semilocal and local convergence of a fifth order iteration with frechet derivative satisfying holder condition the semilocal and local convergence in banach spaces is described for a fifth order iteration for the solutions of nonlinear equations when the frechet derivative satisfies the holder condition the holder condition generalizes the lipschtiz condition the importance of our work lies in the fact that many examples are available which fail to satisfy the lipschtiz condition but satisfy the holder condition the existence and uniqueness theorem is established with error bounds for the solution the convergence analysis is finally worked out on different examples and convergence balls for each of them are obtained these examples include nonlinear hammerstein and fredholm integral equations and a boundary value problem it is found that the larger radius of convergence balls is obtained for all the examples in comparison to existing methods using stronger conditions

randomized clustering forests for image classification some of the most effective recent methods for content based image classification work by quantizing image descriptors and accumulating histograms of the resulting visual word codes large numbers of descriptors and large codebooks are required for good results and this becomes slow using k means we introduce extremely randomized clustering forests ensembles of randomly created clustering trees and show that they provide more accurate results much faster training and testing and good resistance to background clutter second an efficient image classification method is proposed it combines erc forests and saliency maps very closely with the extraction of image information for a given image a classifier builds a saliency map online and uses it to classify the image we show in several state of the art image classification tasks that this method can speed up the classification process enormously finally we show that the proposed erc forests can also be used very successfully for learning distance between images the distance computation algorithm consists of learning the characteristic differences between local descriptors sampled from pairs of same or different objects these differences are vector quantized by erc forests and the similarity measure is computed from this quantization the similarity measure has been evaluated on four very different datasets and always outperforms the state of the art competitive approaches

a necessary condition for feedback stabilization abstract we give a new necessary condition for the existence of a static or dynamic continuous asymptotically stabilizing feedback control for the system x dot f x u we apply our condition to give an example of a system in r 3 which is small time locally controllable satisfies brockett s second and third condition and cannot be locally asymptotically stabilized by employing a static or dynamic continuous feedback law

robust observer design under measurement noise with gain adaptation and saturated estimates abstract we use incremental homogeneity gain adaptation and incremental observability for proving new results on robust observer design for systems with noisy measurement and bounded trajectories a state observer is designed by dominating the incrementally homogeneous nonlinearities of the observation error system with its linear approximation while gain adaptation and incremental observability guarantee an asymptotic upper bound for the estimation error depending on the limsup of the norm of the measurement noise a characteristic and innovative feature of this observer is the mixed low high gain structure in combination with saturated state estimates and dynamically tuned gains and saturation levels the gain adaptation is implemented as the output of a stable filter using the squared norm of the measured output estimation error and the mismatch between each estimate and its saturated value

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

smooth output feedback stabilization of planar systems without controllable observable linearization this note considers the problem of global stabilization by output feedback for a family of planar systems whose jacobian linearization is neither controllable nor observable the problem cannot be dealt with by existing output feedback design methods most of them are based on the separation principle under appropriate growth conditions we propose an output feedback control scheme that does not rely on the separation principle and achieves global asymptotic stabilization the novelty of our control scheme lies in the explicit design of a dynamic output compensator which combines a nonlinear gain observer design and the technique of adding a power integrator as a consequence an interesting global stabilization result by output feedback can be obtained for feedback linearizable systems in a triangular form which turns out to be new even in the two dimensional case

dissimilarity metric learning in the belief function framework the evidential k nearest neighbor ek nn method provided a global treatment of imperfect knowledge regarding the class membership of training patterns it has outperformed traditional k nn rules in many applications but still shares some of their basic limitations e g 1 classification accuracy depends heavily on how to quantify the dissimilarity between different patterns and 2 no guarantee for satisfactory performance when training patterns contain unreliable imprecise and or uncertain input features in this paper we propose to address these issues by learning a suitable metric using a low dimensional transformation of the input space so as to maximize both the accuracy and efficiency of the ek nn classification to this end a novel loss function to learn the dissimilarity metric is constructed it consists of two terms the first one quantifies the imprecision regarding the class membership of each training pattern while by means of feature selection the second one controls the influence of unreliable input features on the output linear transformation the proposed method has been compared with some other metric learning methods on several synthetic and real datasets it consistently led to comparable performance with regard to testing accuracy and class structure visualization

a local stabilization theorem for interconnected systems abstract we prove that if a nonlinear control system is locally asymptotically stabilizable at its equilibrium by means of a continuous feedback then adding an integrator the resulting system is also locally asymptotically stabilizable by means of a feedback law which is smooth except possibly at the equilibrium our approach is based on previous works of arstein sontag and the author

