numerical solution of systems of second order boundary value problems using continuous genetic algorithm in this paper continuous genetic algorithm is introduced as an efficient solver for systems of second order boundary value problems where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variables the solution methodology is based on representing each derivative in the system of differential equations by its finite difference approximation after that the overall residue for all nodes in the given system of differential equations is formulated the solution to the system of differential equations is then converted into the problem of minimizing the overall residue or maximizing the fitness function based on the nodal values generated from the genetic operators three numerical test problems including linear and nonlinear systems were analyzed to illustrate the procedure and confirm the performance of the proposed method in addition to that a convergence and sensitivity analysis to genetic operators and control parameters of the algorithm has been carried out the numerical results show that the proposed algorithm is a robust and accurate procedure for solving systems of second order boundary value problems furthermore the obtained accuracy for the solutions using cga is much better than the results obtained using some modern methods

atomic and molecular decompositions of anisotropic besov spaces in this work we develop the theory of weighted anisotropic besov spaces associated with general expansive matrix dilations and doubling measures with the use of discrete wavelet transforms this study extends the isotropic littlewood paley methods of dyadic transforms of frazier and jawerth 19 21 to non isotropic settings

fuzzy rough classifiers for class imbalanced multi instance data in multi instance learning each learning object consists of many descriptive instances in the corresponding classification problems each training object is labeled but its constituent instances are not the classification objective is to predict the class label of unseen objects as in traditional single instance classification when the class sizes of multi instance data are imbalanced classification is degraded many multi instance classifiers have been proposed but few take into account the possibility of class imbalance which causes them to fail in this situation in this paper we propose a new type of classifier that embodies a solution to the multi instance class imbalance problem our proposal relies on the use of fuzzy rough set theory we present two families of classifiers respectively based on information extracted at bag level and at instance level we experimentally show that our algorithms outperform state of the art solutions to multi instance imbalanced data classification evaluated by the popular metrics auc and geometric mean highlightswe propose a new type of classifier for imbalanced multi instance data our classification method is based on fuzzy rough set theory we develop a framework consisting of two classifier families our proposal is experimentally shown to outperform the state of the art

mixture of grouped regressors and its application to visual mapping mixture of regressors mor is a widely used regression approach for approximating nonlinear mappings between input and target outputs however existing learning procedures for mor are prone to overfitting when only limited amounts of training data are available to address this problem we propose a new mixture regression model named mixture of grouped regressors mogr it partitions the individual regressors in the model into a set of groups where the parameters of the regressors within each group are encouraged to take on similar values as the parameters for each local regressor are learned using all data within a group they tend to be better conditioned and more robust to noise in the training data extensive experiments on real world head pose and gaze data demonstrate the benefits of our proposed mogr model highlightsmixture of grouped regressors mogr is proposed to tackle overfitting problems of existing mixture of regressors methods mogr partitions the individual regressors in mixture regression model into a number of groups the parameters of each regressor are learned using all data within a group rather than a cluster mogr requires a small number of training data and is robust to noise it has shown obviously improved performance when compared with state of the art nonlinear visual mapping methods

recursive projection twin support vector machine via within class variance minimization in this paper a novel binary classifier coined projection twin support vector machine ptsvm is proposed the idea is to seek two projection directions one for each class such that the projected samples of one class are well separated from those of the other class in its respective subspace in order to further boost performance a recursive algorithm for ptsvm is proposed to generate more than one projection axis for each class to overcome the singularity problem principal component analysis pca is utilized to transform the data in the original space into a low dimensional subspace wherein the optimization problem of ptsvm is convex and can be solved efficiently the experimental results on several uci benchmark data sets and usps digit database show the feasibility and effectiveness of the proposed method

a possibilistic regression based on gradual interval b splines application for hyperspectral imaging lake sediments abstract according to an epistemic view of intervals this paper proposes a possibilistic regression based on gradual interval b splines to represent the input output data mapping in this context an improvement of the parametric fuzzy regression through the notion of gradual interval b splines is proposed the proposed gradual regression based on b splines can be regarded as an extension of the nonparametric interval based regression where an uncertain dimension is integrated the proposed method is validated through illustrative and comparative examples moreover it is applied for modeling the input output behavior between reflectance and wavelengths in an application for hyperspectral imaging for lake sediments

