rough support vector regression abstract this paper describes the relationship between support vector regression svr and rough or interval patterns svr is the prediction component of the support vector techniques rough patterns are based on the notion of rough values which consist of upper and lower bounds and are used to effectively represent a range of variable values predictions of rough values in a variety of different forms within the context of interval algebra and fuzzy theory are attracting research interest an extension of svr called rough support vector regression rsvr is proposed to improve the modeling of rough patterns in particular it is argued that the upper and lower bounds should be modeled separately the proposal is shown to be a more flexible version of lower possibilistic regression model using insensitivity experimental results on the dow jones industrial average demonstrate the suggested rsvr modeling technique

blind received signal strength difference based source localization with system parameter errors the problem of passive source localization has been extensively studied due to its many applications in signal processing and wireless communications signal strength based localization methods have the advantages of low cost and simple implementation in this paper blind source localization with unknown transmit power and unknown path loss exponent is considered based on the received signal strength difference rssd a nonlinear rssd based model is formulated for systems perturbed by noise solutions obtained using conventional least squares methods suffer from significant performance degradation as they only consider errors in the data vector thus an extended total least squares etls method is developed for blind localization which considers perturbations in the system parameters as well as the constraints imposed by the relationship between the observation matrix and data vector the nonlinear and nonconvex rssd based localization problem is then transformed to an etls problem with fewer constraints this is transformed to a convex semidefinite programming sdp problem using relaxation the corresponding etls sdp method is extended to the case with an unknown path loss exponent to jointly estimate the unknown source location and path loss exponent without resorting to transmit power estimation which is sensitive to errors the mean squared error of the proposed etls method is obtained and the corresponding cramer rao lower bound crlb is derived as a performance benchmark performance results are presented that show that the rssd based etls sdp method attains the crlb for a sufficiently large signal to noise ratio snr

conservative and aggressive rough svr modeling support vector regression provides an alternative to the neural networks in modeling non linear real world patterns rough values with a lower and upper bound are needed whenever the variables under consideration cannot be represented by a single value this paper describes two approaches for the modeling of rough values with support vector regression svr one approach by attempting to ensure that the predicted high value is not greater than the upper bound and that the predicted low value is not less than the lower bound is conservative in nature on the contrary we also propose an aggressive approach seeking a predicted high which is not less than the upper bound and a predicted low which is not greater than the lower bound the proposal is shown to use e insensitivity to provide a more flexible version of lower and upper possibilistic regression models the usefulness of our work is realized by modeling the rough pattern of a stock market index and can be taken advantage of by conservative and aggressive traders

exponential parameter estimation in the presence of known components and noise in the determination of the natural modes of an electromagnetic scatterer the measured time series will contain desired information noise and quite often known transient components introduced by the excitation source or measuring equipment this paper describes a linearly constrained total least squares lctls prony method for extracting the exponential model parameters from observed transient data for such problems the tls criterion yields better parameter estimates than ls moreover the incorporation of known signal information via constraints leads to even greater improvements in performance mathematical connections between lctls prony and a tls variation of time series deflation tsd are used to derive constraints for higher order excitation poles also we use tsd concepts to derive numerically superior data transformations for lctls simulation studies involving idealized test data and synthetic scattering response data of a perfectly conducting sphere demonstrate the advantages of the method

structured least squares to improve the performance of esprit type algorithms esprit type spatial frequency estimation techniques obtain their frequency estimates from the solution of a highly structured overdetermined system of equations the so called invariance equation here the structure is defined in terms of two selection matrices applied to a matrix spanning the estimated signal subspace structured least squares sls is a new algorithm that solves the invariance equation by preserving its structure formally sls is derived as a linearized iterative solution of a nonlinear optimization problem if sls is initialized with the least squares solution of the invariance equation only one iteration i e the solution of one linear system of equations is performed to achieve a significant improvement of the estimation accuracy therefore the proposed estimation scheme that uses only one iteration of sls is not iterative in nature

inversion error condition number and approximate inverses of uncertain matrices abstract the classical condition number is a very rough measure of the effect of perturbations on the inverse of a square matrix first it assumes that the perturbation is infinitesimally small second it does not take into account the perturbation structure e g vandermonde similarly the classical notion of the inverse of a matrix neglects the possibility of large structured perturbations we define a new quantity the structured maximal inversion error that takes into account both structure and non necessarily small perturbation size when the perturbation is infinitesimal we obtain a structured condition number we introduce the notion of approximate inverse as a matrix that best approximates the inverse of a matrix with structured perturbations when the perturbation varies in a given range for a wide class of perturbation structures we show how to use convex semidefinite programming to compute bounds on the structured maximal inversion error and structured condition number and compute an approximate inverse the results are exact when the perturbation is unstructured we then obtain an analytic expression for the approximate inverse when the perturbation is unstructured and additive we recover the classical condition number the approximate inverse is the operator related to the total least squares orthogonal regression problem