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

optimal controllers and output feedback stabilization abstract in this paper the output feedback stabilizability problem is explored in terms of control lyapunov functions sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem our main results extends those developed in 31 and generalize a theorem due to sontag 23

avoiding the computation of the second fre chet derivative in the convex acceleration of newton s method we introduce a new two step method to approximate a solution of a nonlinear operator equation in a banach space an existence uniqueness theorem and error estimates are provided for this iteration using newton kantorovich type assumptions and a technique based on a new system of recurrence relations for a special choice of the parameter involved we use our method is of fourth order

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

adding one power integrator a tool for global stabilization of high order lower triangular systems a new feedback design tool called adding a power integrator is introduced and used to solve the problem of global robust stabilization for a significant class of uncertain nonlinear systems that are of a lower triangular form but neither necessarily feedback linearizable fully or partially nor affine in the control input and therefore cannot be dealt with via conventional approaches sufficient conditions are presented under which a globally stabilizing smooth state feedback control law can be explicitly constructed using repeatedly the adding one power integrator technique this novel design technique permits removal of the feedback linearizability and linearity of the control input which have been two common assumptions so far in the literature of nonlinear control

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 lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

on the r order of the halley method an r order bound for the halley method is obtained in this work where an analysis of the convergence of the method is also presented under mild differentiability conditions to do this a new technique is developed where the involved operator must satisfy some recurrence relations

on an output feedback finite time stabilization problem studies the problem of finite time output feedback stabilization for the double integrator system a class of output feedback controllers that can achieve global finite time stability for the double integrator system are constructed based on a finite time separation principle furthermore it is shown that the closed loop system resulting from our control law can maintain its local finite time stability regardless of some nonlinear perturbations thus our control law actually applies to a large class of nonlinear second order systems

continuous finite time stabilization of the translational and rotational double integrators a class of bounded continuous time invariant finite time stabilizing feedback laws is given for the double integrator lyapunov theory is used to prove finite time convergence for the rotational double integrator these controllers are modified to obtain finite time stabilizing feedback that avoid unwinding

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

global stabilization of discrete time homogeneous systems abstract the feedback stabilization of continuous time r homogeneous systems has been studied by several authors see for instance dayawansa and martin proceedings of the 28th c d c tampa florida december 1989 hermes j differential equations 92 1991 76 89 hermes systems control lett 24 1995 7 11 kawski proceedings of the 27th c d c texas 1988 texas kawski control theory and advanced technology vol 6 mita press tokyo 1996 pp 497 516 sepulchre and aeyels math control signal systems 9 1996 34 58 in kawski analysis of controlled dynamical systems birkhauser basel 1991 kawski proceedings of ifac nolcos 1995 kawski gave an intrinsic concept of homogeneity with respect to general smooth dilations in this note we define the homogeneity of transition maps w r t continuous dilations and we show how one can construct a global stabilizing feedback control for discrete time homogeneous systems which are locally asymptotically stabilizable

lyapunov design of stabilizing controllers for cascaded systems the design of a state feedback law for an affine nonlinear system to render a as small as possible compact neighborhood of the equilibrium of interest globally attractive is discussed following z artstein s theorem 1983 the problem can be solved by designing a so called control lyapunov function for systems which are in a cascade form a lyapunov function meeting artstein s conditions is designed assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem in particular for planar systems this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized

irahc instance reduction algorithm using hyperrectangle clustering abstract in instance based classifiers there is a need for storing a large number of samples as training set in this work we propose an instance reduction method based on hyperrectangle clustering called instance reduction algorithm using hyperrectangle clustering irahc irahc removes non border interior instances and keeps border and near border ones this paper presents an instance reduction process based on hyperrectangle clustering a hyperrectangle is an n dimensional rectangle with axes aligned sides which is defined by min and max points and a corresponding distance function the min max points are determined by using the hyperrectangle clustering algorithm instance based learning algorithms are often confronted with the problem of deciding which instances must be stored to be used during an actual test storing too many instances can result in a large memory requirements and a slow execution speed in irahc core of instance reduction process is based on set of hyperrectangles the performance has been evaluated on real world data sets from uci repository by the 10 fold cross validation method the results of the experiments have been compared with state of the art methods which show superiority of the proposed method in terms of classification accuracy and reduction percentage

finding prototypes for nearest neighbour classification by means of gradient descent and deterministic annealing a new method is presented to find prototypes for a nearest neighbour classifier the prototype locations are optimised through a gradient descent and a deterministic annealing process the proposed algorithm also includes an initialisation strategy which aims to provide the maximum classification rate on the training set with the minimum number of prototypes experiments show the efficiency of this algorithm on both real and artificial data

recurrence relations for semilocal convergence of a newton like method in banach spaces abstract the aim of this paper is to establish the semilocal convergence of a multipoint third order newton like method for solving f x 0 in banach spaces by using recurrence relations the convergence of this method is studied under the assumption that the second frechet derivative of f satisfies holder continuity condition this continuity condition is milder than the usual lipschitz continuity condition a new family of recurrence relations are defined based on the two new constants which depend on the operator f these recurrence relations give a priori error bounds for the method two numerical examples are worked out to demonstrate the applicability of the method in cases where the lipschitz continuity condition over second derivative of f fails but holder continuity condition holds

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

asymptotically stabilizing feedback controls abstract the problem considered is the existence and construction of an asymptotically stabilizing feedback control for a rest solution of an n dimensional single input affine control system the method is to construct high order homogeneous approximations of the vector fields defining the control system which then describe an approximating control system such that an asymptotically stabilizing control of the latter system is a local asymptotically stabilizing control of the original system unlike linear approximations there are many possible nonlinear homogeneous approximations these are constructed from lie algebra filtrations obtained by assigning various weights to the defining vector fields one seeks a weighting hence an approximating system which satisfies the various known necessary conditions for the existence of an asymptotically stabilizing feedback control and for which such a control can be constructed as the solution to a homogeneous hamilton jacobi bellman equation associated with an optimization regulator problem

robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization this paper investigates the problem of robust output feedback stabilization for a family of uncertain nonlinear systems with uncontrollable unobservable linearization to achieve global robust stabilization via smooth output feedback we introduce a rescaling transformation with an appropriate dilation which turns out to be very effective in dealing with uncertainty of the system using this rescaling technique combined with the nonseparation principle based design method we develop a robust output feedback control scheme for uncertain nonlinear systems in the p normal form under a homogeneous growth condition the construction of smooth state feedback controllers and homogeneous observers uses only the knowledge of the bounding homogeneous system rather than the uncertain system itself the robust output feedback design approach is then extended to a class of uncertain cascade systems beyond a strict triangular structure examples are provided to illustrate the results of the paper

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

combining estimates in regression and classification abstract we consider the problem of how to combine a collection of general regression fit vectors to obtain a better predictive model the individual fits may be from subset linear regression ridge regression or something more complex like a neural network we develop a general framework for this problem and examine a cross validation based proposal called model mix or stacking in this context we also derive combination methods based on the bootstrap and analytic methods and compare them in examples finally we apply these ideas to classification problems where the estimated combination weights can yield insight into the structure of the problem

stabilisation of nonlinear systems by discontinuous dynamic state feedback in this paper a dynamic state feedback that stabilizes general nonlinear affine in the control systems is proposed it is deduced from the solution of an hamilton jacobi like equality with two boundary conditions the asymptotic stability of the closed loop system is proved and some examples are given an interesting feature of this method is that the so obtained feedback takes the form of a generalised sliding mode control in the sense that it is a dynamic feedback on one half part of the space and a static feedback on the other half with eventually a discontinuity on the surface dividing the space