instance categorization by support vector machines to adjust weights in adaboost for imbalanced data classification we proposed an improved weighted svm for imbalanced classification different factor scores are computed by categorizing instances based on the svm margin numerical experiments showed the proposed method outperforming the existing approaches in terms of f measure auc to address class imbalance in data we propose a new weight adjustment factor that is applied to a weighted support vector machine svm as a weak learner of the adaboost algorithm different factor scores are computed by categorizing instances based on the svm margin and are assigned to related instances the svm margin is used to define borderline and noisy instances and the factor scores are assigned to only borderline instances and positive noise the adjustment factor is then employed as a multiplier to the instance weight in the adaboost algorithm when learning a weighted svm using 10 real class imbalanced datasets we compare the proposed method to a standard svm and other svms combined with various sampling and boosting methods numerical experiments show that the proposed method outperforms existing approaches in terms of f measure and area under the receiver operating characteristic curve which means that the proposed method is useful for relaxing the class imbalance problem by addressing well known degradation issues such as overlap small disjunct and data shift problems

generalized coorbit space theory and inhomogeneous function spaces of besov lizorkin triebel type coorbit space theory is an abstract approach to function spaces and their atomic decom positions the original theory developed by feichtinger and grochenig in the late 1980ies heavily uses integrable representations of locally compact groups their theory covers in particular homogeneous besov lizorkin triebel spaces modulation spaces bergman spaces and the recent shearlet spaces however inhomogeneous besov lizorkin triebel spaces cannot be covered by their group theoretical approach later it was recognized by fornasier and the first named author 24 that one may replace coherent states related to the group representation by more general abstract continuous frames in the first part of the present paper we significantly extend this abstract generalized coorbit space theory to treat a wider variety of coorbit spaces a unified approach towards atomic decompositions and banach frames with new results for general coorbit spaces is presented in the second part we apply the abstract setting to a specific framework and study coorbits of what we call peetre spaces they allow to recover inhomogeneous besov lizorkin triebel spaces of var ious types of interest as coorbits we obtain several old and new wavelet characterizations based on explicit smoothness decay and vanishing moment assumptions of the respective wavelet as main examples we obtain results for weighted spaces muckenhoupt doubling general 2 microlocal spaces besov lizorkin triebel morrey spaces spaces of dominating mixed smoothness and even mixtures of the mentioned ones due to the generality of our approach there are many more examples of interest where the abstract coorbit space theory is applicable

carleson embeddings for sobolev spaces via heat equation abstract let u t x be the solution of the heat equation t x u t x 0 on r 1 n 0 r n subject to u 0 x f x on r n the main goal of this paper is to characterize such a nonnegative measure on r 1 n that f x u t 2 x induces a bounded embedding from the sobolev space w 1 p r n p 1 n into the lebesgue space l q r 1 n q 0

characterizations of weighted besov and triebel lizorkin spaces via temperatures abstract hardy littlewood type characterizations via temperatures on a half space of weighted besov and triebel lizorkin spaces studied recently by the author are given in the proof of the sufficient parts of the results a sub mean value property of temperatures is used in an elegant way to get control of certain terms by the hardy maximal function or its vector valued version as a byproduct of the results another characterization of weighted hardy spaces as well as characterizations of the gauss weierstrass integrals on a strip domain of distributions in the above weighted spaces is obtained also

a characterization of hajlasz sobolev and triebel lizorkin spaces via grand littlewood paley functions abstract in this paper we establish the equivalence between the hajlasz sobolev spaces or classical triebel lizorkin spaces and a class of grand triebel lizorkin spaces on euclidean spaces and also on metric spaces that are both doubling and reverse doubling in particular when p n n 1 we give a new characterization of the hajlasz sobolev spaces m 1 p r n via a grand littlewood paley function

decompositions of besov morrey spaces and triebel lizorkin morrey spaces the aim of this paper is to define the besov morrey spaces and the triebel lizorkin morrey spaces and to present a decomposition of functions belonging to these spaces our results contain an answer to the conjecture proposed by mazzucato

pointwise characterizations of besov and triebel lizorkin spaces and quasiconformal mappings abstract in this paper the authors characterize in terms of pointwise inequalities the classical besov spaces b p q s and triebel lizorkin spaces f p q s for all s 0 1 and p q n n s both in r n and in the metric measure spaces enjoying the doubling and reverse doubling properties applying this characterization the authors prove that quasiconformal mappings preserve f n s q s on r n for all s 0 1 and q n n s a metric measure space version of the above morphism property is also established

