optimal estimates and asymptotics for the stress concentration between closely located stiff inclusions if stiff inclusions are closely located then the stress which is the gradient of the solution may become arbitrarily large as the distance between two inclusions tends to zero in this paper we investigate the asymptotic behavior of the stress concentration factor which is the normalized magnitude of the stress concentration as the distance between two inclusions tends to zero for that purpose we show that the gradient of the solution to the case when two inclusions are touching decays exponentially fast near the touching point we also prove a similar result when two inclusions are closely located and there is no potential difference on boundaries of two inclusions we then use these facts to show that the stress concentration factor converges to a certain integral of the solution to the touching case as the distance between two inclusions tends to zero we then present an efficient way to compute this integral

gradient estimates for solutions to the conductivity problem in this paper we derive very precise gradient estimates for solutions to the conductivity problem in the case where two circular conductivity inclusions are very close but not touching the novelty of these estimates is that they give very specific information about the blow up of the gradient as the conductivities of the inclusions degenerate

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

similarity metric learning for a variable kernel classifier nearest neighbor interpolation algorithms have many useful properties for applications to learning but they often exhibit poor generalization in this paper it is shown that much better generalization can be obtained by using a variable interpolation kernel in combination with conjugate gradient optimization of the similarity metric and kernel size the resulting method is called variable kernel similarity metric vsm learning it has been tested on several standard classification data sets and on these problems it shows better generalization than backpropagation and most other learning methods the number of parameters that must be determined through optimization are orders of magnitude less than for backpropagation or radial basis function rbf networks which may indicate that the method better captures the essential degrees of variation in learning other features of vsm learning are discussed that make it relevant to models for biological learning in the brain

learning prototypes and distances a prototype reduction technique based on nearest neighbor error minimization a prototype reduction algorithm is proposed which simultaneously trains both a reduced set of prototypes and a suitable local metric for these prototypes starting with an initial selection of a small number of prototypes it iteratively adjusts both the position features of these prototypes and the corresponding local metric weights the resulting prototypes metric combination minimizes a suitable estimation of the classification error probability good performance of this algorithm is assessed through experiments with a number of benchmark data sets and with a real task consisting in the verification of images of human faces

class conditional density estimation using mixtures with constrained component sharing we propose a generative mixture model classifier that allows for the class conditional densities to be represented by mixtures having certain subsets of their components shared or common among classes we argue that when the total number of mixture components is kept fixed the most efficient classification model is obtained by appropriately determining the sharing of components among class conditional densities in order to discover such an efficient model a training method is derived based on the em algorithm that automatically adjusts component sharing we provide experimental results with good classification performance

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

linear reconstruction measure steered nearest neighbor classification framework the linear reconstruction measure lrm which determines the nearest neighbors of the query sample in all known training samples by sorting the minimum l 2 norm error linear reconstruction coefficients is introduced in this paper the intuitive interpretation and mathematical proofs are presented to reveal the efficient working mechanism of lrm through analyzing the physical meaning of coefficients and regularization items we find that lrm provides more useful information and advantages than the conventional similarity measure model which calculates the distance between two entities i e conventional point to point c ptp inspired by the advantages of lrm the linear reconstruction measure steered nearest neighbor classification framework lrm nncf is designed with eight classifiers according to different decision rules and models of lrm evaluation on several face databases and the experimental results demonstrate that these proposed classifiers can achieve greater performance than the c ptp based 1 nns and competitive recognition accuracy and robustness compared with the state of the art classifiers

locally linear reconstruction for instance based learning instance based learning ibl so called memory based reasoning mbr is a commonly used non parametric learning algorithm k nearest neighbor k nn learning is the most popular realization of ibl due to its usability and adaptability k nn has been successfully applied to a wide range of applications however in practice one has to set important model parameters only empirically the number of neighbors k and weights to those neighbors in this paper we propose structured ways to set these parameters based on locally linear reconstruction llr we then employed sequential minimal optimization smo for solving quadratic programming step involved in llr for classification to reduce the computational complexity experimental results from 11 classification and eight regression tasks were promising enough to merit further investigation not only did llr outperform the conventional weight allocation methods without much additional computational cost but also llr was found to be robust to the change of k

optimal boundary gradient estimates for lame systems with partially infinite coefficients abstract in this paper we derive the pointwise upper bounds and lower bounds on the gradients of solutions to the lame systems with partially infinite coefficients as the surface of discontinuity of the coefficients of the system is located very close to the boundary when the distance tends to zero the optimal blow up rates of the gradients are established for inclusions with arbitrary shapes and in all dimensions

