localization of laplacian eigenfunctions in circular spherical and elliptical domains we consider laplacian eigenfunctions in circular spherical and elliptical domains in order to discuss three kinds of high frequency localization whispering gallery modes bouncing ball modes and focusing modes although the existence of these modes has been known for a class of convex domains the separation of variables for circular spherical and elliptical domains helps us to better understand the mechanism of localization i e how an eigenfunction is getting distributed in a small region of the domain and decays rapidly outside this region using the properties of bessel and mathieu functions we derive inequalities which imply and clearly illustrate localization moreover we provide an example of a nonconvex domain an elliptical annulus for which the high frequency localized modes are still present at the same time we show that there is no localization in most rectangle like domains this observation leads us to formulate an open problem of localization in polygonal domains and more ge

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

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

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

boundary layer techniques for solving the helmholtz equation in the presence of small inhomogeneities we consider solutions to the helmholtz equation in two and three dimensions based on layer potential techniques we provide for such solutions a rigorous systematic derivation of complete asymptotic expansions of perturbations resulting from the presence of diametrically small inhomogeneities with constitutive parameters different from those of the background medium it is expected that our results will find important applications for developing effective algorithms for reconstructing small dielectric inhomogeneities from boundary measurements

numerical solution of an inverse problem of imaging of antipersonnel land mines by the globally convergent convexification algorithm the globally convergent convexification algorithm has been successfully applied to some coefficient inverse problems in this paper a new numerical implementation of this algorithm is presented and applied to a model problem of imaging of antipersonnel plastic land mines using electric signal propagation a smoothing technique is introduced to smooth out the spikes on the image for the reconstructed unknown coefficient some artifacts of resulting images are explained based on numerical evidences with the new implementation the convexification algorithm is computationally efficient and is feasible to be applied in real time to detect and image antipersonnel land mines in the field

music imaging and electromagnetic inverse scattering of multiple scattering small anisotropic spheres the foldy lax equation is used to derive a multiple scattering model for the multiple scattering small anisotropic spheres by this model if the number of the non zero singular values of the multistatic response msr matrix is smaller than the number of the antennas the range space of the msr matrix is found to be spanned by the background green s function vectors corresponding to the and components of the electric and magnetic dipoles induced in each scatterer which indicates that the multiple signal classification music method could be implemented to obtain the locations of the scatterers after estimating the positions of the scatterers a non iterative analytical method is proposed for retrieving the polarization strength tensors as well as the orientations of the principle axes of each scatterer two numerical simulations show that the music method and the non iterative method are efficacious for the nonlinear inverse scattering problem of determining the locations and polarization strength tensors of multiple scattering small anisotropic spheres such methods could also be applied to the inversion of small isotropic spheres or extended to the inversion of small bianisotropic spheres

music type electromagnetic imaging of a collection of small three dimensional inclusions in this paper we consider the localization of a collection of small three dimensional bounded homogeneous inclusions via time harmonic electromagnetic means typically using arrays of electric or magnetic dipole transmitters and receivers with given polarization s at some distance from the collection possibly also lying in the far field the inclusions somewhat apart or closely spaced are buried within a homogeneous medium and are of arbitrary contrast of permittivity conductivity and permeability vis ag vis this embedding medium the problem is formulated as an inverse scattering problem for the full maxwell equations and it involves a robust asymptotic modeling of the multistatic response matrix no specific application is studied at this stage but characterization of obstacles in subsoils nondestructive evaluation of man made structures and medical imaging are primary fields of application envisaged the proposed approach uses a music multiple signal classification type algorithm and it yields fast numbering accurate localization and estimates of the electromagnetic and geometric parameters polarization tensors of the inclusions the mathematical machinery is detailed first some specific attention being given to triaxial ellipsoidal inclusions and degenerate spherical shapes for the latter known results are retrieved then the viability of this algorithm which would be easily extended to planarly layered environments by introduction of their green s functions is documented by a variety of numerical results from synthetic noiseless and severely noisy field data

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

numerical resolution of an electromagnetic inverse medium problem at fixed frequency the aim of this paper is to solve numerically the inverse problem of determining the complex refractive index of an electromagnetic medium from partial boundary field measurements at a fixed frequency the governing equations are the time harmonic maxwell equations formulated in electric field in a two dimensional bounded domain we express the inverse problem as the minimization of a cost function representing the difference between the measured and predicted fields our numerical reconstruction algorithm combines the bfgs method and an iterative process called the adaptive eigenspace inversion the unknown complex coefficient is expanded in terms of eigenfunctions of an elliptic operator both the eigenspace and the mesh are iteratively adapted during the minimization procedure numerical experiments illustrate the performance of the reconstruction for various configurations