support function machine for set based classification with application to water quality evaluation in some applications measurement errors and multiple repeated measurements often lead to a set based classification task where objects are represented with a set of samples and the traditional support vector machines svms do not work in these settings to deal with this problem we construct a new classifier called support function machine sfm in this work first sets in d dimensional euclidean space r d are mapped into an infinite dimensional banach space c s whose elements are functions via support functions and then set based classification in r d is converted into function based classification in c s second we define the hyperplane via the riesz representation theorem in banach space and discuss the hausdorff distance of hyperpalnes and maximum margin principle mmp in c s based on mmp we construct an optimal problem and discuss some of its properties thereafter we establish an sfm to solve set based classification experiments about water quality evaluation and set valued data classifications show the superiority of sfm

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

orthogonal spline collocation methods for partial differential equations abstract this paper provides an overview of the formulation analysis and implementation of orthogonal spline collocation osc also known as spline collocation at gauss points for the numerical solution of partial differential equations in two space variables advances in the osc theory for elliptic boundary value problems are discussed and direct and iterative methods for the solution of the osc equations examined the use of osc methods in the solution of initial boundary value problems for parabolic hyperbolic and schrodinger type systems is described with emphasis on alternating direction implicit methods the osc solution of parabolic and hyperbolic partial integro differential equations is also mentioned finally recent applications of a second spline collocation method modified spline collocation are outlined

twin support vector machines for pattern classification we propose twin svm a binary svm classifier that determines two nonparallel planes by solving two related svm type problems each of which is smaller than in a conventional svm the twin svm formulation is in the spirit of proximal svms via generalized eigenvalues on several benchmark data sets twin svm is not only fast but shows good generalization twin svm is also useful for automatically discovering two dimensional projections of the data

ptsvrs regression models via projection twin support vector machine abstract taking motivation from projection twin support vector machine ptsvm formulation for recognition this paper proposes two novel projection twin support vector regression ptsvr models called pair shifted ptsvr pptsvr and single shifted ptsvr sptsvr respectively ptsvrs construct indirectly the target regressor by two functions hyperplanes obtained from two smaller sized quadratic programming problems qpps in which each normal direction makes the within class variance of the projection of shifted set or original set be minimized and the projected center be at a distance of at least 1 from the projection of the other shifted set as other twin support vector machine twsvm models the learning speed of ptsvrs is faster than classical support vector regression svr since each of their qpp has only half size experimental results on several synthetic as well as benchmark datasets indicate the significant advantage of pptsvr and sptsvr in the generalization performance

distance metric optimization driven convolutional neural network for age invariant face recognition propose a new distance metric optimization driven deep learning framework for age invariant face recognition learn feature representations and the similarity measure simultaneously in an end to end way train the joint network using a novel optimization method and carefully designed training strategies the experimental results demonstrate the effectiveness of our approach despite the great advances in face related works in recent years face recognition across age remains a challenging problem the traditional approaches to this problem usually include two basic steps feature extraction and the application of a distance metric sometimes common space projection is also involved on the one hand handling these steps separately ignores the interactions of these components and on the other hand the fixed distance threshold of measurement affects the models robustness in this paper we present a novel distance metric optimization driven learning approach that integrates these traditional steps via a deep convolutional neural network which learns feature representations and the decision function in an end to end way given the labelled training images we first generate a large number of pairs with a certain proportion of matched and unmatched pairs for matched pairs we try to select as many different age instances as possible for each person to learn the identification information that is not affected by age then taking these pairs as input we aim to enlarge the differences between the unmatched pairs while reducing the variations between the matched pairs and we update the model parameters by using the mini batch stochastic gradient descent sgd algorithm specifically the distance matrix is used as the top fully connected layer and the bottom layers representing the image features are integrated with it seamlessly thus the image features and the distance metric can be optimized simultaneously by backward propagation in particular we introduce several training strategies to reduce the computational cost and overcome insufficient memory capacity we evaluate our method on three tasks age invariant face identification on the morph database age invariant face retrieval on the cacd database and age invariant face verification on cacd vs database the experimental results demonstrate the effectiveness of our approach

atomic and molecular decompositions of anisotropic triebel lizorkin spaces weighted anisotropic triebel lizorkin spaces are introduced and studied with the use of discrete wavelet transforms this study extends the isotropic methods of dyadic transforms of frazier and jawerth 1985 1989 to non isotropic settings associated with general expansive matrix dilations and a weights in close analogy with the isotropic theory we show that weighted anisotropic triebel lizorkin spaces are characterized by the magnitude of the transforms in appropriate sequence spaces we also introduce non isotropic analogues of the class of almost diagonal operators and we obtain atomic and molecular decompositions of these spaces thus extending isotropic results of frazier and jawerth