structured total least squares and l2 approximation problems abstract it is shown how structured and weighted total least squares and l 2 approximation problems lead to a nonlinear generalized singular value decomposition an inverse iteration scheme to find a local minimum is proposed the emphasis of the paper is not on the convergence analysis of the algorithm rather the purpose is to illustrate its use in numerous applications in systems and control including total least squares with relative errors and or fixed elements inverse singular value problems an errors in variables variant of the kalman filter impulse response realization from noisy data h 2 model reduction h 2 system identification and calculating the largest stability radius of uncertain linear systems several numerical examples are given

constrained total least square solution for gps compass attitude determination gps compass attitude determination problem has been solved by using least square ls approach conventionally however in this problem carrier phase measurement noises affect both system matrix and observation vector and total least square tls technique which is a generalized least square method to solve an over determined set of equations whose coefficients are noisy is more appropriate for this problem by using the relationship between the carrier phase noise and the resulting baseline displacement vector error the system matrix error and the observation vector error are shown to be linear correlated and this relationship is utilized to formulate the problem as a constrained total least square ctls problem iterative technique based on newton s method is utilized to solve for the unknown initial baseline vector in the resulting nonlinear optimization problem an integrity check criterion is proposed to determine if the estimated integer ambiguities have converged to the true values simulation results show that the ctls solution converges faster and has smaller error than ls solution

possibilistic linear systems and their application to the linear regression model abstract it is the purpose of this paper to illustrate possibilistic linear systems based on possibility measure and to formulate a linear regression analysis by possibilistic linear models linear regression by a possibilistic model is called possibilistic linear regression this is a new interpretation of fuzzy linear regression and also includes a new method by which interval analysis can be done in fuzzy numbers

developing a fuzzy bicluster regression to estimate heat tolerance in plants by chlorophyll fluorescence this paper presents a straightforward and useful fuzzy regression approach to estimate heat tolerance of plants by chlorophyll fluorescence measurement the chlorophyll fluorescence measurement is an indicator of functional change of photosynthesis and is sensitive to temperature using the fluorescence temperature curves the experimenter may determine the heat tolerance tc of plants by intersections of two linear regression lines however as traditional statistical regression analysis shows the experiment may contain uncertain factors or phenomena such as leaf nature and growth environment which concludes that data may vary among individual plants and different species this research presents a fuzzy bicluster regression fbcr analysis with genetic algorithms which helps derive a fuzzy intersection set and fuzzy heat tolerance of plants in addition to the traditional statistical regression analysis a fuzzy clustering concept and simultaneously optimal determination of data clusters is also developed especially when there are nonlinear inflections in data curves due to the imperative use of linear regression models the traditional regression analysis may become unable to sufficiently model the uncertainties exhibited the fbcr analysis can resolve this problem effectively due to the nonlinear tolerance of the system even in a linear model to demonstrate the fbcr analysis it was applied to estimate the heat tolerance of five plant species the results derived appeared to be more suitable than that of the conventional method the approach may provide a useful means for the experimenters to derive more credible results from their chlorophyll fluorescence temperature data

asymmetrical interval regression using extended e svm with robust algorithm in an asymmetrical interval data set the error ranges of the upper and lower interval ends are different this situation is common in practice because of the usual presence of uncertain influences in prior crisp input and interval output regression analysis a crude symmetrical estimation is obtained and the asymmetrical character of training data cannot be depicted exactly in this paper an asymmetrical interval data analysis is proposed for the first time the two interval ends are studied independently and a set of regression models and e insensitive functions are proposed to strengthen the description of the interval ends the support vector machine svm is imported into this approach for its model free character in nonlinear regression and further extended by e insensitive functions to the extended e svm a robust algorithm is presented to eliminate the effect of outliers experiments are then presented to verify the quality of performance of the extended e svm advantages over other approaches are considered in the conclusion

generalized iterated function systems on the space l x abstract in the last decades there has been a current effort to extend the classical hutchinson theory of iterated function systems composed by contractions on a metric space x into itself to more general spaces and infinitely many mappings in this paper we consider the countable iterated function systems consisting of some generalized contractions on the product space x i into x where i is an arbitrary set of natural numbers some approximations of the attractors of the respective iterated function systems are given