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

modification of the kantorovich assumptions for semilocal convergence of the chebyshev method this study obtains two semilocal convergence results for the well known chebyshev method which is a third order iterative process the hypotheses required are modifications to the normal kantorovich ones the results obtained are applied to the reduction of nonlinear integral equations of the fredholm type and first kind

feature scaling for kernel fisher discriminant analysis using leave one out cross validation kernel fisher discriminant analysis kfd is a successful approach to classification it is well known that the key challenge in kfd lies in the selection of free parameters such as kernel parameters and regularization parameters here we focus on the feature scaling kernel where each feature individually associates with a scaling factor a novel algorithm named fs kfd is developed to tune the scaling factors and regularization parameters for the feature scaling kernel the proposed algorithm is based on optimizing the smooth leave one out error via a gradient descent method and has been demonstrated to be computationally feasible fs kfd is motivated by the following two fundamental facts the leave one out error of kfd can be expressed in closed form and the step function can be approximated by a sigmoid function empirical comparisons on artificial and benchmark data sets suggest that fs kfd improves kfd in terms of classification accuracy

neural decoding with kernel based metric learning in studies of the nervous system the choice of metric for the neural responses is a pivotal assumption for instance a well suited distance metric enables us to gauge the similarity of neural responses to various stimuli and assess the variability of responses to a repeated stimulus exploratory steps in understanding how the stimuli are encoded neurally here we introduce an approach where the metric is tuned for a particular neural decoding task neural spike train metrics have been used to quantify the information content carried by the timing of action potentials while a number of metrics for individual neurons exist a method to optimally combine single neuron metrics into multineuron or population based metrics is lacking we pose the problem of optimizing multineuron metrics and other metrics using centered alignment a kernel based dependence measure the approach is demonstrated on invasively recorded neural data consisting of both spike trains and local field potentials the experimental paradigm consists of decoding the location of tactile stimulation on the forepaws of anesthetized rats we show that the optimized metrics highlight the distinguishing dimensions of the neural response significantly increase the decoding accuracy and improve nonlinear dimensionality reduction methods for exploratory neural analysis

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

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

stabilization of non linear control systems the role of newton diagrams abstract the stabilization of two dimensional non linear control systems is treated although the main technique is applicable to more general systems it combines the theory of centre manifolds and singularities of algebraic functions to design continuous but not necessarily lipschitz stabilizing feedback control laws in particular the devices known as the newton diagram and the newton or puiseux polygon are employed to construct uniformizing transformations finally remarks are made about systems for which no continuous stabilizing feedback control law exists

feature selection based on a modified fuzzy c means algorithm with supervision in this paper we propose a new approach to feature selection based on a modified fuzzy c means algorithm with supervision mfcms mfcms completes the unsupervised learning of classical fuzzy c means with labeled patterns the labeled patterns allow mfcms to accurately model the shape of each cluster and consequently to highlight the features which result to be particularly effective to characterize a cluster these features are distinguished by a low variance of their values for the patterns with a high membership degree to the cluster if with respect to these features the distance between the prototype of the cluster and the prototypes of the other clusters is high then these features have the property of discriminating between the cluster and the other clusters to take these two aspects into account for each cluster and each feature we introduce a purposely defined index the higher the value of the index the higher the discrimination capability of the feature for the cluster we execute mfcms on the training set considering all patterns as labeled then we retain the features which are associated at least for one cluster with an index larger than a threshold we applied mfcms to several real world pattern classification benchmarks we used the well known k nearest neighbors as learning algorithm we show that feature selection performed by mfcms achieved an improvement in generalization on all data sets

feedback stabilization of real analytic systems in the plane abstract we investigate the local feedback stabilization of single input control affine analytic systems x tf x ug x in the plane new necessary and sufficient conditions for local stabilization with feedback laws of the form u v x 1 x 2 x 2 v x 1 0 0 2 v x 1 0 0 2 0 0 v 0 0 0 are obtained by using lyapunov s stability theorems on two dimensional analytic systems if the sufficient conditions are satisfied we also provide explicit feedback laws

asymptotic stabilization of a class of smooth two dimensional systems this paper studies the asymptotic stabilizability of two dimensional control systems the class under consideration includes c infty systems that satisfy a certain genericity assumption and all real analytic systems necessary and sufficient conditions for feedback stabilization using continuous feedback and a sufficient condition for c 1 feedback stabilization are given this latter condition is given in terms of an inequality involving two indices if the direction of the inequality is changed an obstruction to c infty feedback stabilizability is obtained a subclass of polynomial systems is also studied and given complete necessary and sufficient conditions for global asymptotic stabilization using c 1 feedback