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

hardy spaces with variable exponents and generalized campanato spaces in the present paper we define hardy spaces with variable exponents on rn by the grand maximal function and then investigate their several properties the present paper will connect harmonic analysis with function spaces with variable exponents we obtain the atomic decomposition and the molecular decomposition with these decomposition proved we investigate the littlewood paley characterization also we specify the dual spaces of hardy spaces with variable exponents they will turn out to be campanato spaces with variable growth conditions the present paper covers local hardy spaces with variable exponents

orthogonal spline collocation for nonlinear dirichlet problems we study the orthogonal spline collocation osc solution of a homogeneous dirichlet boundary value problem in a rectangle for a general nonlinear elliptic partial differential equation the approximate solution is sought in the space of hermite bicubic splines we prove local existence and uniqueness of the osc solution obtain optimal order h1 and h2 error estimates and prove the quadratic convergence of newton s method for solving the osc problem

improvements on twin support vector machines for classification problems the generalized eigenvalue proximal support vector machine gepsvm and twin support vector machine twsvm are regarded as milestones in the development of the powerful svms as they use the nonparallel hyperplane classifiers in this brief we propose an improved version named twin bounded support vector machines tbsvm based on twsvm the significant advantage of our tbsvm over twsvm is that the structural risk minimization principle is implemented by introducing the regularization term this embodies the marrow of statistical learning theory so this modification can improve the performance of classification in addition the successive overrelaxation technique is used to solve the optimization problems to speed up the training procedure experimental results show the effectiveness of our method in both computation time and classification accuracy and therefore confirm the above conclusion further

mixed finite element methods for nonlinear second order elliptic problems mixed finite element methods are developed to approximate the solution of the dirichlet problem for the most general quasi linear second order elliptic operator in divergence form existence and uniqueness of the approximation are proved and optimal error estimates in l 2 are demonstrated for both the scalar and vector functions approximated by the method error estimates are also derived in l q 2 leq q leq infty newton s method is presented and analyzed to solve the nonlinear algebraic equations

tpmsvm a novel twin parametric margin support vector machine for pattern recognition a novel twin parametric margin support vector machine tpmsvm for classification is proposed in this paper this tpmsvm in the spirit of the twin support vector machine twsvm determines indirectly the separating hyperplane through a pair of nonparallel parametric margin hyperplanes solved by two smaller sized support vector machine svm type problems similar to the parametric margin email protected support vector machine email protected svm this tpmsvm is suitable for many cases especially when the data has heteroscedastic error structure that is the noise strongly depends on the input value but there is an advantage in the learning speed compared with the email protected svm the experimental results on several artificial and benchmark datasets indicate that the tpmsvm not only obtains fast learning speed but also shows good generalization

riesz transforms associated to schrodinger operators on weighted hardy spaces let w be some ap weight and enjoy reverse holder inequality and let l v be a schrodinger operator on rn where v lloc1 rn is a non negative function on rn in this article we introduce weighted hardy spaces hl w1 rn associated to l in terms of the area function characterization and prove their atomic characters we show that the riesz transform l 1 2 associated to l is bounded on lwp rn for 1 p 2 and bounded from hl w1 rn to the classical weighted hardy space hw1 rn

a new class of function spaces connecting triebel lizorkin spaces and q spaces abstract let s r 0 p 1 and q 1 in this paper we introduce a new class of function spaces f p q s r n which unify and generalize the triebel lizorkin spaces with both p 1 and p and q spaces by establishing the carleson measure characterization of q space we then determine the relationship between triebel lizorkin spaces and q spaces which answers a question posed by dafni and xiao in g dafni j xiao some new tent spaces and duality theorem for fractional carleson measures and q r n j funct anal 208 2004 377 422 moreover via the hausdorff capacity we introduce a new class of tent spaces f t p q s r n 1 and determine their dual spaces f w p q s q r n where s r p q 1 max p q 1 0 q max p q and t denotes the conjugate index of t 1 as an application of this we further introduce certain hardy hausdorff spaces f h p q s r n and prove that the dual space of f h p q s r n is just f p q s q r n when p q 1