a tabu harmony search based approach to fuzzy linear regression we propose an unconstrained global continuous optimization method based on tabu search and harmony search to support the design of fuzzy linear regression flr models tabu and harmony search strategies are used for diversification and intensification of flr respectively the proposed approach offers the flexibility to use any kind of an objective function based on client s requirements or requests and the nature of the dataset and then attains its minimum error moreover we elaborate on the error produced by this method and compare it with the errors resulting from the other known estimation methods to study the performance of the method three categories of datasets are considered numeric inputs symmetric fuzzy outputs symmetric fuzzy inputs symmetric fuzzy outputs and numeric inputs asymmetric fuzzy outputs through a series of experiments we demonstrate that in terms of the produced error with different model fitting measurements the proposed method outperforms or is pareto equivalent to the existing methods reported in the literature

on the equivalence of constrained total least squares and structured total least squares several extensions of the total least squares tls method that are able to calculate a structured rank deficient approximation of a data matrix have been developed the main result of this article is the demonstration of the equivalence of two of these approaches namely the constrained total least squares ctls approach and the structured total least squares stls approach we also present a numerical comparison of both methods

building confidence interval based fuzzy random regression models in real world regression analysis statistical data may be linguistically imprecise or vague given the co existence of stochastic and fuzzy uncertainty real data cannot be characterized by using only the formalism of random variables in order to address regression problems in the presence of such hybrid uncertain data fuzzy random variables are introduced in this study to serve as an integral component of regression models a new class of fuzzy regression models that is based on fuzzy random data is built and is called the confidence interval based fuzzy random regression model ci frrm first a general fuzzy regression model for fuzzy random data is introduced then using expectations and variances of fuzzy random variables sigma confidence intervals are constructed for fuzzy random input output data the ci frrm is established based on the sigma confidence intervals the proposed regression model gives rise to a nonlinear programming problem that consists of fuzzy numbers or interval numbers since sign changes in the fuzzy coefficients modify the entire programming structure of the solution process the inherent dynamic nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear programming therefore we resort to some heuristics finally an illustrative example is provided

exact maximum likelihood parameter estimation of superimposed exponential signals in noise a unified framework for the exact maximum likelihood estimation of the parameters of superimposed exponential signals in noise encompassing both the time series and the array problems is presented an exact expression for the ml criterion is derived in terms of the linear prediction polynomial of the signal and an iterative algorithm for the maximization of this criterion is presented the algorithm is equally applicable in the case of signal coherence in the array problem simulation shows the estimator to be capable of providing more accurate frequency estimates than currently existing techniques the algorithm is similar to those independently derived by kumaresan et al in addition to its practical value the present formulation is used to interpret previous methods such as prony s pisarenko s and modifications thereof

fuzzy regression analysis by support vector learning approach support vector machines svms have been very successful in pattern classification and function approximation problems for crisp data in this paper we incorporate the concept of fuzzy set theory into the support vector regression machine the parameters to be estimated in the svm regression such as the components within the weight vector and the bias term are set to be the fuzzy numbers this integration preserves the benefits of svm regression model and fuzzy regression model and has been attempted to treat fuzzy nonlinear regression analysis in contrast to previous fuzzy nonlinear regression models the proposed algorithm is a model free method in the sense that we do not have to assume the underlying model function by using different kernel functions we can construct different learning machines with arbitrary types of nonlinear regression functions moreover the proposed method can achieve automatic accuracy control in the fuzzy regression analysis task the upper bound on number of errors is controlled by the user predefined parameters experimental results are then presented that indicate the performance of the proposed approach

a note on constrained total least squares estimation abstract it is shown here how similarly to the unconstrained case the constrained total least squares estimate ctlse can be generated by solving a certain sequence of eigenvalue problems iteratively for this the normal matrix from the constrained standard least squares approach has to be suitably augmented by one row and one column further modification of the augmented row and column allows the treatment of fiducial constraints for which the rhs vector is affected by random errors but not the constraining matrix itself

a fast algorithm for maximum likelihood estimation of harmonic chirp parameters the analysis of approximately periodic signals is an important element in numerous applications one generalization of standard periodic signals often occurring in practice is harmonic chirp signals where the instantaneous frequency increases decreases linearly as a function of time a statistically efficient estimator for extracting the parameters of the harmonic chirp model in additive white gaussian noise is the maximum likelihood ml estimator which recently has been demonstrated to be robust to noise and accurate even when the model order is unknown the main drawback of the ml estimator is that only very computationally demanding algorithms for computing an estimate are known in this paper we give an algorithm for computing an estimate to the ml estimator for a number of candidate model orders with a much lower computational complexity than previously reported in the literature the lower computational complexity is achieved by exploiting recursive matrix structures including a block toeplitz plus hankel structure the fast fourier transform and using a two step approach composed of a grid and refinement step to reduce the number of required function evaluations the proposed algorithms are assessed via monte carlo and timing studies the timing studies show that the proposed algorithm is orders of magnitude faster than a recently proposed algorithm for practical sizes of the number of harmonics and the length of the signal

