a procedure for simultaneously stabilizing a collection of single input linear systems using non linear state feedback control abstract this paper considers the problem of simultaneously stabilizing a finite collection of single input linear systems this stabilization is achieved using a single non linear state feedback controller the stability of the resulting closed loop system is established using a collection of quadratic lyapunov functions the main result of this paper is a sufficient condition for simultaneous stabilizability furthermore when this sufficient condition is satisfied the paper gives a formula for constructing the stabilizing feedback control law the paper includes an example in which the stabilization procedure is applied to the stabilization of an f4e fighter aircraft

predictive updating methods with application to bayesian classification we propose algorithms based on random draws from predictive distributions of unknown quantities missing values for instance this procedure can either be iterative which is a special variation of the gibbs sampler or be sequential which is a variation of sequential imputation in the latter case one can update the posterior distribution with new observations easily the methods proposed have intuitive statistical implications and can be generalized to accommodate other bayesian like procedures we display some applications of the method in connection with the bayesian bootstrap classification hierarchical models and selection of variables in particular as an application of the method we present a unified treatment of switching regression models driven by a general binary process and we develop a bayesian testing procedure some simulations and a real example are used to illustrate the methods proposed

divergence based feature selection for multimodal class densities a new feature selection procedure based on the kullback j divergence between two class conditional density functions approximated by a finite mixture of parameterized densities of a special type is presented this procedure is suitable especially for multimodal data apart from finding a feature subset of any cardinality without involving any search procedure it also simultaneously yields a pseudo bayes decision rule its performance is tested on real data

theh p version of the finite element method for elliptic equations of order2m the problems of elliptic partial differential equations stemming from engineering problems are usually characterized by piecewise analytic data it has been shown in 3 4 5 that the solutions of the second order and fourth order equations belong to the spacesb 1 where the weighted sobolev norms of thek th derivatives are bounded bycd k l k l k l l 2 wherec andd are constants independent ofk in this case theh p version of the finite element method leads to an exponential rate of convergence measured in the energy norm 6 12 13 theh p version was implemented in the code probe1 18 and has been very successfully used in the industry we will discuss in this paper the generalization of these results for problems of order2m we will show also that the exponential rate can be achieved if the exact solution belongs to the spacesb 1 where the weighted sobolev norm of thek th derivatives is bounded bycd k l k l k l m 1 c andd are independent ofk in addition if the data is piecewise analytic then in fact the exact solution belongs to the spacesb m 1 problems of this type are related obviously to many engineering problems such as problems of plates and shells and are also important in connection with well known locking problems

estimating latent distributions in recurrent choice data this paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data these choice models are derived by specifying elements of the choice process at the individual level probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior due to the explicit consideration of random effect sources the choice models are parsimonious and readily interpretable an easy to implement em algorithm is presented for parameter estimation two applications illustrate the proposed approach

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

a right inverse for the divergence operator in spaces of piecewise polynomials in the first part of this paper we study in detail the properties of the divergence operator acting on continuous piecewise polynomials on some fixed triangulation more specifically we characterize the range and prove the existence of a maximal right inverse whose norm grows at most algebraically with the degree of the piecewise polynomials in the last part of this paper we apply these results to thep version of the finite element method for a nearly incompressible material with homogeneous dirichlet boundary conditions we show that thep version maintains optimal convergence rates in the limit as the poisson ratio approaches 1 2 this fact eliminates the need for any reduced integration such as customarily used in connection with the more standardh version of the finite element method

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

semi supervised cross entropy clustering with information bottleneck constraint abstract in this paper we propose a semi supervised clustering method cec ib that models data with a set of gaussian distributions and that retrieves clusters based on a partial labeling provided by the user partition level side information by combining the ideas from cross entropy clustering cec with those from the information bottleneck method ib our method trades between three conflicting goals the accuracy with which the data set is modeled the simplicity of the model and the consistency of the clustering with side information experiments demonstrate that cec ib performs similar as gaussian mixture models in a classical semi supervised scenario but is faster more robust to noisy labels automatically determines the optimal number of clusters and performs well when not all classes are present in the side information moreover in contrast to many other semi supervised models it can be successfully applied in discovering natural subgroups if the partition level side information is derived from the top levels of a hierarchical clustering

