weighted composition operators on hardy spaces let be analytic functions defined on d such that d d the operator given by f f is called a weighted composition operator in this paper we deal with the boundedness compactness weak compactness and complete continuity of weighted composition operators on hardy spaces hp 1 p in particular we prove that such an operator is compact on h1 if and only if it is weakly compact on this space this result depends on a technique which passes the weak compactness from an operator t to operators dominated in norm by t

out of sample extrapolation of learned manifolds we investigate the problem of extrapolating the embedding of a manifold learned from finite samples to novel out of sample data we concentrate on the manifold learning method called maximum variance unfolding mvu for which the extrapolation problem is still largely unsolved taking the perspective of mvu learning being equivalent to kernel pca our problem reduces to extending a kernel matrix generated from an unknown kernel function to novel points leveraging on previous developments we propose a novel solution which involves approximating the kernel eigenfunction using gaussian basis functions we also show how the width of the gaussian can be tuned to achieve extrapolation experimental results which demonstrate the effectiveness of the proposed approach are also included

t s fuzzy model based piecewise h output feedback controller design for networked nonlinear systems with medium access constraint abstract this paper investigates the problem of h output feedback control for a class of networked nonlinear systems subject to medium access constraint where the nonlinear systems are represented by takagi sugeno t s fuzzy models with norm bounded uncertainties the communication constraint concerned is that only one sensor node and one actuator node can access the shared network which is the case in network environment the accessibility of sensor nodes and or actuator nodes is determined by medium access control with a prescribed probability the attention is focused on the design of a piecewise static output feedback controller such that the closed loop control system is stochastically stable with a guaranteed h performance based on piecewise quadratic lyapunov functions together with some matrix inequality convexifying techniques an approach to the design of h output feedback controller is proposed in terms of linear matrix inequalities finally two simulation examples are provided to illustrate the effectiveness of the proposed methods

approximation numbers of weighted composition operators we study the approximation numbers of weighted composition operators f mapsto w cdot f circ varphi on the hardy space h 2 on the unit disc for general classes of such operators upper and lower bounds on their approximation numbers are derived for the special class of weighted lens map composition operators with specific weights we show how much the weight w can improve the decay rate of the approximation numbers and give sharp upper and lower bounds these examples are motivated from applications to the analysis of relative commutants of special inclusions of von neumann algebras appearing in quantum field theory borchers triples

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

resilient dissipative based controller for stochastic systems with randomly occurring gain fluctuations abstract this paper addresses the dissipativity based resilient sampled data control problem for a class of stochastic systems with actuator failures in particular the controller is assumed to posses probabilistic actuator faults with different failure rates moreover the controller gain fluctuation appears in a random way which obeys certain bernoulli distributed white noise sequences a new set of sufficient conditions is obtained in terms of linear matrix inequalities for the derivation of resilient dissipative sampled data controller by constructing an appropriate lyapunov krasovskii functional together with free weighting matrix technique simulation studies are performed to verify the performance and effectiveness of the proposed control design technique

invertible weighted composition operators a weighted composition operator c takes an analytic map f on the open unit disc of the complex plane to the analytic map f where is an analytic map of the open unit disc into itself and is an analytic map on the open unit disc this paper studies the invertibility of such operators the two maps and are characterized when c acts on the hardy hilbert space of the unit disc h2 d depending upon the nature of the fixed points of spectra are then investigated

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

mean ergodic composition operators on banach spaces of holomorphic functions abstract given a symbol i e a holomorphic endomorphism of the unit disc we consider the composition operator c f f defined on the banach spaces of holomorphic functions a d and h d we obtain different conditions on the symbol which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces these conditions are related to the asymptotic behavior of the iterates of the symbol finally we deal with some particular case in the setting of weighted banach spaces of holomorphic functions

networked control for a class of t s fuzzy systems with stochastic sensor faults this paper is concerned with networked control for a class of t s fuzzy systems with stochastic sensor faults first a unified model of networked control system is proposed which has two significant features a the fault statistics of each sensor is individually quantified and b stochastic sensor faults and nonideal network quality of services qos such as data dropout and network induced delay are coupled in a unified framework secondly based on the lyapunov krasovskii functional and the stochastic analysis technique sufficient network qos dependent conditions are derived for the stability analysis and controller design respectively moreover a modified cone complementary linearisation ccl algorithm is also introduced to solve the nonlinear matrix inequalities in the controller design finally two examples are given to demonstrate the effectiveness of the proposed method