recurrence relations for a newton like method in banach spaces the convergence of iterative methods for solving nonlinear operator equations in banach spaces is established from the convergence of majorizing sequences an alternative approach is developed to establish this convergence by using recurrence relations for example the recurrence relations are used in establishing the convergence of newton s method l b rall computational solution of nonlinear operator equations robert e krieger new york 1979 and the third order methods such as halley s chebyshev s and super halley s v candela a marquina recurrence relations for rational cubic methods i the halley method computing 44 1990 169 184 v candela a marquina recurrence relations for rational cubic methods ii the halley method computing 45 1990 355 367 j a ezquerro m a hernandez recurrence relations for chebyshev type methods appl math optim 41 2000 227 236 j m gutierrez m a hernandez third order iterative methods for operators with bounded second derivative j comput appl math 82 1997 171 183 j m gutierrez m a hernandez recurrence relations for the super halley method comput math appl 7 36 1998 1 8 m a hernandez chebyshev s approximation algorithms and applications comput math appl 41 2001 433 445 10 in this paper an attempt is made to use recurrence relations to establish the convergence of a third order newton like method used for solving a nonlinear operator equation f x 0 where f email protected x y be a nonlinear operator on an open convex subset w of a banach space x with values in a banach space y here first we derive the recurrence relations based on two constants which depend on the operator f then based on this recurrence relations a priori error bounds are obtained for the said iterative method finally some numerical examples are worked out for demonstrating our approach

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

local discriminative learning for pattern recognition abstract local discriminative learning methods approximate a target function a posteriori class probability function directly by partitioning the feature space into a set of local regions and appropriately modeling a simple input output relationship function in each one this paper presents a new method for judiciously partitioning the input feature space in order to accurately represent the target function the method accomplishes this by approximating not only the target function itself but also its derivatives as such the method partitions the input feature space along those dimensions for which the class probability function changes most rapidly thus minimizing bias the efficacy of the method is validated using a variety of simulated and real world data

almost disturbance decoupling for a class of high order nonlinear systems the problem of almost disturbance decoupling with internal stability add is formulated in terms of an l sub 2 l sub 2p instead of an l sub 2 gain for a class of high order nonlinear systems which consist of a chain of power integrators perturbed by a lower triangular vector field a significant feature of the systems considered in the paper is that they are neither feedback linearizable nor affine in the control input which have been two basic assumptions made in all the existing add nonlinear control schemes using the technique of adding a power integrator we solve the add problem via static smooth state feedback under a set of growth conditions that can be viewed as a high order version of the feedback linearization conditions we also show how to explicitly construct a smooth state feedback controller that attenuates the disturbance s effect on the output to an arbitrary degree of accuracy with internal stability

convergence of the family of the deformed euler halley iterations under the holder condition of the second derivative the convergence problem of the family of the deformed euler halley iterations with parameters for solving nonlinear operator equations in banach spaces is studied under the assumption that the second derivative of the operator satisfies the holder condition a convergence criterion of the order 2 p of the iteration family is established an application to a nonlinear hammerstein integral equation of the second kind is provided

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

remarks on asymptotic controllability and sampled data feedback stabilization for autonomous systems a weak concept of sampled data feedback stabilization for the case of autonomous systems is presented and its lyapunov characterization is established sufficient conditions are derived for the existence of a time varying sampled data feedback exhibiting global stabilization for certain class of nonlinear systems

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

asymptotic stabilization of two dimensional real analytic systems abstract we investigate the local asymptotic stabilizability of a real analytic control system around an equilibrium point and give necessary and sufficient conditions for local asymptotic stabilization using continuous feedback