thresholding method for dimensionality reduction in recognition systems often recognition systems must be designed with a relatively small amount of training data plug in test statistics suffer from large estimation errors often causing the performance to degrade as the measurement vector dimension increases choosing a better test statistic or applying a method of dimensionality reduction are two possible solutions to this problem in this paper we consider a recognition problem where the data for each population are assumed to have the same parametric distribution but differ in their unknown parameters the collected vectors of data as well as their components are assumed to be independent the system is designed to implement a plug in log likelihood ratio test with maximum likelihood ml estimates of the unknown parameters instead of the true parameters because a small amount of data is available to estimate the parameters the performance of such a system is strongly degraded relative to the performance with known parameters to improve the performance of the system we define a thresholding function that when incorporated into the plug in log likelihood ratio significantly decreases the probability of error for binary and multiple hypothesis testing problems for the exponential class of populations we analyze the modified test statistic and present the results of monte carlo simulation special attention is paid to the complex gaussian model with zero mean and unknown variances

simultaneous feature selection and gaussian mixture model estimation for supervised classification problems abstract a new expectation maximization em algorithm for time critical supervised classification tasks in remote sensing is proposed compared to standard em and other approaches it has the following advantages 1 no knowledge about the class distributions is needed 2 the number of components is estimated 3 it does not require careful initialization 4 singular estimates are avoided due to the ability of pruning components 5 the best discriminating features are identified simultaneously 6 the features are identified by incorporating mahalanobis distances three experiments are carried out in order to demonstrate the relevance of the method the main findings are the following 1 feature selection is very important in terms of prediction quality of models 2 in the experiments the proposed method estimates better models than other state of the art methods 3 the incorporation of mahalanobis distances is very valuable for the identification of relevant features 4 the proposed method is more robust than the compared methods 5 in case of complex data distributions the new approach is able to provide better results

application of the em algorithm for the multitarget multisensor tracking problem an important problem in surveillance and reconnaissance systems is the tracking of multiple moving targets in cluttered noise environments using outputs from a number of sensors possessing wide variations in individual characteristics and accuracies a number of approaches have been proposed for this multitarget multisensor tracking problem ranging from reasonably simple though ad hoc schemes to fairly complex but theoretically optimum approaches in this paper we describe an iterative procedure for time recursive multitarget multisensor tracking based on use of the expectation maximization em algorithm more specifically we pose the multitarget multisensor tracking problem as an incomplete data problem with the observable sensor outputs representing the incomplete data whereas the target associated sensor outputs constitute the complete data target updates at each time use an em based approach that calculates the maximum a posteriori map estimate of the target states under the assumption of appropriate motion models based on the outputs of disparate sensors the approach uses a markov random field mrf model of the associations between observations and targets and allows for estimation of joint association probabilities without explicit enumeration the advantage of this em based approach is that it provides a computationally efficient means for approaching the performance offered by theoretically optimum approaches that use explicit enumeration of the joint association probabilities we provide selected results illustrating the performance complexity characteristics of this em based approach compared with competing schemes

feature selection based on the approximation of class densities by finite mixtures of special type abstract a new method of feature selection based on the approximation of class conditional densities by a mixture of parameterized densities of a special type suitable especially for multimodal data is presented no search procedure is needed when using the proposed method its performance is tested both on real simulated data

anderson acceleration for fixed point iterations this paper concerns an acceleration method for fixed point iterations that originated in work of d g anderson j assoc comput mach 12 1965 pp 547 560 which we accordingly call anderson acceleration here this method has enjoyed considerable success and wide usage in electronic structure computations where it is known as anderson mixing however it seems to have been untried or underexploited in many other important applications moreover while other acceleration methods have been extensively studied by the mathematics and numerical analysis communities this method has received relatively little attention from these communities over the years a recent paper by h fang and y saad numer linear algebra appl 16 2009 pp 197 221 has clarified a remarkable relationship of anderson acceleration to quasi newton secant updating methods and extended it to define a broader anderson family of acceleration methods in this paper our goals are to shed additional light on anderson acceleration and to draw further attention to its usefulness as a general tool we first show that on linear problems anderson acceleration without truncation is essentially equivalent in a certain sense to the generalized minimal residual gmres method we also show that the type 1 variant in the fang saad anderson family is similarly essentially equivalent to the arnoldi full orthogonalization method we then discuss practical considerations for implementing anderson acceleration and illustrate its performance through numerical experiments involving a variety of applications