selecting critical patterns based on local geometrical and statistical information pattern selection methods have been traditionally developed with a dependency on a specific classifier in contrast this paper presents a method that selects critical patterns deemed to carry essential information applicable to train those types of classifiers which require spatial information of the training data set critical patterns include those edge patterns that define the boundary and those border patterns that separate classes the proposed method selects patterns from a new perspective primarily based on their location in input space it determines class edge patterns with the assistance of the approximated tangent hyperplane of a class surface it also identifies border patterns between classes using local probability the proposed method is evaluated on benchmark problems using popular classifiers including multilayer perceptrons radial basis functions support vector machines and nearest neighbors the proposed approach is also compared with four state of the art approaches and it is shown to provide similar but more consistent accuracy from a reduced data set experimental results demonstrate that it selects patterns sufficient to represent class boundary and to preserve the decision surface

exploring margin setting for good generalization in multiple class discrimination in earlier publications we showed that it is possible to achieve both low vc dimension and high accuracy if we divide the given training set into a sequence of subsets each of which does admit such a solution here we explore in substantially more detail how the various steps in what was called margin setting impact false classification and indecision rates a complex relationship exists between margin size the number of steps in the process and those two classification failures after mapping those relationships we offer a qualitative explanation of them

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

on the theory of frobenius extensions and its application to lie superalgebras by using an approach to the theory of frobenius extensions that emphasizes notions related to associative forms we obtain results concerning the trace and corestriction mappings and transitivity these are employed to show that the extension of enveloping algebras determined by a subalgebra of a lie superalgebra is a frobenius extension and to study certain questions in representation theory

on the spectrum of the poincare variational problem for two close to touching inclusions in 2d we study the spectrum of the poincare variational problem for two close to touching inclusions in r2 we derive the asymptotics of its eigenvalues as the distance between the inclusions tends to zero

local discriminative distance metrics ensemble learning the ultimate goal of distance metric learning is to incorporate abundant discriminative information to keep all data samples in the same class close and those from different classes separated local distance metric methods can preserve discriminative information by considering the neighborhood influence in this paper we propose a new local discriminative distance metrics lddm algorithm to learn multiple distance metrics from each training sample a focal sample and in the vicinity of that focal sample focal vicinity to optimize local compactness and local separability those locally learned distance metrics are used to build local classifiers which are aligned in a probabilistic framework via ensemble learning theoretical analysis proves the convergence rate bound the generalization bound of the local distance metrics and the final ensemble classifier we extensively evaluate lddm using synthetic datasets and large benchmark uci datasets

adaptive local linear regression with application to printer color management local learning methods such as local linear regression and nearest neighbor classifiers base estimates on nearby training samples neighbors usually the number of neighbors used in estimation is fixed to be a global ldquooptimalrdquo value chosen by cross validation this paper proposes adapting the number of neighbors used for estimation to the local geometry of the data without need for cross validation the term enclosing neighborhood is introduced to describe a set of neighbors whose convex hull contains the test point when possible it is proven that enclosing neighborhoods yield bounded estimation variance under some assumptions three such enclosing neighborhood definitions are presented natural neighbors natural neighbors inclusive and enclosing k nn the effectiveness of these neighborhood definitions with local linear regression is tested for estimating lookup tables for color management significant improvements in error metrics are shown indicating that enclosing neighborhoods may be a promising adaptive neighborhood definition for other local learning tasks as well depending on the density of training samples

locally adaptive metric nearest neighbor classification nearest neighbor classification assumes locally constant class conditional probabilities this assumption becomes invalid in high dimensions with finite samples due to the curse of dimensionality severe bias can be introduced under these conditions when using the nearest neighbor rule we propose a locally adaptive nearest neighbor classification method to try to minimize bias we use a chi squared distance analysis to compute a flexible metric for producing neighborhoods that are highly adaptive to query locations neighborhoods are elongated along less relevant feature dimensions and constricted along most influential ones as a result the class conditional probabilities are smoother in the modified neighborhoods whereby better classification performance can be achieved the efficacy of our method is validated and compared against other techniques using both simulated and real world data

the optimal distance measure for nearest neighbor classification a local distance measure is shown to optimize the performance of the nearest neighbor two class classifier for a finite number of samples the difference between the finite sample error and the asymptotic error is used as the criterion of improvement this new distance measure is compared to the well known euclidean distance an algorithm for practical implementation is introduced this algorithm is shown to be computationally competitive with the present nearest neighbor procedures and is illustrated experimentally a closed form for the corresponding second order moment of this criterion is found finally the above results are extended to

a distributed approach toward discriminative distance metric learning distance metric learning dml is successful in discovering intrinsic relations in data however most algorithms are computationally demanding when the problem size becomes large in this paper we propose a discriminative metric learning algorithm develop a distributed scheme learning metrics on moderate sized subsets of data and aggregate the results into a global solution the technique leverages the power of parallel computation the algorithm of the aggregated dml adml scales well with the data size and can be controlled by the partition we theoretically analyze and provide bounds for the error induced by the distributed treatment we have conducted experimental evaluation of the adml both on specially designed tests and on practical image annotation tasks those tests have shown that the adml achieves the state of the art performance at only a fraction of the cost incurred by most existing methods