stabilization of networked stochastic time delay fuzzy systems with data dropout this paper deals with the problem of stabilization for networked stochastic systems with transmitted data dropout the plant in the networked control system ncs under consideration is a discrete stochastic time delay nonlinear system represented by a takagi sugeno fuzzy model exponential stability criteria of the ncs are developed by using a common quadratic lyapunov function and a fuzzy lyapunov function respectively a stabilization controller with convergence rate constraint can be designed by solving a set of linear matrix inequalities that is numerically feasible with commercially available software three numerical examples are presented to demonstrate the effectiveness of the proposed methods

weighted composition operators ofc0 x s abstract in this paper we prove that into isometries and disjointness preserving linear maps from c 0 x into c 0 y are essentially weighted composition operators tf h f for some continuous map and some continuous scalar valued function h

locally linear discriminant analysis for multimodally distributed classes for face recognition with a single model image we present a novel method of nonlinear discriminant analysis involving a set of locally linear transformations called locally linear discriminant analysis llda the underlying idea is that global nonlinear data structures are locally linear and local structures can be linearly aligned input vectors are projected into each local feature space by linear transformations found to yield locally linearly transformed classes that maximize the between class covariance while minimizing the within class covariance in face recognition linear discriminant analysis lida has been widely adopted owing to its efficiency but it does not capture nonlinear manifolds of faces which exhibit pose variations conventional nonlinear classification methods based on kernels such as generalized discriminant analysis gda and support vector machine svm have been developed to overcome the shortcomings of the linear method but they have the drawback of high computational cost of classification and overfitting our method is for multiclass nonlinear discrimination and it is computationally highly efficient as compared to gda the method does not suffer from overfitting by virtue of the linear base structure of the solution a novel gradient based learning algorithm is proposed for finding the optimal set of local linear bases the optimization does not exhibit a local maxima problem the transformation functions facilitate robust face recognition in a low dimensional subspace under pose variations using a single model image the classification results are given for both synthetic and real face data

communication delay distribution dependent networked control for a class of t s fuzzy systems this paper investigates a robust networked control for a class of takagi sugeno t s fuzzy systems the controller design specifically takes probabilistic interval distribution of the communication delay into account a general framework of networked control is first proposed the two main features are 1 the zero order hold can choose the latest control input signal when the packets received are out of order and 2 as the result of 1 the models of the all kinds of uncertainties in networked signal transfer including network induced delay and data packet dropout are under a unified framework next if the probability distribution of communication delay is known or specified in a design process sufficient stability conditions for networked t s fuzzy systems are derived which are based on the lyapunov theory following this a stabilizing controller design method is developed which shows that the solvability of the design depends not only on the upper and lower bounds of the delay but on its probability distribution as well finally a numerical example is used to show the application of the theoretical results obtained in this paper

a new fault detection scheme for networked control systems subject to uncertain time varying delay fault detection of networked control systems ncs subject to uncertain time varying delay is studied in this paper for the convenience of residual generator design influence caused by network induced delay is first transformed into time varying polytopic uncertainty which greatly facilitates further manipulation then design of the optimal residual generator is formulated as a model matching problem i e to design a residual generator best matching the optimal residual generator of ncs in the delay free case this procedure is assisted by parameter dependent lyapunov function matrix based bounded real lemma which has been proved to be much better than single constant lyapunov function matrix based results this approach not only can be used in conditions that the variation part of the delay is less than one sampling period but also can be applied to scenarios where the variation part of the delay is larger than one sampling period simulation results are also given to illustrate effectiveness of the proposed method

