th harmonic moment m k to measurable quantities surface tension viscosity the distance between the plates and a line integral over the contour encompassing the growing bubble the laboratory observations are in good accord with the expression we derive for d m k dt which is proportional to the surface tension thus in the zero surface tension limit the moments above k 0 are all conserved in accord with richardson s theory in addition from the measurements of the time evolution of the harmonic moments we obtain a value for the surface tension that is within 20 of the accepted value in conclusion our analysis and laboratory observations demonstrate that an interface dynamics description in terms of harmonic moments is physically realizable and robust

joint induction of shape features and tree classifiers we introduce a very large family of binary features for two dimensional shapes the salient ones for separating particular shapes are determined by inductive learning during the construction of classification trees there is a feature for every possible geometric arrangement of local topographic codes the arrangements express coarse constraints on relative angles and distances among the code locations and are nearly invariant to substantial affine and nonlinear deformations they are also partially ordered which makes it possible to narrow the search for informative ones at each node of the tree different trees correspond to different aspects of shape they are statistically and weakly dependent due to randomization and are aggregated in a simple way adapting the algorithm to a shape family is then fully automatic once training samples are provided as an illustration we classified handwritten digits from the nist database the error rate was 0 7 percent

hyperasymptotic evaluation of the pearcey integral via hadamard expansions we describe high precision computations of the pearcey integral pe x y for real x and y by means of hadamard expansions numerical results for x y situated in different regions of the x y plane are given to illustrate the levels of precision that can be achieved particular emphasis is given to computation in the neighbourhood of the two cusped curves associated with pe x y across which there is either a coalescence of saddles or a stokes phenomenon

fuzzy integration of classification results this paper attempts to solve the problem of integrating classification results in a multiple classifier system using fuzzy reasoning we present three fuzzy classification result integration algorithms covering all forms of classification output we describe algorithms to model classification results and to reason about the unique output result from all types of classification results the proposed algorithms were implemented and tested through experiments on a training and test data set of handwritten digits cropped from u s postal mail pieces

ssc a classifier combination method based on signal strength we propose a new classifier combination method the signal strength based combining ssc approach to combine the outputs of multiple classifiers to support the decision making process in classification tasks as ensemble learning methods have attracted growing attention from both academia and industry recently it is critical to understand the fundamental issues of the combining rule motivated by the signal strength concept our proposed ssc algorithm can effectively integrate the individual vote from different classifiers in an ensemble learning system comparative studies of our method with nine major existing combining rules namely geometric average rule arithmetic average rule median value rule majority voting rule borda count max and min rule weighted average and weighted majority voting rules is presented furthermore we also discuss the relationship of the proposed method with respect to margin based classifiers including the boosting method adaboost m1 and adaboost m2 and support vector machines by margin analysis detailed analyses of margin distribution graphs are presented to discuss the characteristics of the proposed method simulation results for various real world datasets illustrate the effectiveness of the proposed method

brief paper experience consistent modeling regression and classification problems in this study we are concerned with system modeling which involves limited data and reconciles the developed model with some previously acquired domain knowledge being captured in the format of already constructed models each of these previously available models was formed on a basis of extensive data sets which are not available for the current identification pursuits to emphasize the nature of modeling being guided by the reconciliation mechanisms we refer to this mode of identification as experience consistent modeling the paper presents the conceptual and algorithmic framework by focusing on regression models by forming a certain extended form of the performance index it is shown that the domain knowledge captured by regression models can play a similar role as a regularization component used quite commonly in system identification experimental results involve both synthetic low dimensional data and selected data coming from machine learning repository the data used in the experiments tackle regression models as well as classification problems two class classifiers

existence and uniqueness of analytic solution for unsteady crystals with zero surface tension abstract we study the initial value problem for two dimensional dendritic crystal growth with zero surface tension if the initial data is analytic and close to ivantsov steady solution it is proved that unique analytic solution exists locally in time the analysis is based on a nirenberg theorem on abstract cauchy kovalevsky problem in properly chosen banach spaces

analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations abstract for singular perturbation problems the renormalization group rg method of chen goldenfeld and oono phys rev e 49 1994 4502 4511 has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system it has been applied to a variety of problems traditionally analyzed using disparate methods including the method of multiple scales boundary layer theory the wkbj method the poincare lindstedt method the method of averaging and others in this article we show how the rg method may be used to generate normal forms for large classes of ordinary differential equations first we apply the rg method to systems with autonomous perturbations and we show that the reduced or amplitude equations generated by the rg method are equivalent to the classical poincare birkhoff normal forms for these systems up to and including terms of o 2 where is the perturbation parameter this analysis establishes our approach and generalizes to higher order second we apply the rg method to systems with nonautonomous perturbations and we show that the reduced or amplitude equations so generated constitute time asymptotic normal forms which are based on kbm averages moreover for both classes of problems we show that the main coordinate changes are equivalent up to translations between the spaces in which they are defined in this manner our results show that the rg method offers a new approach for deriving normal forms for nonautonomous systems and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves finally we establish how well the solution to the rg equations approximates the solution of the original equations on time scales of o 1

asymptotic expansions of some integral transforms by using generalized functions the technique devised by wong to derive the asymptotic expansions of multiple fourier transforms by using the theory of schwartz distributions is extended to a large class of integral transforms the extension requires establishing a general procedure to extend these integral transforms to generalized functions wong s technique is then applied to some of these integral transforms to obtain their asymptotic expansions this class of integral transforms encompasses among others the laplace the airy the k and the hankel transforms

on output independence and complementariness in rank based multiple classifier decision systems this study presents a theoretical analysis of output independence and complementariness between classifiers in a rank based multiple classifier decision system in the context of the partitioned observation space theory to enable such an analysis an information theoretic interpretation of a rank based multiple classifier system is developed and basic concepts from information theory are applied to develop measures for output independence and complementariness it is shown that output independence of classifiers is not a requirement for achieving complementariness between these classifiers namely output independence does not imply a performance improvement by combining multiple classifiers a condition called dominance is shown to be important instead the information theoretic measures proposed for output independence and complementariness are justified by simulated examples

on the use of hadamard expansions in hyperasymptotic evaluation ii complex variables this paper extends the method of hyperasymptotic evaluation using absolutely convergent hadamard expansions developed in the first part to the confluent hypergeometric functions of complex argument z it is shown that the representation of this class of functions involves an infinite number of hadamard expansions associated with a decreasing sequence of subdominant exponential levels for large z numerical examples involving the bessel functions are given to illustrate the attainable levels of accuracy

effective laguerre asymptotics it is known that the generalized laguerre polynomials can enjoy subexponential growth for large primary index in particular for certain fixed parameter pairs a z one has the large n asymptotic behavior l n a z sim c a z n a 2 1 4 e 2 sqrt nz we introduce a computationally motivated contour integral that allows efficient numerical laguerre evaluations yet also leads to the complete asymptotic series over the full parameter domain of subexponential behavior we present a fast algorithm for symbolic generation of the rather formidable expansion coefficients along the way we address the difficult problem of establishing effective i e rigorous and explicit error bounds on the general expansion a primary tool for these developments is an exp arc method giving a natural bridge between converging series and effective asymptotics

interface dynamics in hele shaw flows with centrifugal forces preventing cusp singularities with rotation a class of exact solutions of hele shaw flows without surface tension in a rotating cell is reported we show that the interplay between injection and rotation modifies the scenario of formation of finite time cusp singularities for a subclass of solutions we show that for any given initial condition there exists a critical rotation rate above which cusp formation is suppressed we also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions within the above subclass

double bagging combining classifiers by bootstrap aggregation the combination of classifiers leads to substantial reduction of misclassification error in a wide range of applications and benchmark problems we suggest using an out of bag sample for combining different classifiers in our setup a linear discriminant analysis is performed using the observations in the out of bag sample and the corresponding discriminant variables computed for the observations in the bootstrap sample are used as additional predictors for a classification tree two classifiers are combined and therefore method and variable selection bias is no problem for the corresponding estimate of misclassification error the need of an additional test sample disappears moreover the procedure performs comparable to the best classifiers used in a number of artificial examples and applications