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

recurrence relations for the super halley method in this paper we give sufficient conditions in order to assure the convergence of the super halley method in banach spaces we use a system of recurrence relations analogous to those given in the classical newton kantorovich theorem or those given for chebyshev and halley methods by different authors 1998 elsevier science ltd all rights reserved

a third order method for fixed points in banach spaces this paper deals with a third order stirling like method used for finding fixed points of nonlinear operator equations in banach spaces the semilocal convergence of the method is established by using recurrence relations under the assumption that the first frechet derivative of the involved operator satisfies the holder continuity condition a theorem is given to establish the error bounds and the existence and uniqueness regions for fixed points the r order of the method is also shown to be equal to at least 2p 1 for p 0 1 the efficacy of our approach is shown by solving three nonlinear elementary scalar functions and two nonlinear integral equations by using both stirling like method and newton like method it is observed that our convergence analysis is more effective and give better results

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

third order convergence theorem by using majorizing function for a modified newton method in banach space abstract following the ideas of frontini and sormani we present a modified newton method in banach space which is used to solve the nonlinear operator equation we establish the newton kantorovich convergence theorem for the modified newton method with third order convergence in banach space by using majorizing function we also get the error estimate finally two examples are provided to show the application of our theorem

h control stabilization and input output stability of nonlinear systems with homogeneous properties new relations are established between h control and stabilization and between input output stability and lyapunov stability of nonlinear systems with homogeneous properties these results can be applied to h controller design and stability analysis

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

asymptotic stabilization of planar systems abstract sufficient conditions for the existence of a c1 asymptotically stabilizing feedback control for planar affine systems are given the methods are constructive and yield homogeneous feedback controls for homogeneous systems which allow the results to be extended to more general systems

practical output tracking of nonlinear systems with uncontrollable unstable linearization the paper focuses on the problem of having the output of nonlinear systems track a prescribed c sup 1 reference signal it is proved that under mild assumptions global practical output tracking is achievable by smooth state feedback although asymptotic output tracking is usually not possible even locally because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed based on a modified adding a power integrator approach this feedback design method also leads to solutions to challenging benchmark control problems including practical output tracking of an underactuated unstable two degrees of freedom mechanical system

an extension of artstein s theorem on stabilization by using ordinary feedback integrators abstract we prove that under suitable lyapunov like conditions a single input nonlinear system although it may not be stabilized by an ordinary state feedback law is dynamically stabilize by means of an ordinary feedback integrator

finite time stability and stabilization of a class of continuous systems abstract finite time stability is investigated for continuous system x f x which satisfies uniqueness of solutions in forward time a necessary and sufficient condition for finite time stability is given for this class of systems using lyapunov functions then a necessary and sufficient condition is developed for finite time stabilization of class cl k affine systems x f x g x u involving a class cl 0 settling time function for the closed loop system finally an explicit feedback control is addressed by using a control lyapunov function verifying a certain inequality

global stabilization of cascade systems by c sup 0 partial state feedback this paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization and the notion and properties of the input to state stability lyapunov function can be effectively coupled resulting in globally stabilizing c sup 0 partial state feedback controllers for a class of cascade systems which may not be smoothly stabilizable even locally

quantifying the informativeness of similarity measurements in this paper we describe an unsupervised measure for quantifying the informativeness of correlation matrices formed from the pairwise similarities or relationships among data instances the measure quantifies the heterogeneity of the correlations and is defined as the distance between a correlation matrix and the nearest correlation matrix with constant off diagonal entries this non parametric notion generalizes existing test statistics for equality of correlation coefficients by allowing for alternative distance metrics such as the bures and other distances from quantum information theory for several distance and dissimilarity metrics we derive closed form expressions of informativeness which can be applied as objective functions for machine learning applications empirically we demonstrate that informativeness is a useful criterion for selecting kernel parameters choosing the dimension for kernel based nonlinear dimensionality reduction and identifying structured graphs we also consider the problem of finding a maximally informative correlation matrix around a target matrix and explore parameterizing the optimization in terms of the coordinates of the sample or through a lower dimensional embedding in the latter case we find that maximizing the bures based informativeness measure which is maximal for centered rank 1 correlation matrices is equivalent to minimizing a specific matrix norm and present an algorithm to solve the minimization problem using the norm s proximal operator the proposed correlation denoising algorithm consistently improves spectral clustering overall we find informativeness to be a novel and useful criterion for identifying non trivial correlation structure