fuzzy regression models using the least squares method based on the concept of distance fuzzy regression models are developed to construct the relationship between explanatory variables and responses in a fuzzy environment in order to increase the explanatory performance of the model the least squares method is applied to determine the numeric coefficients based on the concept of distance unlike most existing approaches the numeric coefficients in the proposed model can have negative values the proposed model minimizes total estimation error in terms of the sum of the average squared distance between the observed and estimated responses based on a few alpha cuts the proposed approach is not limited to triangular fuzzy numbers it can be used to carry out a large number of fuzzy observations efficiently because the model is based on traditional statistical methods comparisons with existing methods show that based on the total estimation error using the mean squared error and kim and bishu s criterion the explanatory performance of the proposed model is satisfactory

constrained maximum likelihood solution of linear equations the total least squares tls is used to solve a set of inconsistent linear equations ax spl ap y when there are errors not only in the observations y but in the modeling matrix a as well the tls seeks the least squares perturbation of both y and a that leads to a consistent set of equations when y and a have a defined structure we usually want the perturbations to also have this structure unfortunately standard tls does not generally preserve the perturbation structure so other methods are required we examine this problem using a probabilistic framework and derive an approach to determining the most probable set of perturbations given an a priori perturbation probability density function while our approach is applicable to both gaussian and non gaussian distributions we show in the uncorrelated gaussian case that our method is equivalent to several existing methods our approach is therefore more general and can be applied to a wider variety of signal processing problems

an algorithm for pole zero modeling and spectral analysis an explicit connection between fitting exponential models and pole zero models to observed data is made the fitting problem is formulated as a constrained nonlinear minimization problem this problem is then solved using a simplified iterative algorithm the algorithm is applied to simulated data and the performance of the algorithm is compared to previous results

regularized constrained total least squares image restoration in this paper the problem of restoring an image distorted by a linear space invariant lsi point spread function psf that is not exactly known is formulated as the solution of a perturbed set of linear equations the regularized constrained total least squares rctls method is used to solve this set of equations using the diagonalization properties of the discrete fourier transform dft for circulant matrices the rctls estimate is computed in the dft domain this significantly reduces the computational cost of this approach and makes its implementation possible even for large images an error analysis of the rctls estimate based on the mean squared error mse criterion is performed to verify its superiority over the constrained total least squares ctls estimate numerical experiments for different errors in the psf are performed to test the rctls estimator objective and visual comparisons are presented with the linear minimum mean squared error lmmse and the regularized least squares rls estimator our experiments show that the rctls estimator reduces significantly ringing artifacts around edges as compared to the two other approaches

attractors of generalized ifss that are not attractors of ifss abstract mihail and miculescu introduced the notion of a generalized iterated function system gifs in short and proved that every gifs generates an attractor in our previous paper we gave this notion a more general setting in this paper we show that for any m 2 there exists a cantor subset of the plane which is an attractor of some gifs of order m but is not an attractor of a gifs of order m 1 in particular this result shows that there is a subset of the plane which is an attractor of some gifs but is not an attractor of an ifs we also give an example of a cantor set which is not an attractor of a gifs

interval regression analysis using quadratic loss support vector machine support vector machines svms have been very successful in pattern recognition and function estimation problems for crisp data this paper proposes a new method to evaluate interval linear and nonlinear regression models combining the possibility and necessity estimation formulation with the principle of quadratic loss svm this version of svm utilizes quadratic loss function unlike the traditional svm for data sets with crisp inputs and interval outputs the possibility and necessity models have been recently utilized which are based on quadratic programming approach giving more diverse spread coefficients than a linear programming one the quadratic loss svm also uses quadratic programming approach whose another advantage in interval regression analysis is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression however this is not a computationally expensive way the quadratic loss svm allows us to perform interval nonlinear regression analysis by constructing an interval linear regression function in a high dimensional feature space the proposed algorithm is a very attractive approach to modeling nonlinear interval data and is model free method in the sense that we do not have to assume the underlying model function for interval nonlinear regression model with crisp inputs and interval output experimental results are then presented which indicate the performance of this algorithm

a kernel fuzzy c means clustering based fuzzy support vector machine algorithm for classification problems with outliers or noises the support vector machine svm has provided higher performance than traditional learning machines and has been widely applied in real world classification problems and nonlinear function estimation problems unfortunately the training process of the svm is sensitive to the outliers or noises in the training set in this paper a common misunderstanding of gaussian function based kernel fuzzy clustering is corrected and a kernel fuzzy c means clustering based fuzzy svm algorithm kfcm fsvm is developed to deal with the classification problems with outliers or noises in the kfcm fsvm algorithm we first use the fcm clustering to cluster each of two classes from the training set in the high dimensional feature space the farthest pair of clusters where one cluster comes from the positive class and the other from the negative class is then searched and forms one new training set with membership degrees finally we adopt fsvm to induce the final classification results on this new training set the computational complexity of the kfcm fsvm algorithm is analyzed a set of experiments is conducted on six benchmarking datasets and four artificial datasets for testing the generalization performance of the kfcm fsvm algorithm the results indicate that the kfcm fsvm algorithm is robust for classification problems with outliers or noises