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

simultaneous stabilization of a set of nonlinear port controlled hamiltonian systems this paper investigates simultaneous stabilization of a set of nonlinear port controlled hamiltonian pch systems and proposes a number of results on the design of simultaneous stabilization controllers for the pch systems firstly the case of two pch systems is studied using the dissipative hamiltonian structural properties the two systems are combined to generate an augmented pch system with which some results on the control design are then obtained for the case that there exist parametric uncertainties in the two systems hamiltonian structures an adaptive simultaneous stabilization controller is proposed when there are external disturbances and parametric uncertainties in the two systems two simultaneous stabilization controllers are designed for the systems one is a robust controller and the other is a robust adaptive one secondly the case of more than two pch systems is investigated and a new result is proposed for the simultaneous stabilization of the systems finally two illustrative examples are studied by using the results proposed in this paper simulations show that the simultaneous stabilization controllers obtained in this paper work very well

spectral tau approximation of the two dimensional stokes problem we analyse the spectral tau method for the approximation of the stokes system on a square with dirichlet boundary conditions we provide an error estimate in the norm of the sobolev spaceh s for the approximation of a divergence free vector field with polynomial divergence free vector fields we apply this result to prove some convergence estimates for the solution of the discrete stokes problem

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

simultaneous h infty control for nonlinear systems this note develops a novel method for designing simultaneous h infin state feedback controllers for a collection of single input nonlinear systems based on the kalman yakubovich popov lemma necessary and sufficient conditions for the existence of simultaneous h infin controllers are derived by the control storage function approach a universal formula for constructing continuous time invariant simultaneous h infin state feedback controllers is presented

p version of mixed finite element methods for stokes like problems abstract we investigate various sample extremum saddle point and minimization problems from the point of view of stability of increasing order mixed finite element methods problems discussed include the stokes poisson and linear elasticity problems

simultaneous stabilization of linear and nonlinear systems by means of nonlinear state feedback the simultaneous stabilization resp asymptotic stabilization of a countable family of control systems consists of finding a control which stabilizes resp asymptotically stabilizes all the systems in the family in this paper we introduce a new method which enables us to show that given any countable family of stabilizable nonlinear systems there exists a continuous state feedback law which simultaneously stabilizes not asymptotically the family then by enriching this method we prove that any finite family of stabilizable linear time invariant lti systems can be simultaneously exponentially stabilized by means of nonlinear time varying state feedback we also derive sufficient conditions for the simultaneous asymptotic stabilizability of countably infinite families of lti systems finally sufficient conditions for the simultaneous asymptotic stabilizability of finite families of nonlinear systems are provided and used for the simultaneous asymptotic stabilization of certain pairs of nonlinear homogeneous systems

simultaneous quadratic stabilization for discrete time nonlinear systems a constructive method is developed for designing simultaneously quadratically stabilizing state feedback controllers for a collection of single input discrete time nonlinear systems in the context of quadratic control lyapunov functions a necessary and sufficient condition for the existence of simultaneously quadratically stabilizing state feedback laws is derived an explicit formula for constructing continuous simultaneously stabilizing controllers is presented the obtained results are verified by a numerical example

experimental study on prototype optimisation algorithms for prototype based classification in vector spaces prototype based classification relies on the distances between the examples to be classified and carefully chosen prototypes a small set of prototypes is of interest to keep the computational complexity low while maintaining high classification accuracy an experimental study of some old and new prototype optimisation techniques is presented in which the prototypes are either selected or generated from the given data these condensing techniques are evaluated on real data represented in vector spaces by comparing their resulting reduction rates and classification performance usually the determination of prototypes is studied in relation with the nearest neighbour rule we will show that the use of more general dissimilarity based classifiers can be more beneficial an important point in our study is that the adaptive condensing schemes here discussed allow the user to choose the number of prototypes freely according to the needs if such techniques are combined with linear dissimilarity based classifiers they provide the best trade off of small condensed sets and high classification accuracy