characterization of electric fields between two spherical perfect conductors with general radii in 3d abstract in composite materials the inclusions are frequently spaced very closely the electric field concentrated in the narrow regions between two adjacent perfectly conducting inclusions will always become arbitrarily large in this paper we establish an asymptotic formula of the electric field in the zone between two spherical inclusions with different radii in three dimensions an explicit blowup factor relying on radii is obtained which also involves the digamma function and euler mascheroni constant and so the role of inclusions radii played in such blowup analysis is identified

lda svm driven nearest neighbor classification nearest neighbor nn classification relies on the assumption that class conditional probabilities are locally constant this assumption becomes false in high dimensions with finite samples due to the curse of dimensionality the nn rule introduces severe bias under these conditions we propose a locally adaptive neighborhood morphing classification method to try to minimize bias we use local support vector machine learning to estimate an effective metric for producing neighborhoods that are elongated along less discriminant feature dimensions and constricted along most discriminant ones as a result the class conditional probabilities can be expected to be approximately constant in the modified neighborhoods whereby better classification performance can be achieved the efficacy of our method is validated and compared against other competing techniques using a number of datasets

distance learning for similarity estimation in this paper we present a general guideline to find a better distance measure for similarity estimation based on statistical analysis of distribution models and distance functions a new set of distance measures are derived from the harmonic distance the geometric distance and their generalized variants according to the maximum likelihood theory these measures can provide a more accurate feature model than the classical euclidean and manhattan distances we also find that the feature elements are often from heterogeneous sources that may have different influence on similarity estimation therefore the assumption of single isotropic distribution model is often inappropriate to alleviate this problem we use a boosted distance measure framework that finds multiple distance measures which fit the distribution of selected feature elements best for accurate similarity estimation the new distance measures for similarity estimation are tested on two applications stereo matching and motion tracking in video sequences the performance of boosted distance measure is further evaluated on several benchmark data sets from the uci repository and two image retrieval applications in all the experiments robust results are obtained based on the proposed methods

asymptotics of the solution to the conductivity equation in the presence of adjacent circular inclusions with finite conductivities abstract we consider the conductivity problem in the presence of adjacent circular inclusions with constant conductivities when two inclusions get closer and their conductivities degenerate to zero or infinity the gradient of the solution can be arbitrary large in this paper we derive an asymptotic formula of the solution which characterizes the gradient blow up of the solution in terms of conductivities of inclusions as well as the distance between inclusions the asymptotic formula is expressed in bipolar coordinates in terms of the lerch transcendent function and it is valid for inclusions with arbitrary constant conductivities we illustrate our results with numerical calculations

adaptive quasiconformal kernel nearest neighbor classification nearest neighbor classification assumes locally constant class conditional probabilities this assumption becomes invalid in high dimensions due to the curse of dimensionality severe bias can be introduced under these conditions when using the nearest neighbor rule we propose an adaptive nearest neighbor classification method to try to minimize bias we use quasiconformal transformed kernels to compute neighborhoods over which the class probabilities tend to be more homogeneous as a result better classification performance can be expected the efficacy of our method is validated and compared against other competing techniques using a variety of data sets

the first fundamental theorem of invariant theory for the orthosymplectic super group we give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of atiyah bott and patodi to the supergroup context we use methods from super algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space in this way super schur weyl brauer duality is established between the orthosymplectic supergroup of superdimension m 2n and the brauer algebra with parameter m 2n the result may be interpreted either in terms of the group scheme osp v over mathbb c where v is a finite dimensional super space or as a statement about the orthosymplectic lie supergroup over the infinite dimensional grassmann algebra lambda we take the latter point of view here and also state a corresponding theorem for the orthosymplectic lie superalgebra which involves an extra invariant generator the super pfaffian

discriminant adaptive nearest neighbor classification nearest neighbour classification expects the class conditional probabilities to be locally constant and suffers from bias in high dimensions we propose a locally adaptive form of nearest neighbour classification to try to ameliorate this curse of dimensionality we use a local linear discriminant analysis to estimate an effective metric for computing neighbourhoods we determine the local decision boundaries from centroid information and then shrink neighbourhoods in directions orthogonal to these local decision boundaries and elongate them parallel to the boundaries thereafter any neighbourhood based classifier can be employed using the modified neighbourhoods the posterior probabilities tend to be more homogeneous in the modified neighbourhoods we also propose a method for global dimension reduction that combines local dimension information in a number of examples the methods demonstrate the potential for substantial improvements over nearest neighbour classification