set theoretic signal restoration using an error in variables criterion the restoration of a signal degraded by a stochastic impulse response is formulated as a problem with uncertainties in both the measurements and the impulse response the method of total least squares and variants thereof are effective techniques for solving this class of problems however unlike set theoretic estimation schemes these methods do not allow the incorporation of other a priori information in the estimate in this correspondence two new sets motivated by total least squares are introduced for set theoretic estimation the convexity of these sets is established and the projection operators onto these sets are given through simulations the advantages of the new technique over conventional and older set theoretic schemes for restoration are demonstrated

interval regression by tolerance analysis approach in interval linear regression analysis we are given crisp or interval data and we are to determine appropriate interval regression parameters there are various methods for interval regression many of them possess the property that while some of the resulting interval regression parameters are very wide the other parameters are crisp this drawback is the main limiting factor for such methods and much effort has been devoted to overcoming it we propose a method motivated by tolerance analysis in linear systems our method yields intervals for regression parameters the widths of which are proportional to an in advance given vector of parameters moreover the method is computationally very cheap and provides a natural measure of quality of a model first we formulate the method for the basic model of crisp input crisp output data and then extend it to crisp input interval output and interval input interval output models for the interval valued cases we study several formulations of the solution concept possibility strong possibility weak possibility necessity here strong possibility is a new concept proposed as a natural counterpart to the remaining ones we prove that the method provides optimal interval parameters meeting centrality and proportionality requirements we also show that the method provides interval regression parameters satisfying various versions of tanaka lee s inclusion property we also derive a form of a complementarity theorem for the weak possibility and necessity solution concepts since practical problems may be affected by outlying observations we show that our approach is easily adapted to deal with them we illustrate the theory by examples

formulation and solution of structured total least norm problems for parameter estimation the total least squares tls method is a generalization of the least squares ls method for solving overdetermined sets of linear equations ax spl ap b the tls method minimizes spl par e r spl par sub f where r b a e x so that b r spl isin range a e given a spl isin c sup m spl times n with m spl ges n and b spl isin c sup m spl times 1 the most common tls algorithm is based on the singular value decomposition svd of a b however the svd based methods may not be appropriate when the matrix a has a special structure since they do not preserve the structure previously a new problem formulation known as structured total least norm stln and the algorithm for computing the stln solution have been developed the stln method preserves the special structure of a or a b and can minimize the error in the discrete l sub p norm where p 1 2 or spl infin in this paper the stln problem formulation is generalized for computing the solution of stln problems with multiple right hand sides ax spl ap b it is shown that these problems can be converted to ordinary stln problems with one right hand side in addition the method is shown to converge to the optimal solution in certain model reduction problems furthermore the application of the stln method to various parameter estimation problems is studied in which the computed correction matrix applied to a or a b keeps the same toeplitz structure as the data matrix a of a b respectively in particular the l sub 2 norm stln method is compared with the ls and tls methods in deconvolution transfer function modeling and linear prediction problems

the constrained total least squares technique and its applications to harmonic superresolution the constrained total least squares ctls method is a natural extension of tls to the case when the noise components of the coefficients are algebraically related the ctls technique is developed and some of its applications to superresolution harmonic analysis are presented the ctls problem is reduced to an unconstrained minimization problem over a small set of variables a perturbation analysis of the ctls solution is derived and from it the root mean square error rmse of the ctls solution which is valid for small noise levels is obtained in closed form the complex version of the newton method is derived and applied to determine the ctls solution it is also shown that the ctls problem is equivalent to a constrained parameter maximum likelihood problem the ctls technique is applied to estimate the frequencies of sinusoids in white noise and the angle of arrival of narrowband wavefronts at a linear uniform array in both cases the ctls method shows superior or similar accuracy to other advanced techniques