multiple classifiers for color flag and trademark image retrieval a novel region based multiple classifier color image retrieval system is presented in our approach a region growing technique is first employed to cluster connected color pixels with the same color in an image to form color regions which are the primitive elements utilized in our proposed approach then three complementary region based classifiers that we developed are selected in the classifier selection stage which include color classifier shape classifier and relational classifier in each classifier a virtue probability representing the probability that an image is similar to the query image is defined thereafter a set of virtue probabilities is calculated in each classifier next the measurement dependent methods are applied to combine the virtue probabilities of classifiers in the decision combination stage the dynamic selection scheme designed in the decision combination stage can further improve the system performance dramatically experimental results reveal the feasibility and validity of our proposed approach in solving the color image retrieval problem

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

generalizing the majority voting scheme to spatially constrained voting generating ensembles from multiple individual classifiers is a popular approach to raise the accuracy of the decision as a rule for decision making majority voting is a usually applied model in this paper we generalize classical majority voting by incorporating probability terms pn k to constrain the basic framework these terms control whether a correct or false decision is made if k correct votes are present among the total number of n this generalization is motivated by object detection problems where the members of the ensemble are image processing algorithms giving their votes as pixels in the image domain in this scenario the terms pn k can be specialized by a geometric constraint namely the votes should fall inside a region matching the size and shape of the object to vote together we give several theoretical results in this new model for both dependent and independent classifiers whose individual accuracies may also differ as a real world example we present our ensemble based system developed for the detection of the optic disc in retinal images for this problem experimental results are shown to demonstrate the characterization capability of this system we also investigate how the generalized model can help us to improve an ensemble with extending it by adding a new algorithm

levy flights exact results and asymptotics beyond all orders a comprehensive study of the symmetric levy stable probability density function is presented this is performed for orders both less than 2 and greater than 2 the latter class of functions are traditionally neglected because of a failure to satisfy non negativity the complete asymptotic expansions of the symmetric levy stable densities of order greater than 2 are constructed and shown to exhibit intricate series of transcendentally small terms asymptotics beyond all orders it is demonstrated that the symmetric levy stable densities of any arbitrary rational order can be written in terms of generalized hypergeometric functions and a number of new special cases are given representations in terms of special functions a link is shown between the symmetric levy stable density of order 4 and pearcey s integral which is used widely in problems of optical diffraction and wave propagation this suggests the existence of applications for the symmetric levy stable densities of order greater than 2 despite their failure to define a probability density function

analytical and numerical studies of a singularly perturbed boussinesq equation we study the singularly perturbed sixth order boussinesq equation recently introduced by daripa and hua appl math comput 101 1999 159 motivated by their work we formally derive this equation from two dimensional potential flow equations governing the small amplitude long capillary gravity waves on the surface of shallow water for bond number very close to but less than 1 3 on the basis of far field analyses and heuristic arguments we show that the traveling wave solutions of this equation are weakly non local solitary waves characterized by small amplitude fast oscillations in the far field we review various analytical and numerical methods originally devised to obtain this type of weakly non local solitary wave solutions of the singularly perturbed fifth order kdv equation using these methods we obtain weakly non local solitary wave solutions of the singularly perturbed sixth order boussinesq equation and provide estimates of the amplitude of oscillations which persist in the far field

shock layer movement for burgers equation this paper considers the motion of the shock layer exhibited by the solution of the initial boundary value problem for the equation epsilon u xx uu x u t with small values of epsilon 0 this burgers equation occurs as a model for a number of physical problems and is representative of many convection dominated evolution equations a specific example will be solved explicitly using the cole hopf transformation the result suggests a corresponding asymptotic approach which provides the shock layer location x epsilon t as the solution of an initial value problem that method which can be applied to a far wider class of equations also shows how the steady state shock location can be changed substantially by asymptotic exponentially small perturbations

the random subspace method for constructing decision forests much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes the dilemma between overfitting and achieving maximum accuracy is seldom resolved a method to construct a decision tree based classifier is proposed that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity the classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector that is trees constructed in randomly chosen subspaces the subspace method is compared to single tree classifiers and other forest construction methods by experiments on publicly available datasets where the method s superiority is demonstrated we also discuss independence between trees in a forest and relate that to the combined classification accuracy