a direct design procedure for linear state functional observers we propose a constructive procedure to design a luenberger observer to estimate a linear multiple linear state functional for a linear time invariant system among other features the proposed design algorithm is not based on the solution of a sylvester equation nor on the use of canonical state space forms the design is based on the solution set of a linear equation and a realization method the consistency of this equation and the stability of the observer can be used as a functional observability test

focusing and imaging using eigenfunctions of the scattering operator an inverse scattering method that uses eigenfunctions of the scattering operator is presented this approach provides a unified framework that encompasses eigenfunction methods of focusing and quantitative image reconstruction in arbitrary media scattered acoustic fields are described using a compact normal operator the eigenfunctions of this operator are shown to correspond to the far field patterns of source distributions that are directly proportional to the position dependent contrast of a scattering object conversely the eigenfunctions of the scattering operator specify incident wave patterns that focus on these effective source distributions these focusing properties are employed in a new inverse scattering method that represents unknown scattering media using products of numerically calculated fields of eigenfunctions a regularized solution to the nonlinear inverse scattering problem is shown to result from combinations of these products so that the products comprise a natural basis for efficient and accurate reconstructions of unknown inhomogeneities the corresponding linearized problem is solved analytically resulting in a simple formula for the low pass filtered scattering potential the linear formula is analytically equivalent to known filtered backpropagation formulas for born inversion and at least in the case of small scattering objects has advantages of computational simplicity and efficiency a similarly efficient and simple formula is derived for the nonlinear problem in which the total acoustic pressure can be determined based on an estimate of the medium computational results illustrate focusing of eigenfunctions on discrete and distributed scattering media quantitative imaging of inhomogeneous media using products of retransmitted eigenfunctions inverse scattering in an inhomogeneous background medium and reconstructions for data corrupted by noise

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

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

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

recent developments in inverse acoustic scattering theory we survey some of the highlights of inverse scattering theory as it has developed over the last 15 years with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects

e bounded state estimation for time delay systems with bounded disturbances a new problem on e bounded functional state estimation for time delay systems with unknown bounded disturbances is studied in this paper in the presence of unknown bounded disturbances the common assumption regarding the observer s matching condition is no longer required in this regard instead of achieving asymptotic convergence for the observer error the error is now required to converge exponentially within a ball with a small radius e 0 this means that the estimate converges exponentially within an e bound of the true value a general observer that utilises multiple delayed output and input information is proposed sufficient conditions for the existence of the proposed observer are first given we then employ an extended lyapunov krasovskii functional which combines the delay decomposition technique with a triple integral term to study the e convergence problem of the observer error system moreover the obtained results are shown to be more effective than the existing results for the cases w

inverse problems for the anisotropic maxwell equations we prove that the electromagnetic material parameters are uniquely determined by boundary measurements for the time harmonic maxwell equations in certain anisotropic settings we give a uniqueness result in the inverse problem for maxwell equations on an admissible riemannian manifold and a uniqueness result for maxwell equations in euclidean space with admissible matrix coefficients the proofs are based on a new fourier analytic construction of complex geometrical optics solutions on admissible manifolds and involve a proper notion of uniqueness for such solutions

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

a direct impedance tomography algorithm for locating small inhomogeneities impedance tomography seeks to recover the electrical conductivity distribution inside a body from measurements of current flows and voltages on its surface in its most general form impedance tomography is quite ill posed but when additional a priori information is admitted the situation changes dramatically in this paper we consider the case where the goal is to find a number of small objects inhomogeneities inside an otherwise known conductor taking advantage of the smallness of the inhomogeneities we can use asymptotic analysis to design a direct i e non iterative reconstruction algorithm for the determination of their locations the viability of this direct approach is documented by numerical examples

existence conditions for unknown input functional observers this article presents necessary and sufficient conditions for the existence and design of an unknown input functional observer the existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions the existence of the observer does not require the satisfaction of the observer matching condition i e equation 16 in hou and muller 1992 design of observers for linear systems with unknown inputs ieee transactions on automatic control 37 871 875 is not limited to estimating scalar functionals and allows for arbitrary pole placement the proposed observer always exists when a state observer exists for the unknown input system and furthermore the proposed observer can exist even in some instances when an unknown input state observer does not exist