interval regression analysis by quadratic programming approach when we use linear programming in possibilistic regression analysis some coefficients tend to become crisp because of the characteristic of linear programming on the other hand a quadratic programming approach gives more diverse spread coefficients than a linear programming one therefore to overcome the crisp characteristic of linear programming we propose interval regression analysis based on a quadratic programming approach another advantage of adopting a quadratic programming approach is to be able to integrate both the property of central tendency in least squares and the possibilistic property in fuzzy regression by changing the weights of the quadratic function we can analyze the given data from different viewpoints for data with crisp inputs and interval outputs the possibility and necessity models can be considered therefore the unified quadratic programming approach obtaining the possibility and necessity regression models simultaneously is proposed even though there always exist possibility estimation models the existence of necessity estimation models is not guaranteed if we fail to assume a proper function fitting to the given data as a regression model thus we consider polynomials as regression models since any curve can be represented by the polynomial approximation using polynomials we discuss how to obtain approximation models which fit well to the given data where the measure of fitness is newly defined to gauge the similarity between the possibility and the necessity models furthermore from the obtained possibility and necessity regression models a trapezoidal fuzzy output can be constructed

a reduced support vector machine approach for interval regression analysis the support vector machine svm has been shown to be an efficient approach for a variety of classification problems it has also been widely used in pattern recognition regression and distribution estimation for separable data however there are two problems with using the svm model 1 large scale when dealing with large scale data sets the solution may be difficult to find when using svm with nonlinear kernels 2 unbalance the number of samples from one class is much larger than the number of samples from the other classes it causes the excursion of separation margin under these circumstances developing an efficient method is necessary recently the use of the reduced support vector machine rsvm was proposed as an alternative to the standard svm it has been proven more efficient than the traditional svm in processing large scaled data in this paper we introduce the principle of rsvm to evaluate interval regression analysis the main idea of the proposed method is to reduce the number of support vectors by randomly selecting a subset of samples

on a typical compact set as the attractor of generalized iterated function systems of infinite order abstract in 2013 balka and mathe showed that in uncountable polish spaces the typical compact set is not a fractal of any ifs in 2008 miculescu and mihail introduced a concept of a generalized iterated function system gifs in short a particular extension of classical ifs in which they considered families of mappings defined on finite cartesian product x m with values in x recently secelean extended these considerations to mappings defined on the space l x of all bounded sequences of elements of x endowed with supremum metric in the paper we show that in euclidean spaces a typical compact set is an attractor in sense of secelean and that in general in the polish spaces it can be perceived as selfsimilar in such sense

a locally recurrent fuzzy neural network with support vector regression for dynamic system modeling this paper proposes a new recurrent model known as the locally recurrent fuzzy neural network with support vector regression lrfnn svr that handles problems with temporal properties structurally an lrfnn svr is a five layered recurrent network the recurrent structure in an lrfnn svr comes from locally feeding the firing strength of each fuzzy rule back to itself the consequent layer in an lrfnn svr is a takagi sugeno kang t s k type consequent which is a linear function of current states regardless of system input and output delays for the structure learning a one pass clustering algorithm clusters the input training data and determines the number of network nodes in hidden layers for the parameter learning an iterative linear svr algorithm is proposed to tune free parameters in the rule consequent part and feedback loops the motivation for using svr for parameter learning is to improve the lrfnn svr generalization ability this paper demonstrates lrfnn svr capabilities by conducting simulations in dynamic system prediction and identification problems with noiseless and noisy data in addition this paper compares simulation results from the lrfnn svr with other recurrent fuzzy models

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

extended support vector interval regression networks for interval input output data in many applications it is natural to use interval data because of uncertainty existence in the measurements variability in defining terms such as the temperature during a given day description for extremely behavior such as the maximum wind speed in a given area etc in order to handle such interval data a novel approach called the interval support vector interval regression networks isvirns is proposed the isvirns is extended from our previous work the support vector interval regression networks svirns it is easy to find that svirns can handle interval output data but for input data they must be crisp in this study the hausdorff distance is employed as the distance measure of interval data and is incorporated into the kernel functions of svirns to determine the initial structure of isvirns because the proposed approach can provide a better initial structure for isvirns it can have a faster convergent speed the experimental results with real data sets show the validity of the proposed isvirns

total least squares for affinely structured matrices and the noisy realization problem structured rank deficient matrices arise in many applications in signal processing system identification and control theory the author discusses the structured total least squares stls problem which is the problem of approximating affinely structured matrices i e matrices affine in the parameters by similarly structured rank deficient ones while minimizing an l sub 2 error criterion it is shown that the optimality conditions lead to a nonlinear generalized singular value decomposition which can be solved via an algorithm that is inspired by inverse iteration next the author concentrates on the so called l sub 2 optimal noisy realization problem which is equivalent with approximating a given data sequence by the impulse response of a finite dimensional time invariant linear system of a given order this can be solved as a structured total least squares problem it is shown with some simple counter examples that classical algorithms such as the steiglitz mcbride 1965 iterative quadratic maximum likelihood and cadzow s 1988 iteration do not converge to the optimal l sub 2 solution despite misleading claims in the literature