a method of learning weighted similarity function to improve the performance of nearest neighbor the performance of nearest neighbor nn classifier is known to be sensitive to the distance or similarity function used in classifying a test instance another major disadvantage of nn is that it uses all training instances in the generalization phase this can cause slow execution speed and high storage requirement when dealing with large datasets in the past research many solutions have been proposed to handle one or both of the above problems in the scheme proposed in this paper we tackle both of these problems by assigning a weight to each training instance the weight of a training instance is used in the generalization phase to calculate the distance or similarity of a query pattern to that instance the basic nn classifier can be viewed as a special case of this scheme that treats all instances equally by assigning equal weight to all training instances using this form of weighted similarity measure we propose a learning algorithm that attempts to maximize the leave one out lv1 classification rate of the nn rule by adjusting the weights of the training instances at the same time the algorithm reduces the size of the training set and can be viewed as a powerful instance reduction technique an instance having zero weight is not used in the generalization phase and can be virtually removed from the training set we show that our scheme has comparable or better performance than some recent methods proposed in the literature for the task of learning the distance function and or prototype reduction

multiparametric quantum deformation of the general linear supergroup in the work l d faddeev and his collaborators and subsequently v g drinfeld m jimbo s l woronowicz a new class of hopf algebras was constructed they can be considered as one parametric deformations of either group ring or the universal enveloping algebra of a simple algebraic group in this paper we define and investigate a multiparametric deformation of the general linear supergroup this is the simplest example of some general constructions described in 5 6

gradient estimates for solutions of the lame system with partially infinite coefficients we establish upper bounds on the blow up rate of the gradients of solutions of the lame system with partially infinite coefficients in dimension two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero

a memetic algorithm for evolutionary prototype selection a scaling up approach prototype selection problem consists of reducing the size of databases by removing samples that are considered noisy or not influential on nearest neighbour classification tasks evolutionary algorithms have been used recently for prototype selection showing good results however due to the complexity of this problem when the size of the databases increases the behaviour of evolutionary algorithms could deteriorate considerably because of a lack of convergence this additional problem is known as the scaling up problem memetic algorithms are approaches for heuristic searches in optimization problems that combine a population based algorithm with a local search in this paper we propose a model of memetic algorithm that incorporates an ad hoc local search specifically designed for optimizing the properties of prototype selection problem with the aim of tackling the scaling up problem in order to check its performance we have carried out an empirical study including a comparison between our proposal and previous evolutionary and non evolutionary approaches studied in the literature the results have been contrasted with the use of non parametric statistical procedures and show that our approach outperforms previously studied methods especially when the database scales up

from classifiers to discriminators a nearest neighbor rule induced discriminant analysis the current discriminant analysis method design is generally independent of classifiers thus the connection between discriminant analysis methods and classifiers is loose this paper provides a way to design discriminant analysis methods that are bound with classifiers we begin with a local mean based nearest neighbor lm nn classifier and use its decision rule to supervise the design of a discriminator therefore the derived discriminator called local mean based nearest neighbor discriminant analysis lm nnda matches the lm nn classifier optimally in theory in contrast to that lm nnda is a nn classifier induced discriminant analysis method we further show that the classical fisher linear discriminant analysis flda is a minimum distance classifier i e nearest class mean classifier induced discriminant analysis method the proposed lm nnda method is evaluated using the cenparmi handwritten numeral database the nust603 handwritten chinese character database the eth80 object category database and the feret face image database the experimental results demonstrate the performance advantage of lm nnda over other feature extraction methods with respect to the lm nn or nn classifier

gradient estimates for the perfect conductivity problem we establish both upper and lower bounds of the gradient estimates for the perfect conductivity problem in the case where perfect stiff conductors are closely spaced inside an open bounded domain and away from the boundary these results give the optimal blow up rates of the stress for conductors with arbitrary shape and in all dimensions

a characteristic point based fuzzy inference classifier by a closeness matrix in this paper a characteristic point based fuzzy inference classifier cpfic is proposed to perform two class classification through fuzzy interpolation a subset of classified samples can be taken as representatives of all samples they are called characteristic points cps a closeness matrix representing the closeness of two samples in a same class is proposed in selecting cps by solving a number of constrained minimizations the cpfic is systematically built experiments were conducted on four classification problems with known bayes errors two benchmark classification problems and a real world application used in our research the cpfic performs well in accuracy evaluations in all the seven experiments the summarizing abilities from the cps into the linguistic descriptions of the fuzzy rule bases were also demonstrated in these examples

local distance functions a taxonomy new algorithms and an evaluation we present a taxonomy for local distance functions where most existing algorithms can be regarded as approximations of the geodesic distance defined by a metric tensor we categorize existing algorithms by how where and when they estimate the metric tensor we also extend the taxonomy along each axis how we introduce hybrid algorithms that use a combination of techniques to ameliorate overfitting where we present an exact polynomial time algorithm to integrate the metric tensor along the lines between the test and training points under the assumption that the metric tensor is piecewise constant when we propose an interpolation algorithm where the metric tensor is sampled at a number of references points during the offline phase the reference points are then interpolated during the online classification phase we also present a comprehensive evaluation on tasks in face recognition object recognition and digit recognition

evolved feature weighting for random subspace classifier the problem addressed in this letter concerns the multiclassifier generation by a random subspace method rsm in the rsm the classifiers are constructed in random subspaces of the data feature space in this letter we propose an evolved feature weighting approach in each subspace the features are multiplied by a weight factor for minimizing the error rate in the training set an efficient method based on particle swarm optimization pso is here proposed for finding a set of weights for each feature in each subspace the performance improvement with respect to the state of the art approaches is validated through experiments with several benchmark data sets

decomposition theorems and fine estimates for electrical fields in the presence of closely located circular inclusions abstract when two inclusions get closer and their conductivities degenerate to zero or infinity the gradient of the solution to the conductivity equation blows up in general in this paper we show that the solution to the conductivity equation can be decomposed into two parts in an explicit form one of them has a bounded gradient and the gradient of the other part blows up using the decomposition we derive the best possible estimates for the blow up of the gradient we then consider the case when the inclusions have positive permittivities we show quantitatively that in this case the size of the blow up is reduced

the multi class metric problem in nearest neighbour discrimination rules abstract nearest neighbour rules classify a new data point on the basis of the class of the closest design set point a prerequisite for this is a choice of metric by which distance may be calculated metrics which have been suggested for the two class case fall into two classes global and local in this paper local metrics are described and are generalized to the multi class case properties of various possible generalizations are compared and the results of a simulation study are described

invariant integration on orthosymplectic and unitary supergroups the orthosymplectic supergroup osp m 2n and unitary supergroup u p q are studied following a new approach that starts from harish chandra pairs and links the sheaf theoretical supermanifold approach of berezin and others with the differential geometry approach of rogers and others the matrix elements of the fundamental representation of the lie supergroup are expressed in terms of functions on the product supermanifold with the underlying lie group and n the odd dimension of this product supermanifold is isomorphic to the supermanifold of this leads to a new expression for the standard generators of the corresponding lie superalgebra as invariant derivations on using these results a new and transparent formula for the invariant integrals on osp m 2n and u p q is obtained

integration on lie supergroups a hopf superalgebra approach abstract let g g 0 g 1 be a finite dimensional complex lie superalgebra such that g 0 is reductive and the adjoint representation of g 0 in g 1 is completely reducible a lie supergroup associated to g is defined by fixing the hopf superalgebra of regular functions on the supergroup then it is shown that on this hopf superalgebra there exists a non zero left integral according to an earlier work by the authors this integral is unique up to scalar multiples

gradient estimates for solutions of the lame system with partially infinite coefficients in dimensions greater than two abstract we establish upper bounds on the blow up rate of the gradients of solutions of the lame system with partially infinite coefficients in dimensions greater than two as the distance between the surfaces of discontinuity of the coefficients of the system tends to zero

gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients in this paper we derive global w1 and piecewise c1 estimates for solutions to divergence form elliptic equations with piecewise holder continuous coefficients the novelty of these estimates is that even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients they are independent of the distance between these surfaces

spectral analysis of the neumann poincare operator and characterization of the stress concentration in anti plane elasticity when holes or hard elastic inclusions are closely located stress which is the gradient of the solution to the anti plane elasticity equation can be arbitrarily large as the distance between two inclusions tends to zero it is important to precisely characterize the blow up of the gradient of such an equation in this paper we show that the blow up of the gradient can be characterized by a singular function defined by the single layer potential of an eigenfunction corresponding to the eigenvalue 1 2 of a neumann poincare type operator defined on the boundaries of the inclusions by comparing the singular function with the one corresponding to two disks osculating to the inclusions we quantitatively characterize the blow up of the gradient in terms of explicit functions in electrostatics our results apply to the electric field which is the gradient of the solution to the conductivity equation in the case where perfectly conducting or insulating inclusions are closely located

optimal bound on high stresses occurring between stiff fibers with arbitrary shaped cross sections abstract we consider high stresses in stiff fiber reinforced materials which increase rapidly as fibers approximate to one another this paper presents the optimal blow up rate of the stresses with respect to the distance between a pair of stiff fibers in r 3 the blow up result plays an important role in our understanding of low strengths of fiber reinforced composites referring to a problem of anti plane shear the stresses can be interpreted as the electric fields outside closely spaced perfect conductors in r 2 under the action of applied electric field h it has been shown by ammari kang et al that in the particular case of circular inclusions the electric field blows up at the optimal rate 1 2 as 0 where is the distance between conductors recently yun has extended the blow up result to pairs of conductors associated with a large class of shapes whose complements can be transformed conformally to the outside of a circle with c 2 mapping however it presented a suboptimal result that only for a special uniform field h 1 0 the electric fields blow up at the exact rate 1 2 in this paper an upper bound with the rate 1 2 of electric field for any harmonic function h is established this yields the optimal blow up rate 1 2 for the inclusions in the same class of shapes as yun

metric learning by discriminant neighborhood embedding in this paper we learn a distance metric in favor of classification task from available labeled samples multi class data points are supposed to be pulled or pushed by discriminant neighbors we define a discriminant adjacent matrix in favor of classification task and learn a map transforming input data into a new space such that intra class neighbors become even more nearby while extra class neighbors become as far away from each other as possible our method is non parametric non iterative and immune to small sample size sss problem target dimensionality of the new space is selected by spectral analysis in the proposed method experiments on real world data sets demonstrate the effectiveness of our method

random forests and adaptive nearest neighbors in this article we study random forests through their connection with a new framework of adaptive nearest neighbor methods we introduce a concept of potential nearest neighbors k pnns and show that random forests can be viewed as adaptively weighted k pnn methods various aspects of random forests can be studied from this perspective we study the effect of terminal node sizes on the prediction accuracy of random forests we further show that random forests with adaptive splitting schemes assign weights to k pnns in a desirable way for the estimation at a given target point these random forests assign voting weights to the k pnns of the target point according to the local importance of different input variables we propose a new simple splitting scheme that achieves desirable adaptivity in a straightforward fashion this simple scheme can be combined with existing algorithms the resulting algorithm is computationally faster and gives comparable results other possible aspects of random forests such

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

prototype selection for dissimilarity based classifiers a conventional way to discriminate between objects represented by dissimilarities is the nearest neighbor method a more efficient and sometimes a more accurate solution is offered by other dissimilarity based classifiers they construct a decision rule based on the entire training set but they need just a small set of prototypes the so called representation set as a reference for classifying new objects such alternative approaches may be especially advantageous for non euclidean or even non metric dissimilarities the choice of a proper representation set for dissimilarity based classifiers is not yet fully investigated it appears that a random selection may work well in this paper a number of experiments has been conducted on various metric and non metric dissimilarity representations and prototype selection methods several procedures like traditional feature selection methods here effectively searching for prototypes mode seeking and linear programming are compared to the random selection in general we find out that systematic approaches lead to better results than the random selection especially for a small number of prototypes although there is no single winner as it depends on data characteristics the k centres works well in general for two class problems an important observation is that our dissimilarity based discrimination functions relying on significantly reduced prototype sets 3 10 of the training objects offer a similar or much better classification accuracy than the best k nn rule on the entire training set this may be reached for multi class data as well however such problems are more difficult

a semi supervised metric learning for content based image retrieval in this paper the authors propose a kernel based approach to improve the retrieval performances of cbir systems by learning a distance metric based on class probability distributions unlike other metric learning methods which are based on local or global constraints the proposed method learns for each class a nonlinear kernel which transforms the original feature space to a more effective one the distances between query and database images are then measured in the new space experimental results show that the kernel based approach not only improves the retrieval performances of kernel distance without learning but also outperforms other kernel metric learning methods

invariant integration on classical and quantum lie supergroups invariant integrals on hopf superalgebras in particular the classical and quantum lie supergroups are studied the uniqueness up to scalar multiples of a left integral is proved and a z2 graded version of maschke s theorem is discussed a construction of left integrals is developed for classical and quantum lie supergroups applied to several classes of examples the construction yields the left integrals in explicit form

electric field concentration in the presence of an inclusion with eccentric core shell geometry in this paper we analyze the gradient blow up of the solution to the conductivity problem in two dimensions in the presence of an inclusion with eccentric core shell geometry assuming that the core and shell have circular boundaries that are nearly touching we derive an asymptotic formula for the solution in terms of the single and double layer potentials with image line charges we also deduce an integral formula with image line charges for the problem relating to two nearly touching separated conductors

quantitative characterization of stress concentration in the presence of closely spaced hard inclusions in two dimensional linear elasticity in the region between close to touching hard inclusions stress may be arbitrarily large as the inclusions get closer this stress is represented by the gradient of a solution to the lame system of linear elasticity we consider the problem of characterizing the gradient blow up of the solution in the narrow region between two inclusions and estimating its magnitude we introduce singular functions which are constructed in terms of nuclei of strain and hence are solutions of the lame system and then show that the singular behavior of the gradient in the narrow region can be precisely captured by singular functions as a consequence of the characterization we are able to regain the existing upper bound on the blow up rate of the gradient namely 1 2 where is the distance between two inclusions we then show that it is in fact an optimal bound by showing that there are cases where 1 2 is also a lower bound this work is the first to completely reveal the singular nature of the gradient blow up and to obtain the optimal blow up rate in the context of the lame system with hard inclusions the singular functions introduced in this paper play essential roles in overcoming the difficulties in applying the methods of previous works the main tools of this paper are the layer potential techniques and the variational principle the variational principle can be applied because the singular functions of this paper are solutions of the lame system

a novel template reduction approach for the k nearest neighbor method the k nearest neighbor knn rule is one of the most widely used pattern classification algorithms for large data sets the computational demands for classifying patterns using knn can be prohibitive a way to alleviate this problem is through the condensing approach this means we remove patterns that are more of a computational burden but do not contribute to better classification accuracy in this brief we propose a new condensing algorithm the proposed idea is based on defining the so called chain this is a sequence of nearest neighbors from alternating classes we make the point that patterns further down the chain are close to the classification boundary and based on that we set a cutoff for the patterns we keep in the training set experiments show that the proposed approach effectively reduces the number of prototypes while maintaining the same level of classification accuracy as the traditional knn moreover it is a simple and a fast condensing algorithm

regularized margin based conditional log likelihood loss for prototype learning the classification performance of nearest prototype classifiers largely relies on the prototype learning algorithm the minimum classification error mce method and the soft nearest prototype classifier snpc method are two important algorithms using misclassification loss this paper proposes a new prototype learning algorithm based on the conditional log likelihood loss cll which is based on the discriminative model called log likelihood of margin logm a regularization term is added to avoid over fitting in training as well as to maximize the hypothesis margin the cll in the logm algorithm is a convex function of margin and so shows better convergence than the mce in addition we show the effects of distance metric learning with both prototype dependent weighting and prototype independent weighting our empirical study on the benchmark datasets demonstrates that the logm algorithm yields higher classification accuracies than the mce generalized learning vector quantization glvq soft nearest prototype classifier snpc and the robust soft learning vector quantization rslvq and moreover the logm with prototype dependent weighting achieves comparable accuracies to the support vector machine svm classifier

the first fundamental theorem of invariant theory for the orthosymplectic supergroup we give an elementary and explicit proof of the first fundamental theorem of invariant theory for the orthosymplectic supergroup by generalising the geometric method of atiyah bott and patodi to the supergroup context we use methods from super algebraic geometry to convert invariants of the orthosymplectic supergroup into invariants of the corresponding general linear supergroup on a different space in this way super schur weyl brauer duality is established between the orthosymplectic supergroup of superdimension m 2n and the brauer algebra with parameter m 2n the result may be interpreted either in terms of the group scheme osp v over mathbb c where v is a finite dimensional super space or as a statement about the orthosymplectic lie supergroup over the infinite dimensional grassmann algebra lambda we take the latter point of view here and also state a corresponding theorem for the orthosymplectic lie superalgebra which involves an extra invariant generator the super pfaffian

stress concentration for closely located inclusions in nonlinear perfect conductivity problems abstract we study the stress concentration which is the gradient of the solution when two smooth inclusions are closely located in a possibly anisotropic medium r n n 2 the governing equation may be degenerate of p laplace type with 1 p n we prove optimal l estimates for the blow up of the gradient of the solution as the distance between the inclusions tends to zero

relaxational metric adaptation and its application to semi supervised clustering and content based image retrieval the performance of many supervised and unsupervised learning algorithms is very sensitive to the choice of an appropriate distance metric previous work in metric learning and adaptation has mostly been focused on classification tasks by making use of class label information in standard clustering tasks however class label information is not available in order to adapt the metric to improve the clustering results some background knowledge or side information is needed one useful type of side information is in the form of pairwise similarity or dissimilarity information recently some novel methods e g the parametric method proposed by xing et al for learning global metrics based on pairwise side information have been shown to demonstrate promising results in this paper we propose a nonparametric method called relaxational metric adaptation rma for the same metric adaptation problem while rma is local in the sense that it allows locally adaptive metrics it is also global because even patterns not in the vicinity can have long range effects on the metric adaptation process experimental results for semi supervised clustering based on both simulated and real world data sets show that rma outperforms xing et al s method under most situations besides applying rma to semi supervised learning we have also used it to improve the performance of content based image retrieval systems through metric adaptation experimental results based on two real world image databases show that rma significantly outperforms other methods in improving the image retrieval performance

locally linear metric adaptation with application to semi supervised clustering and image retrieval many computer vision and pattern recognition algorithms are very sensitive to the choice of an appropriate distance metric some recent research sought to address a variant of the conventional clustering problem called semi supervised clustering which performs clustering in the presence of some background knowledge or supervisory information expressed as pairwise similarity or dissimilarity constraints however existing metric learning methods for semi supervised clustering mostly perform global metric learning through a linear transformation in this paper we propose a new metric learning method that performs nonlinear transformation globally but linear transformation locally in particular we formulate the learning problem as an optimization problem and present three methods for solving it through some toy data sets we show empirically that our locally linear metric adaptation llma method can handle some difficult cases that cannot be handled satisfactorily by previous methods we also demonstrate the effectiveness of our method on some uci data sets besides applying llma to semi supervised clustering we have also used it to improve the performance of content based image retrieval systems through metric learning experimental results based on two real world image databases show that llma significantly outperforms other methods in boosting the image retrieval performance

a kernel approach for semisupervised metric learning while distance function learning for supervised learning tasks has a long history extending it to learning tasks with weaker supervisory information has only been studied recently in particular some methods have been proposed for semisupervised metric learning based on pairwise similarity or dissimilarity information in this paper we propose a kernel approach for semisupervised metric learning and present in detail two special cases of this kernel approach the metric learning problem is thus formulated as an optimization problem for kernel learning an attractive property of the optimization problem is that it is convex and hence has no local optima while a closed form solution exists for the first special case the second case is solved using an iterative majorization procedure to estimate the optimal solution asymptotically experimental results based on both synthetic and real world data show that this new kernel approach is promising for nonlinear metric learning

optimal estimates for the conductivity problem by green s function method we study a class of second order elliptic equations of divergence form with discontinuous coefficients and data which models the conductivity problem in composite materials we establish optimal gradient estimates by showing the explicit dependence of the elliptic coefficients and the distance between interfacial boundaries of inclusions these extend the known results in the literature and answer open problem b proposed by li and vogelius 2000 for the isotropic conductivity problem we also obtain more interesting higher order derivative estimates which answers open problem c of li and vogelius 2000 it is worth pointing out that the equations under consideration in this paper are non homogeneous

invariants of the orthosymplectic lie superalgebra and super pfaffians given a complex orthosymplectic superspace v the orthosymplectic lie superalgebra mathfrak osp v and general linear algebra mathfrak gl n both act naturally on the coordinate super ring mathcal s n of the dual space of v otimes mathbb c n and their actions commute hence the subalgebra mathcal s n mathfrak osp v of mathfrak osp v invariants in mathcal s n has a mathfrak gl n module structure sergeev has indicated how to define a pfaffian in this space and announced that together with the invariants of the group mathrm osp v it generates all invariants of mathfrak osp v we introduce a space of super pfaffians show it is a simple mathfrak gl n submodule of mathcal s n mathfrak osp v give an explicit formula for its highest weight vector and prove that the super pfaffians and the mathrm osp v invariants generate mathcal s n mathfrak osp v as an algebra the decomposition of mathcal s n mathfrak osp v as a direct sum of simple mathfrak gl n submodules is obtained and shown to be multiplicity free using howe s mathfrak gl v mathfrak gl n duality on mathcal s n we further analyse the module structure of that space these results also enable us to determine the mathfrak osp v invariants in the tensor powers v otimes r for all r

an efficient prototype merging strategy for the condensed 1 nn rule through class conditional hierarchical clustering abstract a generalized prototype based classification scheme founded on hierarchical clustering is proposed the basic idea is to obtain a condensed 1 nn classification rule by merging the two same class nearest clusters provided that the set of cluster representatives correctly classifies all the original points apart from the quality of the obtained sets and its flexibility which comes from the fact that different intercluster measures and criteria can be used the proposed scheme includes a very efficient four stage procedure which conveniently exploits geometric cluster properties to decide about each possible merge empirical results demonstrate the merits of the proposed algorithm taking into account the size of the condensed sets of prototypes the accuracy of the corresponding condensed 1 nn classification rule and the computing time

input space versus feature space in kernel based methods this paper collects some ideas targeted at advancing our understanding of the feature spaces associated with support vector sv kernel functions we first discuss the geometry of feature space in particular we review what is known about the shape of the image of input space under the feature space map and how this influences the capacity of sv methods following this we describe how the metric governing the intrinsic geometry of the mapped surface can be computed in terms of the kernel using the example of the class of inhomogeneous polynomial kernels which are often used in sv pattern recognition we then discuss the connection between feature space and input space by dealing with the question of how one can given some vector in feature space find a preimage exact or approximate in input space we describe algorithms to tackle this issue and show their utility in two applications of kernel methods first we use it to reduce the computational complexity of sv decision functions second we combine it with the kernel pca algorithm thereby constructing a nonlinear statistical denoising technique which is shown to perform well on real world data