sar amplitude probability density function estimation based on a generalized gaussian model in the context of remotely sensed data analysis an important problem is the development of accurate models for the statistics of the pixel intensities focusing on synthetic aperture radar sar data this modeling process turns out to be a crucial task for instance for classification or for denoising purposes in this paper an innovative parametric estimation methodology for sar amplitude data is proposed that adopts a generalized gaussian gg model for the complex sar backscattered signal a closed form expression for the corresponding amplitude probability density function pdf is derived and a specific parameter estimation algorithm is developed in order to deal with the proposed model specifically the recently proposed method of log cumulants molc is applied which stems from the adoption of the mellin transform instead of the usual fourier transform in the computation of characteristic functions and from the corresponding generalization of the concepts of moment and cumulant for the developed gg based amplitude model the resulting molc estimates turn out to be numerically feasible and are also analytically proved to be consistent the proposed parametric approach was validated by using several real ers 1 xsar e sar and nasa jpl airborne sar images and the experimental results prove that the method models the amplitude pdf better than several previously proposed parametric models for backscattering phenomena

parameter estimation and tissue segmentation from multispectral mr images a statistical method is developed to classify tissue types and to segment the corresponding tissue regions from relaxation time t sub 1 t sub 2 and proton density p sub d weighted magnetic resonance images the method assumes that the distribution of image intensities associated with each tissue type can be expressed as a multivariate likelihood function of three weighted signal intensity values t sub 1 t sub 2 p sub d at each location within that tissue regions the method further assumes that the underlying tissue regions are piecewise contiguous and can be characterized by a markov random field prior in classifying the tissue types the method models the likelihood of realizing the images as a finite multivariate mixture function the class parameters associated with the tissue types i e the weighted intensity means variances and correlation coefficients of the multivariate function as well as the number of voxels within regions of the tissue types of are estimated by maximum likelihood the estimation fits the class parameters to the image data via the expectation maximization algorithm the number of classes associated with the tissue types is determined by the information criterion of minimum description length the method segments the tissue regions given the estimated class parameters by maximum a posteriori probability the prior is constructed by the tissue region membership of the first and second order neighborhood the method is tested by a few sets of t sub 1 t sub 2 and p sub d weighted images of the brain acquired with a 1 5 tesla whole body scanner the number of classes and the associated class parameters are automatically estimated the regions of different brain tissues are satisfactorily segmented

on computing the pressure by thep version of the finite element method for stokes problem this paper introduces and analyzes two ways of extracting the hydrostatic pressure when solving stokes problem using thep version of the finite element method when one uses a localh 1 projection we show that optimal rates of convergence for the pressure approximation is achieved when the pressure is not inh 1 or the value of the pressure is only needed at a few points one may extract the pressure pointwise using e g a single layer potential recovery negative zero and higher norm estimates for the stokes velocity are derived within the framework of thep version of the f e m

simultaneous stabilization of three or more plants conditions on the positive real axis do not suffice the problem of the simultaneous stabilizability of a finite family of single input single output time invariant systems by a time invariant controller is studied the link between stabilization and avoidance is shown and is used to derive necessary conditions for the simultaneous stabilization of k plants these necessary conditions are proved to be in general not sufficient this result also disproves a long standing conjecture on the stabilizability condition of a single plant with a stable minimum phase controller the main result is to show that unlike the case of two plants the existence of a simultaneous stabilizing controller for more than two plants is not guaranteed by the existence of a controller such that the closed loops have no real unstable poles

a bayesian approach to finite mixture models in bioassay via data augmentation and gibbs sampling and its application to insecticide resistance after continued treatment with an insecticide within the population of the susceptible insects resistant strains will occur it is important to know whether there are any resistant strains what the proportions are and what the median lethal doses are for the insecticide lwin and martin 1989 biometrics 45 721 732 propose a probit mixture model and use the em algorithm to obtain the maximum likelihood estimates for the parameters this approach has difficulties in estimating the confidence intervals and in testing the number of components we propose a bayesian approach to obtaining the credible intervals for the location and scale of the tolerances in each component and for the mixture proportions by using data augmentation and gibbs sampler we use bayes factor for model selection and determining the number of components we illustrate the method with data published in lwin and martin 1989