dual possibilistic regression analysis using support vector networks abstract this study proposes a novel and efficient dual regression model for possibilistic regression analysis that incorporates the principles of support vector machine svm theory the dual regression model which comprises an upper model and a lower model approximates the observed fuzzy phenomena from the outside and inside directions respectively such that the inclusion relationship between those two models holds the proposed dual regression model better explains the inherent vagueness that exists in a given dataset it provides the outer and inner bounds for the estimated vagueness region and allows an estimation of the degree of confidence in the predicted fuzzy output using the principles for a twin support vector machine tsvm the upper and lower models are estimated by solving two smaller svm type quadratic programming problems qpps instead of a single larger qpp this strategy significantly increases the learning speed for the proposed algorithm the structural risk minimization principle of svm makes the proposed method to yield better generalization ability the kernel function method offers a model independent framework for the proposed dual regression model this paper focuses on the class of radial kernels which enables the proposed method to conquer the problem of increasing spreads the radial kernel also gives the proposed method a unified framework that allows both crisp and fuzzy inputs the experimental results verify the effectiveness and efficiency of the proposed method in comparison with previous svm based dual regression model the proposed approach significantly improves the sparsity prediction speed and training speed

on a basic multivariate eiv model with linear equality constraints abstract multivariate methods have been widely applied to many practical problems arising in sociology environmental study geology etc in this paper we propose an extension of the univariate errors in variables model with equality constraints to meet the demand for multivariate cases we name the multivariate errors in variables model with equality constraints cmeiv model here here we only consider basic cmeiv which has unique solution to solve the cmeiv model tls total least squares principle is applied and an euler lagrange based approach is adopted to convert it into a nonlinear unconstrained problem two kinds of constraints with stochastic and fixed rhs the right hand side are considered respectively the variance covariance matrices are given in first order approximation along with unbiased estimate of the variance components as well as the estimate of the unknown parameter matrix

total least squares approach for frequency estimation using linear prediction the resolution of the estimated closely spaced frequencies of the multiple sinusoids degrades as the signal to noise ratio snr of the received signal becomes low this resolution can be improved by using the total least squares tls method in solving the linear prediction lp equation this approach makes use of the singular value decomposition svd of the augmented matrix for low rank approximation to reduce the noise effect from both the observation vector and the lp data matrix simultaneously comparison is made to the principle eigenvector pe method of tufts and kumaresan both on theoretical and experimental grounds the tls algorithm exhibits superior performance over the pe method where low rank approximation is applied to the data matrix only

possibilistic linear regression with fuzzy data tolerance approach with prior information abstract we introduce the tolerance approach to the construction of fuzzy regression coefficients of a possibilistic linear regression model with fuzzy data both input and output the method is very general the only assumption is that cuts of the fuzzy data are efficiently computable we take into account possible prior restrictions of the parameters space we assume that the restrictions are given by linear and quadratic constraints the method for construction of the possibilistic regression coefficients is in a reduction of the fuzzy valued model to an interval valued model on a given cut which is further reduced to a linear time method i e running in time o n p computing with endpoints of the intervals here n is the number of observations and p is the number of regression parameters the speed of computation makes the method applicable for huge datasets unlike various approaches based on mathematical programming formulations the tolerance based construction preserves central tendency of the resulting regression coefficients in addition we prove further properties if inputs are crisp and outputs are fuzzy then the construction preserves piecewise linearity and convex shape of fuzzy numbers we derive an o n 2 p algorithm for enumeration of breakpoints of the membership function of the estimated coefficients similar results are also derived for the fuzzy input and output model we illustrate the theory for the case of triangular and asymmetric gaussian fuzzy inputs and outputs of an inflation consumption model

survey paper structured low rank approximation and its applications fitting data by a bounded complexity linear model is equivalent to low rank approximation of a matrix constructed from the data the data matrix being hankel structured is equivalent to the existence of a linear time invariant system that fits the data and the rank constraint is related to a bound on the model complexity in the special case of fitting by a static model the data matrix and its low rank approximation are unstructured we outline applications in system theory approximate realization model reduction output error and errors in variables identification signal processing harmonic retrieval sum of damped exponentials and finite impulse response modeling and computer algebra approximate common divisor algorithms based on heuristics and local optimization methods are presented generalizations of the low rank approximation problem result from different approximation criteria e g weighted norm and constraints on the data matrix e g nonnegativity related problems are rank minimization and structured pseudospectra

fast deconvolution with approximated psf by rstls with antireflective boundary conditions the problem of reconstructing signals and images from degraded ones is considered in this paper the latter problem is formulated as a linear system whose coefficient matrix models the unknown point spread function and the right hand side represents the observed image moreover the coefficient matrix is very ill conditioned requiring an additional regularization term different boundary conditions can be proposed in this paper antireflective boundary conditions are considered since both sides of the linear system have uncertainties and the coefficient matrix is highly structured the regularized structured total least squares approach seems to be the more appropriate one to compute an approximation of the true signal image with the latter approach the original problem is formulated as an highly nonconvex one and seldom can the global minimum be computed it is shown that regularized structured total least squares problems for antireflective boundary conditions can be decomposed into single variable subproblems by a discrete sine transform such subproblems are then transformed into one dimensional unimodal real valued minimization problems which can be solved globally some numerical examples show the effectiveness of the proposed approach

adaptively regularized constrained total least squares image restoration in this paper a novel algorithm for image restoration is proposed based on constrained total least squares ctls estimation that is adaptively regularized ctls arctls it is well known that in the regularized ctls rctls method selecting a proper regularization parameter is very difficult for solving this problem we take the first order partial derivative of the classic equation of rctls image restoration and do some simplification with it then we deduce an approximate formula which can be used to adaptively calculate the best regularization parameter along with the degraded image to be restored we proved that the convergence and the stability of the solution could be well satisfied the results of our experiments indicate that using this method can make an arbitrary initial parameter be an optimal one which results in a good restored image of high quality

a cumulant based adaptive technique for coherent radar detection in a mixture of k distributed clutter and gaussian disturbance in this paper we consider the problem of radar signal detection in the presence of disturbance which is assumed to be a mixture of coherent k distributed and gaussian distributed clutter besides thermal noise which is always present in the radar receiver has been considered the optimum detector is determined by thresholding an appropriate likelihood ratio test to properly operate in an interference environment of unknown correlation the optimum detector needs to adaptively estimate from the data the statistical properties of the interferences second order spectral analysis is unable to separately estimate the correlation structure of k distributed and gaussian distributed clutter sources their separate estimation can be accomplished only in higher order spectrum domain to reach this goal an adaptive algorithm based on second and higher order cumulants is proposed that removes these drawbacks and is able to operate in an environment of unknown correlation structure the performance of the adaptive processing scheme has been evaluated by means of monte carlo simulations

on generalized iterated function systems defined on l sum of a metric space abstract miculescu and mihail in 2008 introduced a concept of a generalized iterated function system gifs in short a particular extension of classical ifs instead of families of selfmaps of a metric space x they considered families of mappings defined on finite cartesian product x m it turned out that a great part of the classical hutchinson barnsley theory has natural counterpart in this gifss case recently secelean extended these considerations to mappings defined on the space x of all bounded sequences of elements of x and obtained versions of the hutchinson barnsley theorem for appropriate families of such functions in the paper we study some further aspects of secelean s setting in particular we introduce and investigate a bit more restrictive framework and we show that some problems of the theory have more natural solutions within such a case finally we present an example which shows that this extended theory of gifss gives us fractal sets that cannot be obtained by any ifss or even by any gifss

improved parameter estimates for non linear dynamical models using a bootstrap method it is known that the least squares ls class of algorithms produce unbiased estimates providing certain assumptions are met there are many practical problems however where the required assumptions are violated typical examples include non linear dynamical system identification problems where the input and output observations are affected by measurement uncertainty and possibly correlated noise this will result in biased ls estimates and the identified model will exhibit poor generalisation properties model estimation for this type of error in variables problem is investigated in this study and a new identification scheme based on a bootstrap algorithm is proposed to improve the model estimates for non linear dynamical system identification

support vector fuzzy regression machines support vector machine svm has been very successful in pattern recognition and function estimation problems in this paper we introduce the use of svm for multivariate fuzzy linear and nonlinear regression models using the basic idea underlying svm for multivariate fuzzy regressions gives computational efficiency of getting solutions

mse based regularization approach to direction estimation of coherent narrowband signals using linear prediction this paper addresses the problem of directions of arrival doas estimation of coherent narrowband signals impinging on a uniform linear array ula when the number of signals is unknown by using an overdetermined linear prediction lp model with a subarray scheme the doas of coherent signals can be estimated from the zeros of the corresponding prediction polynomial although the corrected least squares cls technique can be used to improve the accuracy of the lp parameters estimated from the noisy array data the inversion of the resulting matrix in the cls estimation is ill conditioned and then the cls estimation becomes unstable to combat this numerical instability we introduce multiple regularization parameters into the cls estimation and show that determining the number of coherent signals is closely related to the truncation of the eigenvalues an analytical expression of the mean square error mse of the estimated lp parameters is derived and it is clarified that the number of signals can be determined by comparing the optimal regularization parameters with the corresponding eigenvalues an iterative regularization algorithm is developed for estimating directions without any a priori knowledge where the number of coherent signals and the noise variance are estimated from the noise corrupted received data simultaneously