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

new approach to delay dependent stability analysis and stabilization for continuous time fuzzy systems with time varying delay this paper is concerned with delay dependent stability analysis and stabilization problems for continuous time takagi and sugeno t s fuzzy systems with a time varying delay a new method for the delay dependent stability analysis and stabilization is suggested which is less conservative than other existing ones first based on a fuzzy lyapunov krasovskii functional lkf a delay dependent stability criterion is derived for the open loop fuzzy systems in the derivation process some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation and among the terms in the leibniz newton formula then a delay dependent stabilization condition based on the so called parallel distributed compensation pdc scheme is worked out for the closed loop fuzzy systems the proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities lmis and compared with the existing ones via two examples finally application to control of a truck trailer is also given to illustrate the effectiveness of the proposed design method

normal weighted composition operators on the hardy space h2 u abstract let be an analytic function on the open unit disc u such that u u and let be an analytic function on u such that the weighted composition operator w defined by w f f is bounded on the hardy space h 2 u we characterize those weighted composition operators on h 2 u that are unitary showing that in contrast to the unweighted case 1 every automorphism of u induces a unitary weighted composition operator a conjugation argument using these unitary operators allows us to describe all normal weighted composition operators on h 2 u for which the inducing map fixes a point in u this description shows both and must be linear fractional in order for w to be normal assuming fixes a point in u in general we show that if w is normal on h 2 u and 0 then must be either univalent on u or constant descriptions of spectra are provided for the operator w h 2 u h 2 u when it is unitary or when it is normal and fixes a point in u

spectra of weighted composition operators with automorphic symbols abstract let be an automorphism of the open unit disc d for such we investigate the spectra of invertible weighted composition operators u c acting on a wide class of analytic function spaces this class contains for example hardy spaces h p d weighted bergman spaces a p d and weighted banach spaces of h type we present new techniques for deducing the spectrum and for calculating the spectral radius of u c we also characterize the fredholmness of weighted composition operators on h p d and a p d

fuzzy control design of nonlinear systems under unreliable communication links in this study we propose a systematic homogenous polynomial approach for fuzzy control design of discrete time takagi sugeno fuzzy systems under unreliable communication links a novel delayed fuzzy control scheme which is homogenous polynomially parameter dependent on both the current normalized fuzzy weighting function and the one step past normalized fuzzy weighting function is designed to accomplish the assignment of relaxed control synthesis in contrast to the existing methods the closed loop controlled system is stochastically stable in the mean square sense with less conservative stabilization conditions finally simulation results are provided to verify the advantage and the effectiveness of the proposed approach

stable controller design for t s fuzzy systems based on lie algebras in this paper we study the stability of fuzzy control systems of takagi sugeno t s type based on the classical theory of lie algebras t s fuzzy systems are used to model nonlinear systems as a set of rules with consequents of the type email protected t a lx t b lu t we conduct the stability analysis of such t s fuzzy models using the lie algebra l a generated by the a l matrices of these subsystems for each rule in the rule base we first develop our approach of stability analysis for a commuting algebra l a where all the consequent state matrices a l s commute we then generalize our results to the noncommuting case the basic idea here is to approximate the noncommuting lie algebra with a commuting one such that the approximation error is minimum the results of this approximation are extended to the most general case using the levi decomposition of lie algebras the theory is applied to the control of a flexible joint robot arm where we also present the decomposition procedure

a general framework for dimensionality reducing data visualization mapping in recent years a wealth of dimension reduction techniques for data visualization and preprocessing has been established nonparametric methods require additional effort for out of sample extensions because they provide only a mapping of a given finite set of points in this letter we propose a general view on nonparametric dimension reduction based on the concept of cost functions and properties of the data based on this general principle we transfer nonparametric dimension reduction to explicit mappings of the data manifold such that direct out of sample extensions become possible furthermore this concept offers the possibility of investigating the generalization ability of data visualization to new data points we demonstrate the approach based on a simple global linear mapping as well as prototype based local linear mappings in addition we can bias the functional form according to given auxiliary information this leads to explicit supervised visualization mappings with discriminative properties comparable to state of the art approaches