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

music algorithm for location searching of dielectric anomalies from s parameters using microwave imaging abstract motivated by the biomedical engineering used in early stage breast cancer detection we investigated the use of multiple signal classification music algorithm for location searching of small anomalies using s parameters we considered the application of music to functional imaging where a small number of dipole antennas are used our approach is based on the application of born approximation or physical factorization we analyzed cases in which the anomaly is respectively small and large in relation to the wavelength and the structure of the left singular vectors is linked to the nonzero singular values of a multi static response msr matrix whose elements are the s parameters using simulations we demonstrated the strengths and weaknesses of the music algorithm in detecting both small and extended anomalies

imaging small three dimensional elastic inclusions by an enhanced multiple signal classification method in this paper an enhanced multiple signal classification music algorithm is introduced to retrieve small three dimensional elastic inclusions first the multistatic response msr matrix is built by two different ways depending on considering the multiple scattering effect or not the eigenvalue structure of the msr matrix is analyzed to identify the degenerate case of inclusions second the pseudo spectrum function is built with an optimal test direction on each node where a balancing technique is employed to ensure the numerical stability benefitting from this music indicator the degenerate inclusions can be located with a good performance against noise numerical simulations show the proposed method has wider applicability better resolution and more robust in the presence of noise than the standard music methods

design of scalar functional observers of order less than ν 1 this paper presents a new method of designing scalar functional observers of order less than the well known upper bound 1 a condition for the existence of observers of order p where 1 p 1 is given a simple and effective algorithm for solving the constrained generalized sylvester equation is proposed several numerical examples are given to illustrate the attractiveness of the design algorithm

multi modelling as new estimation schema for high gain observers the presented paper proposes a novel method of observer design a new two layer observer structure is introduced the first layer consists of multiple high gain observers the latter is built to connect the first layer observers into single one as the new contribution the new mapping is defined between an unknown state and measurable outputs allowing to explore new estimation schema hence the proposed method enhances the estimation process for linear and nonlinear systems furthermore it is shown that the introduced observation scheme improves the transients illustrative examples are calculated to show the properties of the new observation method

on the accuracy of the numerical detection of complex obstacles from far field data using the probe method we deal with the acoustic inverse scattering problem for detecting an obstacle with mixed boundary conditions from the far field map we show how the geometrical properties and the material parameter distributed on the surface are involved in the obstacle reconstruction numerically the main advance of this research is the numerical analysis and implementation of our recent theoretical work j j liu and m sini how to make the reconstruction of obstacles more or less accurate from exterior measurements ricam preprint 2008 04 johann radon institute for computational and applied mathematics linz austria 2008 regarding the higher order asymptotic expansion of the probe indicator function and the introduction of complex valued surface impedance an efficient numerical implementation scheme is proposed based on the properties of minimum norm solutions precisely using the relation between the surface impedance and the obstacle curvature contained in the higher order expansion of the indicators we reveal how the obstacle curvature and the surface impedance on the coated part influence the blowing up behavior using this theoretical result we can specify the complex surface impedance in terms of the obstacle curvature to make the reconstruction more or less accurate by establishing properties of the minimum norm solution for approximating the singular sources efficient realizations for approximating the multipoles by the herglotz wave function and therefore the implementations of the probe methods are developed with an error estimate we finally show extensive numerical tests explaining how and to what extent the coupling relation between the curvature and the surface impedance changes the accuracy of the reconstruction of the obstacles

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

minimal single linear functional observers for linear systems a constructive procedure to design a single linear functional observer for a time invariant linear system is given the proposed procedure is simple and is not based on the solution of a sylvester equation or on the use of canonical state space forms both stable observers or fixed poles observers problems are considered for minimality

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

sharp sufficient conditions for the observation control and stabilization of waves from the boundary for the observation or control of solutions of second order hyperbolic equation in mathbb r t times omega ralston s construction of localized states comm pure appl math 22 1969 pp

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

on functional observers for linear time varying systems the technical note deals with existence conditions of a functional observer for linear time varying systems in the case where the order of the observer is equal to the number of observed variables constructive procedures for the design of such a linear functional observer are deduced from the existence conditions as a specific feature the proposed procedures do not require the solution of a differential sylvester equation some examples illustrate the presented results

a system decomposition approach to the design of functional observers this paper reports a system decomposition that allows the construction of a minimum order functional observer using a state observer design approach the system decomposition translates the functional observer design problem to that of a state observer for a smaller decomposed subsystem functional observability indices are introduced and a closed form expression for the minimum order required for a functional observer is derived in terms of those functional observability indices

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

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

adaptive eigenspace for multi parameter inverse scattering problems abstract a nonlinear optimization method is proposed for inverse scattering problems in the frequency domain when the unknown medium is characterized by one or several spatially varying parameters the time harmonic inverse medium problem is formulated as a pde constrained optimization problem and solved by an inexact truncated newton type method combined with frequency stepping instead of a grid based discrete representation each parameter is projected to a separate finite dimensional subspace which is iteratively adapted during the optimization each subspace is spanned by the first few eigenfunctions of a linearized regularization penalty functional chosen a priori the small and slowly increasing finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard tikhonov type regularization numerical results illustrate the accuracy and efficiency of the resulting adaptive eigenspace regularization for single and multi parameter problems including the well known marmousi model from geosciences