distributed cooperative learning over time varying random networks using a gossip based communication protocol abstract motivated by applications of distributed estimation and distributed decision making in wireless sensor networks wsns and unmanned aerial vehicle uav networks we study a distributed learning problem over time varying undirected random networks using a gossip based communication protocol a novel distributed cooperative learning dcl algorithm termed the gossip based dcl gbdcl algorithm is presented to solve the problem by training the raw data distributed and blocked throughout different nodes exploiting the robustness of the gossip based protocol each node is guaranteed to build the same learning model in theory against random disconnections and communication route variations in the network topology it is proved that the gbdcl algorithm converges to the optimal consensus asymptotically the correctness and effectiveness of the presented gbdcl algorithm are verified in the theoretical analysis and simulations

traces of weighted sobolev spaces old and new abstract we give short simple proofs of uspenski s results characterizing besov spaces as trace spaces of weighted sobolev spaces we generalize uspenski s results and prove the optimality of these generalizations we next show how classical results on the functional calculus in the besov spaces can be obtained as straightforward consequences of the theory of weighted sobolev spaces

a discrete transform and decompositions of distribution spaces abstract we study a representation formula of the form q q q for a distribution on r n this formula is obtained by discretizing and localizing a standard littlewood paley decomposition the map taking to the sequence q q with q running over the dyadic cubes in r n is called the transform the functions q and q have a particularly simple form moreover most of the familiar distribution spaces lp spaces 1 r n we also consider pointwise multipliers for the characteristic function of a domain we obtain boundedness results for a general class of domains which properly includes lipschitz domains several interpolation methods are easily analyzed via the sequence spaces for real interpolation we obtain among other things an extension to the case p 0 this in turn gives a new approach to the traditional atomic decomposition of hardy spaces

building sparse twin support vector machine classifiers in primal space abstract twin support vector machines tsvm obtain faster training speeds than classical support vector machines svm however tsvm augmented vectors lose sparsity in this paper a rapid sparse twin support vector machine stsvm classifier in primal space is proposed to improve the sparsity and robustness of tsvm based on a simple back fitting strategy the stsvm iteratively builds each nonparallel hyperplanes by adding one support vector sv from the corresponding class at one time this process is terminated using an adaptive and stable stopping criterion stsvm learning is implemented by linear equation computing systems through introducing a quadratic function to approximate the empirical risk the computational results on several synthetic and benchmark datasets indicate that the stsvm obtains a sparse separating hyperplane at a low cost without sacrificing its generalization performance

on the stability in weak topology of the set of global solutions to the navier stokes equations let x be a suitable function space and let mathcal g subset x be the set of divergence free vector fields generating a global smooth solution to the incompressible homogeneous three dimensional navier stokes equations we prove that a sequence of divergence free vector fields converging in the sense of distributions to an element of mathcal g belongs to mathcal g if n is large enough provided the convergence holds anisotropically in frequency space typically this excludes self similar type convergence anisotropy appears as an important qualitative feature in the analysis of the navier stokes equations it is also shown that initial data which do not belong to mathcal g hence which produce a solution blowing up in finite time cannot have a strong anisotropy in their frequency support

non uniform painless decompositions for anisotropic besov and triebel lizorkin spaces abstract in this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the lebesgue spaces l p r d 1 p the novelty and difficulty of this construction is that we allow for non lattice translations we prove that for an arbitrary expansive matrix a and any set satisfying a certain spreadness condition but otherwise irregular there exists a smooth window whose translations along the elements of and dilations by powers of a provide an atomic decomposition for the whole range of the anisotropic triebel lizorkin spaces the generating window can be either chosen to be bandlimited or to have compact support to derive these results we start with a known general painless construction that has recently appeared in the literature we show that this construction extends to besov and triebel lizorkin spaces by providing adequate dual systems

cumulative attribute space regression for head pose estimation and color constancy abstract two stage cumulative attribute ca regression has been found effective in regression problems of computer vision such as facial age and crowd density estimation the first stage regression maps input features to cumulative attributes that encode correlations between target values the previous works have dealt with single output regression in this work we propose cumulative attribute spaces for 2 and 3 output multivariate regression we show how the original ca space can be generalized to multiple output by the cartesian product cartca however for target spaces with more than two outputs the cartca becomes computationally infeasible and therefore we propose an approximate solution multi view ca mvca where cartca is applied to output pairs we experimentally verify improved performance of the cartca and mvca spaces in 2d and 3d face pose estimation and three output rgb illuminant estimation for color constancy

synchronized submanifold embedding for person independent pose estimation and beyond precise 3 d head pose estimation plays a significant role in developing human computer interfaces and practical face recognition systems this task is challenging due to the particular appearance variations caused by pose changes for a certain subject in this paper the pose data space is considered as a union of submanifolds which characterize different subjects instead of a single continuous manifold as conventionally regarded a novel manifold embedding algorithm dually supervised by both identity and pose information called snchronized submanifold embedding sse is proposed for person independent precise 3 d pose estimation which means that the testing subject may not appear in the model training stage first the submanifold of a certain subject is approximated as a set of simplexes constructed using neighboring samples then these simplexized submanifolds from different subjects are embedded by synchronizing the locally propagated poses within the simplexes and at the same time maximizing the intrasubmanifold variances finally the pose of a new datum is estimated as the propagated pose of the nearest point within the simplex constructed by its nearest neighbors in the dimensionality reduced feature space the experiments on the 3 d pose estimation database chil data for clear07 evaluation and the extended application for age estimation on fg net aging database demonstrate the superiority of sse over conventional regression algorithms as well as unsupervised manifold learning algorithms

littlewood paley characterization and duality of weighted anisotropic product hardy spaces the authors study anisotropic product hardy spaces hwp a associated with a pair a a1 a2 of expansive dilations and a class of product muckenhoupt weights a a on rn rm this article is a continuation of their earlier work in bownik et al 2010 8 the authors establish the littlewood paley g function characterization and the transform characterization of hwp a 0 p 1 the authors also introduce the weighted anisotropic product campanato space lp w a and establish its transform characterization as an application the authors identify the dual space of hwp a with lp w a the results of this article improve the existing results for weighted product hardy spaces on r r and are new even in the weighted isotropic setting

duality and interpolation of anisotropic triebel lizorkin spaces we study properties of anisotropic triebel lizorkin spaces associated with general expansive dilations and doubling measures on mathbb r n using wavelet transforms this paper is a continuation of bownik in j geom anal 2007 to appear trans am math soc 358 1469 1510 2006 where we generalized the isotropic methods of dyadic varphi transforms of frazier and jawerth j funct anal 93 34 170 1990 to non isotropic settings by working at the level of sequence spaces we identify the duals of anisotropic triebel lizorkin spaces we also obtain several real and complex interpolation results for these spaces

an atomic decomposition of weighted hardy spaces associated to self adjoint operators abstract let w be an a p weight on r n 1 p let l be a non negative self adjoint operator acting on l 2 r n satisfying a pointwise gaussian estimate for its heat kernel in this article we obtain a weighted q atomic decomposition with q p for the weighted hardy space h l w 1 r n associated to l which was introduced in 28 the main contribution of this article is to weaken conditions on the weight w of the weighted hardy spaces h l w 1 r n and improve the result in 28

new besov type spaces and triebel lizorkin type spaces including q spaces let s tau in mathbb r and q in 0 infty we introduce besov type spaces dot b s tau p q mathbb r n for p in 0 infty and triebel lizorkin type spaces dot f s tau p q mathbb r n rm for p in 0 infty which unify and generalize the besov spaces triebel lizorkin spaces and q spaces we then establish the varphi transform characterization of these new spaces in the sense of frazier and jawerth using the varphi transform characterization of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n we obtain their embedding and lifting properties moreover for appropriate we also establish the smooth atomic and molecular decomposition characterizations of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n for s in mathbb r p in 1 infty q in 1 infty and tau in 0 frac 1 max p q via the hausdorff capacity we introduce certain hardy hausdorff spaces b dot h s tau p q mathbb r n and prove that the dual space of b dot h s tau p q mathbb r n is just dot b s tau p q mathbb r n where t denotes the conjugate index of t in 1 infty

data dependent label distribution learning for age estimation as an important and challenging problem in computer vision face age estimation is typically cast as a classification or regression problem over a set of face samples with respect to several ordinal age labels which have intrinsically cross age correlations across adjacent age dimensions as a result such correlations usually lead to the age label ambiguities of the face samples namely each face sample is associated with a latent label distribution that encodes the cross age correlation information on label ambiguities motivated by this observation we propose a totally data driven label distribution learning approach to adaptively learn the latent label distributions the proposed approach is capable of effectively discovering the intrinsic age distribution patterns for cross age correlation analysis on the basis of the local context structures of face samples without any prior assumptions on the forms of label distribution learning our approach is able to flexibly model the sample specific context aware label distribution properties by solving a multi task problem which jointly optimizes the tasks of age label distribution learning and age prediction for individuals experimental results demonstrate the effectiveness of our approach

solving the multiple instance problem with axis parallel rectangles the multiple instance problem arises in tasks where the training examples are ambiguous a single example object may have many alternative feature vectors instances that describe it and yet only one of those feature vectors may be responsible for the observed classification of the object this paper describes and compares three kinds of algorithms that learn axis parallel rectangles to solve the multiple instance problem algorithms that ignore the multiple instance problem perform very poorly an algorithm that directly confronts the multiple instance problem by attempting to identify which feature vectors are responsible for the observed classifications performs best giving 89 correct predictions on a musk odor prediction task the paper also illustrates the use of artificial data to debug and compare these algorithms

facial age estimation based on label sensitive learning and age oriented regression this paper provides a new age estimation approach which distinguishes itself with the following three contributions first we combine distance metric learning and dimensionality reduction to better explore the connections between facial features and age labels second to exploit the intrinsic ordinal relationship among human ages and overcome the potential data imbalance problem a label sensitive concept and several imbalance treatments are introduced in the system training phase finally an age oriented local regression is presented to capture the complicated facial aging process for age determination the simulation results show that our approach achieves the lowest estimation error against existing methods

anisotropic variable hardy lorentz spaces and their real interpolation abstract let p r n 0 be a variable exponent function satisfying the globally log holder continuous condition q 0 and a be a general expansive matrix on r n in this article the authors first introduce the anisotropic variable hardy lorentz space h a p q r n associated with a via the radial grand maximal function and then establish its radial or non tangential maximal function characterizations moreover the authors also obtain characterizations of h a p q r n respectively in terms of the atom and the lusin area function as an application the authors prove that the anisotropic variable hardy lorentz space h a p q r n serves as the intermediate space between the anisotropic variable hardy space h a p r n and the space l r n via the real interpolation this together with a special case of the real interpolation theorem of h kempka and j vybiral on the variable lorentz space further implies the coincidence between h a p q r n and the variable lorentz space l p q r n when ess inf x r n p x 1

function spaces of variable smoothness and integrability abstract in this article we introduce triebel lizorkin spaces with variable smoothness and integrability our new scale covers spaces with variable exponent as well as spaces of variable smoothness that have been studied in recent years vector valued maximal inequalities do not work in the generality which we pursue and an alternate approach is thus developed using it we derive molecular and atomic decomposition results and show that our space is well defined i e independent of the choice of basis functions as in the classical case a unified scale of spaces permits clearer results in cases where smoothness and integrability interact such as sobolev embedding and trace theorems as an application of our decomposition we prove optimal trace theorem in the variable indices case

fuzzy rough nearest neighbour classification and prediction nearest neighbour nn approaches are inspired by the way humans make decisions comparing a test object to previously encountered samples in this paper we propose an nn algorithm that uses the lower and upper approximations from fuzzy rough set theory in order to classify test objects or predict their decision value it is shown experimentally that our method outperforms other nn approaches classical fuzzy and fuzzy rough ones and that it is competitive with leading classification and prediction methods moreover we show that the robustness of our methods against noise can be enhanced effectively by invoking the approximations of the vaguely quantified rough set vqrs model which emulates the linguistic quantifiers some and most from natural language

convergence analysis of orthogonal spline collocation for elliptic boundary value problems existence uniqueness and optimal order h2 h1 and l2 error bounds are established for the orthogonal spline collocation solution of a dirichlet boundary value problem on the unit square the linear elliptic nonself adjoint partial differential equation is given in nondivergence form the approximate solution which is a tensor product of continuously differentiable piecewise polynomials of degree r geq 3 is determined by satisfying the partial differential equation at the nodes of a composite gauss quadrature