alignment of overlapping locally scaled patches for multidimensional scaling and dimensionality reduction data observations that lie on a manifold can be approximated by a collection of overlapping local patches the alignment of which in a low dimensional euclidean space provides an embedding of the data this paper describes an embedding method using classical multidimensional scaling as a local model based on the fact that a manifold locally resembles a euclidean space a set of overlapping neighborhoods are chosen by a greedy approximation algorithm of minimum set cover local patches derived from the set of overlapping neighborhoods by classical multidimensional scaling are aligned in order to minimize a residual measure which has a quadratic form of the resulting global coordinates and can be minimized analytically by solving an eigenvalue problem this method requires only distances within each neighborhood and provides locally isometric embedding results the size of the eigenvalue problem scales with the number of overlapping neighborhoods rather than the number of data points experiments on both synthetic and real world data sets demonstrate the effectiveness of this method extensions and variations of the method are discussed

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

a hyperspectral image classification framework and its application a new descriptor called lrp is proposed to describe subtle texture for 2d image texture enhancement is built to extend lrp to represent hsi a supervised manifold learning method called dlpp is proposed to reduce dimension the proposed framework outperforms other methods with experiments classification is a critical step to make full use of the hyperspectral data the most current approaches perform well for analyzing the macro texture but they often fail to deal with the micro texture thus this study proposes a general framework for the material with micro texture based on hyperspectral image hsi technique in this framework local response pattern lrp is firstly proposed to describe 2d image texture to preserve more structural information and keep less sensitive to image conditions then lrp is extended to represent hsi with texture enhancement te by considering opponent relationships between pairs of bands after that discriminated locality preserving projection dlpp is proposed to reduce data dimension in a linearizing nonlinear manifold way finally experiments on the hyperspectral images of fresh and frozen thawed fish fillets are conducted the results demonstrate that the proposed framework is efficient in terms of both recognition rates and robustness

spectra of linear fractional composition operators on the hardy and weighted bergman spaces of the half plane abstract we compute the spectra and the essential spectra of bounded linear fractional composition operators acting on the hardy and weighted bergman spaces of the upper half plane we are also able to extend the results to weighted dirichlet spaces of the upper half plane

dynamics and spectra of composition operators on the schwartz space abstract in this paper we study the dynamics of the composition operators defined in the schwartz space s r of rapidly decreasing functions we prove that such an operator is never supercyclic and for monotonic symbols it is power bounded only in trivial cases for a polynomial symbol of degree greater than one we show that the operator is mean ergodic if and only if it is power bounded and this is the case when has even degree and lacks fixed points we also discuss the spectrum of composition operators

fredholm composition operators on algebras of analytic functions on banach spaces we prove that fredholm composition operators acting on the uniform algebra h be of bounded analytic functions on the open unit ball of a complex banach space e with the approximation property are invertible and arise from analytic automorphisms of the ball

finite time h asynchronous state estimation for discrete time fuzzy markov jump neural networks with uncertain measurements abstract this paper is concerned with the problem of the h asynchronous state estimation for fuzzy markov jump neural networks fmjnns with uncertain measurements over a finite time interval in terms of a bernoulli distributed white sequence the phenomenon of the randomly occurring uncertainties in the output equation is represented by exploiting a random variable with known occurrence probabilities the main focus of this paper is to present a state estimator such that the resulting error system is finite time bounded and satisfies an h performance requirement then by employing the stochastic analysis technique sufficient conditions are provided to ensure that the state estimator is designed by means of solving a convex optimization problem an example is finally given to explain the effectiveness and potentiality of the proposed design method

generalized composition operators on zygmund spaces and bloch type spaces the boundedness and compactness of the generalized composition operator on zygmund spaces and bloch type spaces are investigated in this paper

mean ergodicity of weighted composition operators on spaces of holomorphic functions abstract let be a self map of the unit disc d of the complex plane c and let be a holomorphic function on d we investigate the mean ergodicity and power boundedness of the weighted composition operator c f f with symbol and multiplier on the space h d we obtain necessary and sufficient conditions on the symbol and on the multiplier which characterize when the weighted composition operator is power bounded and uniformly mean ergodic one necessary condition is that the symbol has a fixed point in d if is not a rational rotation the sufficient conditions are related to the modulus of the multiplier on the fixed point of some of our results are valid in an open connected set u of the complex plane