fast numerical solution of the electromagnetic medium scattering problem and applications to the inverse problem we propose a method for computing the scattering of a time harmonic electromagnetic wave in a medium with a locally perturbed refractive index we prove that it converges of arbitrarily high order depending on the smoothness of the refractive index and that the time complexity is o n 3log n as an application we solve the corresponding inverse problem using a preconditioned newton method and discuss how to compute the frechet derivative of the solution operator and its adjoint by the proposed method the performance of both the forward and the inverse solver is illustrated in a number of numerical experiments

a practical functional observer scheme for interconnected time delay systems this paper proposes a partially distributed functional observer scheme for a class of interconnected linear systems with very strong non instantaneous subsystems interaction and with time delays in the local states and in the transmission of output information from the remote subsystems a set of easily verifiable existence conditions is established and upon its satisfaction simple distributed observers are designed using a straightforward design procedure simulation results of a numerical example are given to substantiate the feasibility of the approach

numerical solution of an inverse medium scattering problem for maxwell s equations at fixed frequency consider a time harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in r 3 in this paper well posedness of the variational problem for the direct scattering is examined an energy estimate for the scattered field is obtained on which the born approximation is based a regularized recursive linearization method for the inverse medium scattering which reconstructs the scatterer of an inhomogeneous medium from the boundary measurements of the scattered field is developed the algorithm requires only single frequency data using an initial guess from the born approximation each update is obtained via continuation on the spatial frequency of a two parameter family of plane waves by solving one direct problem and one adjoint problem of the maxwell equation

on the parametrization of conditioned invariant subspaces and observer theory the present paper is an in depth analysis of the set of conditioned invariant subspaces of a given observable pair c a we do this analysis in two different ways one based on polynomial models starting with a characterization obtained in p a fuhrmann linear operators and systems in hilbert space 1981 ieee trans automat control ac 26 1981 284 the other being a state space approach toeplitz operators projections in polynomial and rational models wiener hopf factorizations and factorization indices all appear and are tools in the characterizations we single out an important subclass of conditioned invariant subspaces namely the tight ones which already made an appearance in p a fuhrmann u helmke systems control lett 30 1997 217 a precursor of the present paper of particular importance for the study of the parametrization of the set of conditioned invariant subspaces of an observable pair c a is the structural map that associates with any reachable pair with only the input dimension constrained a uniquely determined conditioned invariant subspace the construction of this map uses polynomial models and the shift realization new objects the partial observability and reachability matrices are introduced which are needed for the state space characterizations kernel and image representations for conditioned invariant subspaces are derived uniqueness of a kernel representation of a conditioned invariant subspace is shown to be equivalent to tightness we pass on to an analysis and derivation of the kronecker hermite canonical form for full column rank rectangular polynomial matrices this extends the work of a e eckberg a characterization of linear systems via polynomial matrices and module theory ph d thesis mit cambridge ma 1974 g d forney siam j control optim 13 1973 493 and d hinrichsen h f munzner and d pratzel wolters systems

solutions of the equation av bw vf and their application to eigenstructure assignment in linear systems two new simple complete analytical and restriction free solutions with complete and explicit freedom of the matrix equation av bw vf are proposed here ab is known and is controllable and f is in the jordan form with arbitrary given eigenvalues based on the proposed solutions of this matrix equation a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed and two new algorithms are presented the proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective

correction of order three for the expansion of two dimensional electromagnetic fields perturbed by the presence of inhomogeneities of small diameter the derivation of the correction of order 3 for the expansion of 2 dimensional electromagnetic fields perturbed by the presence of dielectric inhomogeneities of small diameter was completed in 3 however previous numerical work such as that in 6 and in 14 do not corroborate the existence of these correcting terms the inhomogeneities used in all those numerical simulations were collections of ellipses in this paper we propose to elucidate this discrepancy we prove that the correction of order 3 is zero for any inhomogeneity that has a center of symmetry we present numerical experiments for asymmetric inhomogeneities they illustrate the importance of the correction of order 3 finally we prove that numerical schemes based on the usual quadrature for solving mixed linear integral equations on a smooth contour with smooth integration kernels and kernels involving logarithmic singularities preserve at the discrete level the fact that correcting terms of order 3 are zero for inhomogeneities that are symmetric about their center

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

existence and design of functional observers for linear systems this paper presents straightforward derivations of the functional observers design for linear time invariant multivariable systems the order of these observers is equal to the dimension spl tau of the vector to be estimated necessary and sufficient conditions for the existence and stability of these observers are given illustrative examples are included

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

a note on functional observability in this note we propose an alternative to characterize the functional observability for linear systems the main feature is that we obtain a necessary and sufficient condition for the existence of a stable multi functional observer of a time invariant linear system the proof of this condition is constructive and it leads to design a stable observer via a new procedure neither based on the solution of a sylvester equation nor on the use of canonical state space forms