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

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

stabilizability conditions in terms of critical hamiltonians and symbols symmetric functions of critical hamiltonians called symbols were used in such problems of nonlinear control as the characterization of symmetries and feedback invariants we derive here a stabilizability condition in the class of almost continuous feedback controls based on symbols the methodology proposed consists of defining a selector of the multivalued covector field satisfying an extra degree condition on a sphere close to the origin then the above selector is extended to some neighborhood in order to get an exact differential form integration of that form gives us a control lyapunov function candidate theorem 3 1 the condition proposed is applied to the analysis of a planar control affine system with polynomial homogeneous vector fields unlike known results in the literature we consider the case when each vector field vanishes at the origin and the control is bounded we give stabilizability conditions explicitly in terms of the control system parameters theorem 4 1

chebyshev s approximation algorithms and applications abstract we introduce a new family of multipoint methods to approximate a solution of a nonlinear operator equation in banach spaces an existence uniqueness theorem and error estimates are provided for these iterations using a technique based on a new system of recurrence relations to finish we apply the results obtained to some nonlinear integral equations of the fredholm type

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

non smooth simultaneous stabilization of nonlinear systems an interpolation method abstract in this paper we introduce a method which enables us to construct a continuous simultaneous stabilizer for pairs of systems in r 2 which cannot be simultaneously stabilized by means of c 1 feedback we extend this method to higher dimensional systems and show that any pair of asymptotically stabilizable nonlinear systems can be simultaneously stabilized not asymptotically by means of continuous feedback

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

newton type methods on riemannian manifolds under kantorovich type conditions one of the most studied problems in numerical analysis is the approximation of nonlinear equations using iterative methods in the last years attention has been paid in studying newton s method on manifolds in this paper we generalize this study considering some newton type iterative methods a characterization of the convergence under kantorovich type conditions and optimal estimates of the error are found using normal coordinates the order of convergence is derived the sufficient semilocal convergence criteria are weaker and the majorizing sequences are tighter for the special cases of simplified newton and newton methods than in earlier studies such as argyros 2004 2007 2008 6 8 12 and kantorovich and akilov 1964 32

two global stabilizability results for homogeneous systems from a local stabilizability assumption in this technical note two problems have been investigated the first one concerns the global asymptotic feedback stabilization of homogeneous systems for these systems it is shown that local asymptotic stabilization implies the global dynamic feedback stabilization one the second problem consists to show that under a weak assumption on the observability if a state affine system is locally asymptotically stabilizable then it becomes globally asymptotically stabilizable by using a discontinuous output feedback

transformation invariant clustering using the em algorithm clustering is a simple effective way to derive useful representations of data such as images and videos clustering explains the input as one of several prototypes plus noise in situations where each input has been randomly transformed e g by translation rotation and shearing in images and videos clustering techniques tend to extract cluster centers that account for variations in the input due to transformations instead of more interesting and potentially useful structure for example if images from a video sequence of a person walking across a cluttered background are clustered it would be more useful for the different clusters to represent different poses and expressions instead of different positions of the person and different configurations of the background clutter we describe a way to add transformation invariance to mixture models by approximating the nonlinear transformation manifold by a discrete set of points we show how the expectation maximization algorithm can be used to jointly learn clusters while at the same time inferring the transformation associated with each input we compare this technique with other methods for filtering noisy images obtained from a scanning electron microscope clustering images from videos of faces into different categories of identification and pose and removing foreground obstructions from video we also demonstrate that the new technique is quite insensitive to initial conditions and works better than standard techniques even when the standard techniques are provided with extra data

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

image comparison by compound disjoint information with applications to perceptual visual quality assessment image registration and tracking in this paper we study normalized disjoint information as a metric for image comparison and its applications to perceptual image quality assessment image registration and video tracking disjoint information is the joint entropy of random variables excluding the mutual information this measure of statistical dependence and information redundancy satisfies more rigorous metric conditions than mutual information including self similarity minimality symmetry and triangle inequality it is applicable to two or more random variables and can be computed by vector histogramming vector parzen window density approximation and upper bound approximation involving fewer variables we show such a theoretic advantage does have implications in practice in the domain of digital image and video multiple visual features are extracted and normalized compound disjoint information is derived from a set of marginal densities of the image distributions thus enriching the vocabulary of content representation the proposed metric matching functions are applied to several domain applications to demonstrate their efficacy