spectral theory of some degenerate elliptic operators with local singularities abstract this paper is based on our previous results haroske and skrzypczak 2008 23 haroske and skrzypczak in press 25 on compact embeddings of muckenhoupt weighted function spaces of besov and triebel lizorkin type with example weights of polynomial growth near infinity and near some local singularity our approach also extends haroske and triebel 1994 21 in various ways we obtain eigenvalue estimates of degenerate pseudodifferential operators of type b 2 p x d b 1 where b i l r i r n w i w i a i 1 2 and p x d 1 0 0 finally we deal with the negative spectrum of some operator h a v for where the potential v may have singularities in terms of muckenhoupt weights and a is a positive elliptic pseudodifferential operator of order 0 self adjoint in l 2 r n this part essentially relies on the birman schwinger principle we conclude this paper with a number of examples also comparing our results with preceding ones

characterizations of besov type and triebel lizorkin type spaces via maximal functions and local means abstract let s r in this paper the authors first establish the maximal function characterizations of the besov type space b p q s r n with p q 0 and 0 the triebel lizorkin type space f p q s r n with p 0 q 0 and 0 the besov hausdorff space b h p q s r n with p 1 q 1 and 0 1 max p q and the triebel lizorkin hausdorff space f h p q s r n with p q 1 and 0 1 max p q where t denotes the conjugate index of t 1 using this characterization the authors further obtain the local mean characterizations of these function spaces via functions satisfying the tauberian condition and establish a fourier multiplier theorem on these spaces all these results generalize the existing classical results on besov and triebel lizorkin spaces by taking 0 and are also new even for q spaces and hardy hausdorff spaces

frsvms fuzzy rough set based support vector machines this paper aims to improve hard margin support vector machines svms by considering the membership of every training sample in constraints the membership is computed by employing the technique of fuzzy rough sets so that hard margin svms can be combined with fuzzy rough sets and the inconsistence between conditional features and decision labels can be taken into account at the same time in this paper we first propose fuzzy transitive kernel based fuzzy rough sets for binary classification we use a lower approximation operator in fuzzy transitive kernel based fuzzy rough sets to compute the membership for every training input and then we reformulate hard margin support vector machines into fuzzy rough set based svms frsvms with new constraints in which the membership is taken into account finally comparisons with soft margin svms and fuzzy svms are made the experimental results show that the proposed approach is feasible and valid it significantly improved the performance of the hard margin svms

square functions and h calculus on subspaces of l p and on hardy spaces let x be a closed subspace of l p with 1 p and let a be any sectorial operator on x we consider associated square functions on x of the form open image in new window and we show that if a admits a bounded h functional calculus on x then these square functions are equivalent to the original norm of x then we deduce a similar result when x h1 n is the usual hardy space for an appropriate choice of f for example if n 1 the right choice is the sum open image in new window for h h1 where h denotes the hilbert transform

h 1 norm error bounds for piecewise hermite bicubic orthogonal spline collocation schemes for elliptic boundary value problems two piecewise hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic nonhomogeneous dirichlet boundary value problems on rectangles in the first scheme the nonhomogeneous dirichlet boundary condition is approximated by means of the piecewise hermite cubic interpolant while the piecewise cubic interpolant at the boundary gauss points is used in the second scheme the piecewise hermite bicubic interpolant of the exact solution of the boundary value problem is employed as a comparison function to show that the h 1 norm of the error for each scheme is o h 3

ifrowann imbalanced fuzzy rough ordered weighted average nearest neighbor classification imbalanced classification deals with learning from data with a disproportional number of samples in its classes traditional classifiers exhibit poor behavior when facing this kind of data because they do not take into account the imbalanced class distribution four main kinds of solutions exist to solve this problem modifying the data distribution modifying the learning algorithm for considering the imbalance representation including the use of costs for data samples and ensemble methods in this paper we adopt the second type of solution and introduce a classification algorithm for imbalanced data that uses fuzzy rough set theory and ordered weighted average aggregation the proposal considers different strategies to build a weight vector to take into account data imbalance our methods are validated by an extensive experimental study showing statistically better results than 13 other state of the art methods

new molecular characterizations of anisotropic musielak orlicz hardy spaces and their applications abstract let r n 0 0 be an anisotropic growth function and a a general expansive matrix on r n let h a r n be the anisotropic musielak orlicz hardy space associated with a defined via the non tangential grand maximal function in this article the authors establish a new molecular characterization of h a r n via its known atomic characterizations which positively answer a question mentioned by li et al 2016 34 as an application the authors obtain a criterion on the boundedness of linear operators on h a r n which further implies the boundedness of integral anisotropic calderon zygmund operators on h a r n in addition the boundedness of these operators from h a r n to the musielak orlicz space l r n is also presented