hessian eigenmaps locally linear embedding techniques for high dimensional data we describe a method for recovering the underlying parametrization of scattered data m i lying on a manifold m embedded in high dimensional euclidean space the method hessian based locally linear embedding derives from a conceptual framework of local isometry in which the manifold m viewed as a riemannian submanifold of the ambient euclidean space r n is locally isometric to an open connected subset of euclidean space r d because does not have to be convex this framework is able to handle a significantly wider class of situations than the original isomap algorithm the theoretical framework revolves around a quadratic form h f m h f m f dm defined on functions f m r here hf denotes the hessian of f and h f averages the frobenius norm of the hessian over m to define the hessian we use orthogonal coordinates on the tangent planes of m the key observation is that if m truly is locally isometric to an open connected subset of r d then h f has a d 1 dimensional null space consisting of the constant functions and a d dimensional space of functions spanned by the original isometric coordinates hence the isometric coordinates can be recovered up to a linear isometry our method may be viewed as a modification of locally linear embedding and our theoretical framework as a modification of the laplacian eigenmaps framework where we substitute a quadratic form based on the hessian in place of one based on the laplacian

hermitian weighted composition operators on h 2 weighted composition operators have been related to products of composition operators and their adjoints and to isometries of hardy spaces in this paper we identify the hermitian weighted composition operators on h 2 and compute their spectral measures some relevant semigroups are studied the resulting ideas can be used to find the polar decomposition the absolute value and the aluthge transform of some composition operators on h 2

isometric weighted composition operators on weighted bergman spaces abstract we characterize the isometric weighted composition operators on weighted bergman spaces over the unit disk we also determine the wold decomposition of isometric weighted composition operators acting on a class of general reproducing kernel hilbert spaces in the case when the composition symbol has an interior fixed point and characterize the numerical range of isometric weighted composition operators on weighted bergman spaces

numerical ranges of weighted composition operators abstract the operator that takes the function f to f is a weighted composition operator we study numerical ranges of some classes of weighted composition operators on h 2 the hardy hilbert space of the unit disc we consider the case where is a rotation of the unit disc and identify a class of convexoid operators in the case of isometric weighted composition operators we give a complete classification of their numerical ranges we also consider the inclusion of zero in the interior of the numerical range

self adjoint unitary and normal weighted composition operators in several variables abstract we study weighted composition operators on hilbert spaces of analytic functions on the unit ball with kernels of the form 1 z w for 0 we find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator we then obtain characterizations of self adjoint and unitary weighted composition operators normality of these operators is also investigated

a novel dropout compensation scheme for control of networked t s fuzzy dynamic systems this paper considers the problem of h state feedback control for networked nonlinear systems under unreliable communication links with packet dropouts the nonlinear plant in this paper is described by a takagi sugeno t s fuzzy model the packet dropouts in both sensor to controller s c and controller to actuator c a channels are considered which are modeled by bernoulli processes a new compensation scheme for the estimation of missing packets is proposed and a piecewise state feedback controller is designed so that the resulting closed loop control system is stochastically stable with guaranteed h performance then the results are extended to the case when both network induced delays and packet dropouts exist in communication links finally some numerical examples are given to illustrate the procedure of the proposed approaches and the optimal h performance in comparison to the existing approaches

some examples of composition operators and their approximation numbers on the hardy space of the bi disk we give examples of composition operators c phi on h 2 d 2 showing that the condition phi infty 1 is not sufficient for their approximation numbers a n c phi to satisfy lim n to infty a n c phi 1 sqrt n 1 contrary to the 1 dimensional case we also give a situation where this implication holds we make a link with the monge amp ere capacity of the image of phi

new approach on robust delay dependent h _ infty control for uncertain t s fuzzy systems with interval time varying delay this paper investigates the robust h infin control for takagi sugeno t s fuzzy systems with interval time varying delay by employing a new and tighter integral inequality and constructing an appropriate type of lyapunov functional delay dependent stability criteria are derived for the control problem because neither any model transformation nor free weighting matrices are employed in our theoretical derivation the developed stability criteria significantly improve and simplify the existing stability conditions also the maximum allowable upper delay bound and controller feedback gains can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem numerical examples are given to demonstrate the effectiveness of the proposed methods

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

weighted composition operators on the dirichlet space boundedness and spectral properties boundedness of weighted composition operators w u varphi acting on the classical dirichlet space mathcal d as w u varphi f u f circ varphi is studied in terms of the multiplier space associated to the symbol varphi i e mathcal m varphi u in mathcal d w u varphi hbox is bounded on mathcal d a prominent role is played by the multipliers of the dirichlet space as a consequence the spectrum of w u varphi in mathcal d whenever varphi is an automorphism of the unit disc is studied extending a recent work of hyvarinen et al j funct anal 265 1749 1777 2013 to the context of the dirichlet space

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

weighted composition operators between large fock spaces in several complex variables abstract let be an entire self map of c n and let u be an entire function on c n a weighted composition operator induced by with weight u is given by u c f z u z f z for z in c n and f is an entire function on c n in this paper we study weighted composition operators acting between two large weighted fock spaces f p and f q we characterize the bounded compact and schatten class membership operators u c acting from f p to f q when 0 p and 0 q our results use certain integral transforms that generalize the usual berezin transform

classification of gene expression data the manifold based metric learning way classification of microarray gene expression data can potentially help medical diagnosis and becomes an important topic in bioinformatics however microarray data sets are usually of small sample size relative to an overwhelming number of genes this makes the classification problem fairly challenging instance based learning ibl algorithms such as nearest neighbor k nn are usually the baseline algorithm due to their simplicity however practices show that k nn performs not very well in this field this paper introduces manifold based metric learning to improve the performance of ibl methods a novel metric learning algorithm is proposed by utilizing both local manifold structural information and local discriminant information in addition a random subspace extension is also presented we apply the proposed algorithm to the gene classification problem in three ways one in the original feature space another in the reduced feature space and the third via the random subspace extension statistical evaluation shows that the proposed algorithm can achieve promising results and gain significant performance improvement over traditional ibl algorithms

dimensionality reduction an interpretation from manifold regularization perspective in this paper we propose to unify various dimensionality reduction algorithms by interpreting the manifold regularization mr framework in a new way although the mr framework was originally proposed for learning we utilize it to give a unified treatment for many dimensionality reduction algorithms from linear to nonlinear supervised to unsupervised and single class to multi class approaches in addition the framework can provide a general platform to design new dimensionality reduction algorithms the framework is expressed in the form of a regularized fitting problem in a reproducing kernel hilbert space it consists of one error part and two regularization terms the complexity term and the smoothness term the error part measures the difference between the estimated low dimensional data distribution and the true high dimensional data distribution or the difference between the estimated and targeted low dimensional representations of data the complexity term is a measurement of the complexity of the feature mapping for dimensionality reduction and the smoothness term reflects the intrinsic structure of data based on the framework we propose a manifold regularized kernel least squares mr kls method which can efficiently learn an explicit feature mapping in the semi supervised sense experiments show that our approach is effective for out of sample extrapolation c 2014 elsevier inc all rights reserved

passage method for nonlinear dimensionality reduction of data on multi cluster manifolds nonlinear dimensionality reduction of data lying on multi cluster manifolds is a crucial issue in manifold learning research an effective method called the passage method is proposed in this paper to alleviate the disconnectivity short circuit and roughness problems ordinarily encountered by the existing methods the specific characteristic of the proposed method is that it constructs a globally connected neighborhood graph superimposed on the data set through technically building the smooth passages between separate clusters instead of supplementing some rough inter cluster connections like some existing methods the neighborhood graph so constructed is naturally configured as a smooth manifold and hence complies with the effectiveness condition underlying manifold learning this theoretical argument is supported by a series of experiments performed on the synthetic and real data sets residing on multi cluster manifolds

kernel dimension reduction in regression we present a new methodology for sufficient dimension reduction sdr our methodology derives directly from the formulation of sdr in terms of the conditional independence of the covariate x from the response y given the projection of x on the central subspace cf j amer statist assoc 86 1991 316 342 and regression graphics 1998 wiley we show that this conditional independence assertion can be characterized in terms of conditional covariance operators on reproducing kernel hilbert spaces and we show how this characterization leads to an m estimator for the central subspace the resulting estimator is shown to be consistent under weak conditions in particular we do not have to impose linearity or ellipticity conditions of the kinds that are generally invoked for sdr methods we also present empirical results showing that the new methodology is competitive in practice

which multiplication operators are surjective isometries abstract let f be a banach space of continuous functions over a connected locally compact space x we present several sufficient conditions on f guaranteeing that the only multiplication operators on f that are surjective isometries are scalar multiples of the identity the conditions are given via the properties of the inclusion operator from f into c x as well as in terms of geometry of f an important tool in our investigation is the notion of birkhoff orthogonality

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

efficient isometric multi manifold learning based on the self organizing method geodesic distance as an essential measurement for data similarity has been successfully used in manifold learning however many geodesic based isometric manifold learning algorithms such as the isometric feature mapping isomap and geonlm fail to work on data that distribute on clusters or multiple manifolds this limits their applications because practical data sets generally distribute on multiple manifolds in this paper we propose a new isometric multi manifold learning method called multi manifold proximity embedding mpe which can be efficiently optimized using the gradient descent method or the self organizing method compared with the previous methods the proposed method has two steps which can isometrically learn data distributed on several manifolds and is more accurate in preserving both the intra manifold and the inter manifold geodesic distances the effectiveness of the proposed method in recovering the nonlinear data structure and clustering is demonstrated through experiments on both synthetically and real data sets

attributes reduction using fuzzy rough sets fuzzy rough sets are the generalization of traditional rough sets to deal with both fuzziness and vagueness in data the existing researches on fuzzy rough sets are mainly concentrated on the construction of approximation operators less effort has been put on the attributes reduction of databases with fuzzy rough sets this paper mainly focuses on the attributes reduction with fuzzy rough sets after analyzing the previous works on attributes reduction with fuzzy rough sets we introduce formal concepts of attributes reduction with fuzzy rough sets and completely study the structure of attributes reduction an algorithm using discernibility matrix to compute all the attributes reductions is developed based on these lines of thought we set up a solid mathematical foundation for attributes reduction with fuzzy rough sets the experimental results show that the idea in this paper is feasible and valid

diffusion maps and coarse graining a unified framework for dimensionality reduction graph partitioning and data set parameterization we provide evidence that nonlinear dimensionality reduction clustering and data set parameterization can be solved within one and the same framework the main idea is to define a system of coordinates with an explicit metric that reflects the connectivity of a given data set and that is robust to noise our construction which is based on a markov random walk on the data offers a general scheme of simultaneously reorganizing and subsampling graphs and arbitrarily shaped data sets in high dimensions using intrinsic geometry we show that clustering in embedding spaces is equivalent to compressing operators the objective of data partitioning and clustering is to coarse grain the random walk on the data while at the same time preserving a diffusion operator for the intrinsic geometry or connectivity of the data set up to some accuracy we show that the quantization distortion in diffusion space bounds the error of compression of the operator thus giving a rigorous justification for k means clustering in diffusion space and a precise measure of the performance of general clustering algorithms

stabilization of networked control systems with a logic zoh the technical note is concerned with the stabilization problem of networked control systems a general framework is proposed firstly where the zero order hold has the logical capability of choosing the newest control input packet the continuous time process is discretized as a system with input delays then a sufficient condition for testing the stability of the discretized system and two sufficient conditions for designing a stabilizing controller are established based upon the lyapunov theory finally numerical examples and simulations are used to illustrate the developed theory

relaxed stability and stabilization conditions of networked fuzzy control systems subject to asynchronous grades of membership this paper presents relaxed stability and stabilization conditions for takagi sugeno t s fuzzy systems under network environments subject to asynchronous grades of membership because of the introduction of a communication network the favorable property in the point to point connection that is sharing the identical premises in the fuzzy plant and the fuzzy controllers cannot be arbitrarily employed to widen the applicability of the fuzzy control method under network environments a novel method is provided to reconstruct the synchronous time scale grades of membership at the controller as those in the plant as a result the aforementioned favorable property can be conditionally used in the derivation of the stability and stabilization criteria for the system under consideration controlled over a communication network numerical examples have been given to illustrate the effectiveness of the proposed approach

the spectra of composition operators from linear fractional maps acting upon the dirichlet space abstract let d d be a non constant linear fractional transformation necessarily of the form z az b cz d let d denote the dirichlet space of analytic functions we determine the spectrum of the composition operator c d d defined by c f f eigenfunctions for the operator c h 2 h 2 frequently do not belong to the space d however spectral results for the operator c d d much like those that have already been demonstrated for the operator c h 2 h 2 are presented in this paper

adjoints of linear fractional composition operators on the dirichlet space the adjoint of a linear fractional composition operator acting on the classical dirichlet space is expressed as another linear fractional composition operator plus a two rank operator the key point is that in the dirichlet space modulo constant functions many linear fractional composition operators are similar to multiplication operators and thus normal as a particular application we can easily deduce the spectrum of each linear fractional composition operator acting on such spaces even the norm of each linear fractional composition operator is computed on the dirichlet space modulo constant functions it is also shown that all this work can be carried out in the hardy space of the upper half plane

a modified fuzzy pi controller for a flexible joint robot arm with uncertainties abstract fuzzy control strategy offers an alternative approach for many conventional control systems which has certain advantages over the other techniques for example the improved pi fuzzy controller we designed in this paper which is based on an existing fuzzy pi controller can control an uncertain flexible joint robot arm to produce satisfactory tracking results the improved fuzzy pi controller not only can control stable and unstable conventional linear systems performing as well as the conventional pi controller but also is capable of controlling many nonlinear systems such as the flexible joint robot arm under investigation which contains uncertainties within 10 tolerance of all nominal system parameter values in this improved fuzzy pi controller we used only three simple membership functions plus six simple fuzzy logic control rules in this paper we describe the design principle of this controller and demonstrate its tracking performance in handling nonlinearity flexibility and uncertainty within the flexible joint robot arm system

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements

hardy spaces that support no compact composition operators we consider for g a simply connected domain and 0 p the hardy space hp g formed by fixing a riemann map of the unit disc onto g and demanding of functions f holomorphic on g that the integrals of f p over the curves z r be bounded for 0 r 1 the resulting space is usually not the one obtained from the classical hardy space of the unit disc by conformal mapping this is reflected in our main theorem hp g supports compact composition operators if and only if g has finite one dimensional hausdorff measure our work is inspired by an earlier result of matache proc amer math soc 127 1999 1483 who showed that the hp spaces of half planes support no compact composition operators our methods provide a lower bound for the essential spectral radius which shows that the same result holds with compact replaced by riesz we prove similar results for bergman spaces with the hardy space condition g has finite hausdorff 1 measure replaced by g has finite area finally we characterize those domains g for which every composition operator on either the hardy or the bergman spaces is bounded

orthogonal neighborhood preserving projections a projection based dimensionality reduction technique this paper considers the problem of dimensionality reduction by orthogonal projection techniques the main feature of the proposed techniques is that they attempt to preserve both the intrinsic neighborhood geometry of the data samples and the global geometry in particular we propose a method named orthogonal neighborhood preserving projections which works by first building an affinity graph for the data in a way that is similar to the method of locally linear embedding lle however in contrast with the standard lle where the mapping between the input and the reduced spaces is implicit onpp employs an explicit linear mapping between the two as a result handling new data samples becomes straightforward as this amounts to a simple linear transformation we show how we can define kernel variants of onpp as well as how we can apply the method in a supervised setting numerical experiments are reported to illustrate the performance of onpp and to compare it with a few competing methods

norms and spectral radii of linear fractional composition operators on the ball abstract we give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of hilbert function spaces on the ball and obtain new norm bounds analogous to the standard one variable estimates we also show that cowen s one variable spectral radius formula extends to these operators the key observation underlying these results is that every linear fractional map of the ball belongs to the schur agler class

the spectra of linear fractional composition operators on weighted dirichlet spaces we completely determine the spectra of composition operators induced by linear fractional self maps of the unit disc acting on weighted dirichlet spaces extending earlier results by higdon 8 and answering the open questions in this context