application of global optimization methods to model and feature selection many data mining applications involve the task of building a model for predictive classification the goal of this model is to classify data instances into classes or categories of the same type the use of variables not related to the classes can reduce the accuracy and reliability of classification or prediction model superfluous variables can also increase the costs of building a model particularly on large datasets the feature selection and hyper parameters optimization problem can be solved by either an exhaustive search over all parameter values or an optimization procedure that explores only a finite subset of the possible values the objective of this research is to simultaneously optimize the hyper parameters and feature subset without degrading the generalization performances of the induction algorithm we present a global optimization approach based on the use of cross entropy method to solve this kind of problem

a hybrid feature extraction selection approach for high dimensional non gaussian data clustering this paper presents an unsupervised approach for feature selection and extraction in mixtures of generalized dirichlet gd distributions our method defines a new mixture model that is able to extract independent and non gaussian features without loss of accuracy the proposed model is learned using the expectation maximization algorithm by minimizing the message length of the data set experimental results show the merits of the proposed methodology in the categorization of object images

simultaneous stabilization for a collection of single input nonlinear systems this paper presents a novel method for designing a controller that simultaneously stabilizes a collection of single input nonlinear systems the control lyapunov function approach is used to derive necessary and sufficient conditions for the existence of time invariant simultaneously stabilizing state feedback controllers additionally a universal formula for constructing a continuous simultaneously stabilizing controller when the provided sufficient condition is satisfied is presented for any collection of second order and third order feedback linearizable systems in canonical form global simultaneous stabilization via a single state feedback controller is shown to be always possible two examples are included for illustration

on signal representations within the bayes decision framework this work presents new results in the context of minimum probability of error signal representation mpe sr within the bayes decision framework these results justify addressing the mpe sr criterion as a complexity regularized optimization problem demonstrating the empirically well understood trade off between signal representation quality and learning complexity contributions are presented in three folds first the stipulation of conditions that guarantee a formal tradeoff between approximation and estimation errors under sequence of embedded transformations are provided second the use of this tradeoff to formulate the mpe sr as a complexity regularized optimization problem and an approach to address this oracle criterion in practice is given finally formal connections are provided between the mpe sr criterion and two emblematic feature transformation techniques used in pattern recognition the optimal quantization problem of classification trees cart tree pruning algorithms and some versions of fisher linear discriminant analysis lda

asymptotic convergence rate of the em algorithm for gaussian mixtures it is well known that the convergence rate of the expectation maximization em algorithm can be faster than those of convention first order iterative algorithms when the overlap in the given mixture is small but this argument has not been mathematically proved yet this article studies this problem asymptotically in the setting of gaussian mixtures under the theoretical framework of xu and jordan 1996 it has been proved that the asymptotic convergence rate of the em algorithm for gaussian mixtures locally around the true solution is o e0 5 e where e 0 is an arbitrarily small number o x means that it is a higher order infinitesimal as x 0 and e is a measure of the average overlap of gaussians in the mixture in other words the large sample local convergence rate for the em algorithm tends to be asymptotically superlinear when e tends to zero

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

unsupervised learning of parsimonious mixtures on large spaces with integrated feature and component selection estimating the number of components the order in a mixture model is often addressed using criteria such as the bayesian information criterion bic and minimum message length however when the feature space is very large use of these criteria may grossly underestimate the order here it is suggested that this failure is not mainly attributable to the criterion e g bic but rather to the lack of structure in standard mixtures these models trade off data fitness and model complexity only by varying the order the authors of the present paper propose mixtures with a richer set of tradeoffs the proposed model allows each component its own informative feature subset with all other features explained by a common model shared by all components parameter sharing greatly reduces complexity at a given order since the space of these parsimonious modeling solutions is vast this space is searched in an efficient manner integrating the component and feature selection within the generalized expectation maximization gem learning for the mixture parameters the quality of the proposed unsupervised solutions is evaluated using both classification error and test set data likelihood on text data the proposed multinomial version learned without labeled examples without knowing the true number of topics and without feature preprocessing compares quite favorably with both alternative unsupervised methods and with a supervised naive bayes classifier a gaussian version compares favorably with a recent method introducing feature saliency in mixtures

the p and h p versions of some finite element methods for stokes problem abstract we investigate discretizations of stokes problem as a sample saddle point problem from the point of view of stability of increasing order mixed finite element methods for the cases of velocity pressure space pairs where the stability can be characterized in terms of the growth of a right inverse of the divergence operator we exhibit algebraic instabilities of varying size depending on boundary conditions and the kind of element employed

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem