fuzzy convex set based pattern classification for analysis of mammographic microcalcifications abstract there are many different criteria for the comparative analysis of pattern classifiers they include generalization ability computational complexity and understanding of the feature space in some applications such as the medical diagnostic systems it is crucial to use reliable tools whose behavior is always predictable so that the risk of misdiagnosis is minimized in such applications the use of the popular feedforward backpropagation bp neural network algorithm can be seen as questionable this is because it is not inherent for the backpropagation method to analyze the problem s feature space during training which can sometimes result in inadequate decision surfaces a novel convex set based neuro fuzzy algorithm for classification of difficult to diagnose instances of breast cancer is described in this paper with its structural approach to feature space the new method offers rational advantages over the backpropagation algorithm the classification performance computational and structural efficiencies are analyzed and compared with that of the bp network a 20 dimensional set of difficult to diagnose mammographic microcalcifications was used to evaluate the neuro fuzzy pattern classifier nfpc and the bp methods in order to evaluate the learning ability of both methods the relative size of training sets was varied from 40 to 90 the comparative results obtained using receiver operating characteristic roc analysis show that the ability of the convex set based method to infer knowledge was better than that of backpropagation in all of the tests performed making it more suitable for use in real diagnostic systems

a kernel adaptive algorithm for quaternion valued inputs the use of quaternion data can provide benefit in applications like robotics and image recognition and particularly for performing transforms in 3 d space here we describe a kernel adaptive algorithm for quaternions a least mean square lms based method was used resulting in the derivation of the quaternion kernel lms quat klms algorithm deriving this algorithm required describing the idea of a quaternion reproducing kernel hilbert space rkhs as well as kernel functions suitable with quaternions a modified hr calculus for hilbert spaces was used to find the gradient of cost functions defined on a quaternion rkhs in addition the use of widely linear or augmented filtering is proposed to improve performance the benefit of the quat klms and widely linear forms in learning nonlinear transformations of quaternion data are illustrated with simulations

nonparametric fuzzy regression k nn and kernel smoothing techniques abstract fuzzy regression without predefined functional form or nonparametric fuzzy regression is investigated the two most basic nonparametric regression techniques in statistics namely k nearest neighbor smoothing and kernel smoothing are fuzzified and analyzed algorithms are proposed to obtain the best smoothing parameters based on the minimization of cross validation criteria

forecasting synchronizability of complex networks from data given a complex networked system whose topology and dynamical equations are unknown is it possible to foresee that a certain type of collective dynamics can potentially emerge in the system provided that only time series measurements are available we address this question by focusing on a commonly studied type of collective dynamics namely synchronization in coupled dynamical networks we demonstrate that using the compressive sensing paradigm even when the coupling strength is not uniform so that the network is effectively weighted the full topology the coupling weights and the nodal dynamical equations can all be uncovered accurately the reconstruction accuracy and data requirement are systematically analyzed in a process that includes a validation of the reconstructed eigenvalue spectrum of the underlying coupling matrix a master stability function msf the fundamental quantity determining the network synchronizability can then be calculated based on the reconstructed dynamical system the accuracy of which can be assessed as well with the coupling matrix and msf fully uncovered the emergence of synchronous dynamics in the network can be anticipated and controlled to forecast the collective dynamics on complex networks is an extremely challenging problem with significant applications in many disciplines and our work represents an initial step in this important area

design of asymptotically optimal improper constellations with hexagonal packing this paper addresses the problem of designing asymptotically optimal improper constellations with a given circularity coefficient correlation coefficient between the constellation and its complex conjugate the designed constellations are optimal in the sense that at high signal to noise ratio snr and for a large number of symbols yield the lowest probability of error under an average power constraint for additive white gaussian noise channels as the number of symbols grows the optimal constellation is the intersection of the hexagonal lattice with an ellipse whose eccentricity determines the circularity coefficient based on this asymptotic result we propose an algorithm to design finite improper constellations the proposed constellations provide significant snr gains with respect to previous improper designs which were generated through a widely linear transformation of a standard m ary quadrature amplitude modulation constellation as an application example we study the use of these improper constellations by a secondary user in an underlay cognitive radio network

reconstructing the topology of sparsely connected dynamical networks given a general physical network and measurements of node dynamics methods are proposed for reconstructing the network topology we focus on networks whose connections are sparse and where data are limited under these conditions common in many biological networks constrained optimization techniques based on the l1 vector norm are found to be superior for inference of the network connections

neural network based reliability analysis a comparative study abstract a study on the applicability of different kinds of neural networks for the probabilistic analysis of structures when the sources of randomness can be modeled as random variables is summarized the networks are employed as numerical devices for substituting the finite element code needed by monte carlo simulation the comparison comprehends two network types multi layer perceptrons and radial basis functions classifiers cost functions sum of square errors and cross entropy optimization algorithms back propagation gauss newton newton raphson sampling methods for generating the training population using uniform and actual distributions of the variables and purposes of neural network use as functional approximators and data classifiers the comparative study is performed over four examples corresponding to different types of the limit state function and structural behaviors the analysis indicates some recommended ways of employing neural networks in this field

a new approach to fuzzy regression models with application to business cycle analysis recently fuzzy regression analysis has been largely applied in the modeling of economic or financial data however those data often exhibit certain kinds of linguistic terms for instance very good a little reclining or stable in the business cycle or the growth rate of gdp etc the goal of this paper is to construct a fuzzy regression model by fuzzy parameters estimation using the fuzzy samples it deals with imprecise measurement of observed variables fuzzy least square estimation and nonparametric methods this is different from the assumptions as well as the estimation techniques of the classical analysis empirical results demonstrate that our new approach is efficient and more realistic than the traditional regression analysis

augmented performance bounds on strictly linear and widely linear estimators with complex data novel physical insights are provided into the performances of strictly linear sl and widely linear wl estimators of the generality of complex valued data both proper second order circular and improper second order noncircular this is achieved by first performing a novel complementary mean square error cmse analysis in order to quantify the degrees of improperness second order noncircularity of the sl and wl estimation errors the exact bounds on the cmse difference between the sl and wl estimators are investigated to show that only a joint consideration of the standard mse analysis and the proposed cmse analysis has enough degrees of freedom for a rigorous account of the performance of wl and sl estimators this also makes it possible to rigourously quantify the contributions to the wl performance advantage from the individual real and imaginary channels an important finding not possible to obtain by using the standard mse analysis only

fuzzy nonlinear regression with fuzzified radial basis function network a fuzzified radial basis function network frbfn is a kind of fuzzy neural network that is obtained by direct fuzzification of the well known neural model rbfn a frbfn contains fuzzy weights and can handle fuzzy in fuzzy out data this paper shows that a frbfn can also be interpreted as a kind of fuzzy expert system hence it owns the advantages of simple structure and clear physical meaning some metrics for fuzzy numbers have been extended to the metrics for n dimensional fuzzy vectors which are applicable to computations in frbfns the corresponding metric spaces for n dimensional fuzzy vectors are proved to be complete further frbfns are proved to be able to act as universal function approximators for any continuous fuzzy function defined on a compact set this paper applies the proposed frbfn to nonparametric fuzzy nonlinear regression problems for multidimensional lr type fuzzy data fuzzy nonlinear regression with frbfns can be formulated as a nonlinear mathematical programming problem two training algorithms are proposed to quickly solve the two types of problems under different criteria and constraint conditions namely the two stage and bp back propagation training algorithms simulation studies are carried out to verify the feasibility and demonstrate the advantages of the proposed approaches

complex noise analysis of dmt in this paper we consider discrete multitone dmt or baseband orthogonal frequency division multiplexing ofdm modulation and perform a detailed noise analysis which takes into account dependencies and power variance differences of real and imaginary part after the complex valued discrete fourier transform dft the derivation is based on the so called pseudocovariance matrix of a complex random vector which was introduced by neeser and massey 1993 we show that the relevant pseudocovariance matrix is not the zero matrix in general in contrast to pass band ofdm for which it can be proven under certain assumptions that all occurring pseudocovariance matrices are vanishing we show that for colored noise rotated rectangular symbol constellations are more appropriate than the common quadratic quadrature amplitude modulation qam symbol constellations with respect to capacity and symbol error probability and we derive formulas for the rotation angles and constellation sizes densities finally we extend the results to a multitransceiver multiple input multiple output mimo scenario for which we assume a very general noise model at the inputs of the receivers allowing correlations between the noise signals of different receivers this requires the introduction of pseudocross covariance matrices of complex random vectors which are the important objects together with cross covariance matrices in the mimo situation

approximate series representations of linear operations on second order stochastic processes application to simulation series representations of the more usual linear operations in weak sense on a second order stochastic process are studied the starting point of this analysis is the optimal cambanis expansion of the stochastic process considered likewise the extensions of the approximate series expansions based on the rayleigh ritz method are presented for such linear operations on the process the main advantages of these extensions are that they are computationally feasible and entail a significant reduction in the computational burden finally their applicability as a practical simulation tool is examined

on maximum linearly achievable degrees of freedom region of 2 times 2 times 2 interference network with arbitrary antenna configurations we obtain the exact maximum degrees of freedom dof region achieved by linear transceivers without symbol extensions of the 2 times 2 times 2 multiple input multiple output mimo interference network which is comprised of two sources two relays and two destinations each with arbitrary number of antennas we prove that the maximum achievable dof region for the networks under some antenna configurations coincide with the cut set bound of the networks while there is only one dof gap from the bound for the networks under other configurations which can not be bridged by linear transceivers the basic idea of the proof is to construct a two tier transceiver where the first tier decomposes the general networks to several basic networks with special configurations and the second tier achieves the maximal dof tuples for these basic networks a mechanism for constructing the second tier transceiver is proposed which is referred to as channel scaling assisted interference elimination combined with interference avoidance at sources and interference cancelation at destinations depending on the antenna configurations interference free transmission can be ensured

widely linear estimation with complex data mean square estimation of complex and normal data is not linear as in the real case but widely linear the purpose of the paper is to calculate the optimum widely linear mean square estimate and to present its main properties the advantage with respect to the linear procedure is especially analyzed

modeling temporal functions with granular regression and fuzzy rules modeling of temporal functions has been studied extensively in last few decades temporal functions or time series are found practically in the gamut of applications ranging from engineering analysis to financial and commercial transactions numerous time series models been proposed and they can be found in the relevant time series literature deterministic and stochastic models have dominated much of the research in this area nonetheless these models have their limitations and particularly specific models solve specific problem domains therefore there is no general mechanism that can address the issues of modeling of temporal functions granular information is now being used to address a few of the problems in the theory of time series this paper proposes two models that use the concepts of regression and interleaved information granules intervals and fuzzy sets to identify the structure existing in a given time series in brevity we are attempting to combine regression and fuzzy rules to model temporal systems

fuzzy nonparametric regression based on local linear smoothing technique in a great deal of literature on fuzzy regression analysis most of research has focused on some predefined parametric forms of fuzzy regression relationships especially on the fuzzy linear regression models in many practical situations it may be unrealistic to predetermine a fuzzy parametric regression relationship in this paper a fuzzy nonparametric model with crisp input and lr fuzzy output is considered and based on the distance measure for fuzzy numbers suggested by diamond p diamond fuzzy least squares information sciences 46 1988 141 157 the local linear smoothing technique in statistics with the cross validation procedure for selecting the optimal value of the smoothing parameter is fuzzified to fit this model some simulation experiments are conducted to examine the performance of the proposed method and three real world datasets are analyzed to illustrate the application of the proposed method the results demonstrate that the proposed method works quite well not only in producing satisfactory estimate of the fuzzy regression function but also in reducing the boundary effect significantly

fuzzy linear regression and its applications to forecasting in uncertain environment abstract linear regression has been used for many years in developing mathematical models for application in marketing management and sales forecasting in this paper two different sales forecasting techniques are discussed the first technique involves non fuzzy abstract methods of linear regression and econometrics a study of the international market sales of cameras done in 1968 by john scott armstrong utilized these non fuzzy forecasting techniques the second sales forecasting technique uses fuzzy linear regression introduced by h tanaka s uejima and k asai in 1980 in this paper a study of the computer and peripheral equipment sales in the united states is discussed using fuzzy linear regression moreover fuzzy linear regression is applied to forecasting in an uncertain environment finally some possible improvements and suggestions for further study are mentioned

kinematics of complex valued time series the contribution to a stationary complex valued time series at a single frequency magnitude takes the form of a random ellipse and its properties such as aspect ratio which includes rotational direction and orientation are of great interest in science a case when both the aspect ratio and orientation are fixed is found and their variability in general results from the additional influence of an orthogonal ellipse it is shown how a magnitude squared coherence coefficient controls both the relative influences of these components and the variation of both the orientation and aspect ratio of the resultant ellipse realizations of random ellipses are recovered very accurately from simulated time series the mean orientation of the random ellipse is formally derived

support vector interval regression networks for interval regression analysis in this paper the support vector interval regression networks svirns are proposed for the interval regression analysis the svirns consist of two radial basis function networks one network identifies the upper side of data interval and the other network identifies the lower side of data intervals because the support vector regression svr approach is equivalent to solving a linear constrained quadratic programming problem the number of hidden nodes and the initial values of adjustable parameters can be easily obtained since the selection of a parameter e in the svr approach may seriously affect the modeling performance a two step approach is proposed to properly select the e value after the svr approach with the selected e an initial structure of svirns can be obtained besides outliers will not significantly affect the upper and lower bound interval obtained through the proposed two step approach consequently a traditional back propagation bp learning algorithm can be used to adjust the initial structure networks of svirns under training data sets without or with outliers due to the better initial structure of svirns are obtained by the svr approach the convergence rate of svirns is faster than the conventional networks with bp learning algorithms or with robust bp learning algorithms for interval regression analysis four examples are provided to show the validity and applicability of the proposed svirns

generalized connection graph method for synchronization in asymmetrical networks we present a general framework for studying global complete synchronization in networks of dynamical systems with asymmetrical connections we extend the connection graph stability method originally developed for symmetrically coupled networks to the general asymmetrical case the principal new component of the method is the transformation of the directed connection graph into an undirected graph in our method for symmetrically coupled networks we have to choose a path between each pair of nodes the extension of the method to asymmetrical coupling consists in symmetrizing the graph and associating a weight to each path this weight involves the node unbalance of the two nodes this quantity is defined to be the difference between the sum of connection coefficients of the outgoing edges and the sum of the connection coefficients of the incoming edges to the node the synchronization condition for this symmetrized and weighted network then also guarantees synchronization in the original asymmetrical network

second order analysis of improper complex random vectors and processes we present a comprehensive treatment of the second order theory of complex random vectors and wide sense stationary wss signals the main focus is on the improper case in which the complementary covariance does not vanish accounting for the information present in the complementary covariance requires the use of widely linear transformations based on these we present the eigenanalysis of complex vectors and apply it to the problem of rank reduction through principal components we also investigate joint properties of two complex vectors by introducing canonical correlations which paves the way for a discussion of the wiener filter and its rank reduced version we link the concepts of propriety and joint propriety to eigenanalysis and canonical correlation analysis respectively our treatment is extended to wss signals in particular we give a result on the asymptotic distribution of eigenvalues and examine the connection between wss proper and analytic signals

adaptive fresh filters for compensation of cycle frequency errors this paper deals with the problem of uncertainties in the periodicities of linear almost periodically time variant laptv filters these filters are usually implemented as a set of branches each consisting of a frequency shifter followed by a linear time invariant lti filter this implementation is also known as fresh filters this paper is motivated by the fact that when there exist errors in the frequency shifts the optimum set of lti filters is obtained by canceling the outputs of the corresponding branches the purpose of this paper is to analyze the nonstationary behavior of adaptive filters in order to mitigate this problem our results show that an adaptive filter can offset the errors in the frequency shifts the reason is that the coefficients of the adaptive filter are updated so that the filter actually performs as a linear periodically time variant filter for each branch this allows to track the errors in the frequency shifts when the rate of convergence of the adaptive algorithm is suitably selected an analytical study of the convergence is presented which allows to compute the optimal rate of convergence and the mean squared error attained by the adaptive filter

scaling of noisy fluctuations in complex networks and applications to network prediction we study the collective dynamics of oscillator network systems in the presence of noise by focusing on the time averaged fluctuation of dynamical variable of interest about the mean field we discover a scaling law relating the average fluctuation to the node degree the scaling law is quite robust as it holds for a variety of network topologies and node dynamics analyses and numerical support for different types of networks and node dynamics are provided we also point out an immediate application of the scaling law predicting complex networks based on time series only and we articulate how this can be done

fuzzy regression analysis using neural networks abstract in this paper we propose simple but powerful methods for fuzzy regression analysis using neural networks since neural networks have high capability as an approximator of nonlinear mappings the proposed methods can be applied to more complex systems than the existing lp based methods first we propose learning algorithms of neural networks for determining a nonlinear interval model from the given input output patterns a nonlinear interval model whose outputs approximately include all the given patterns can be determined by two neural networks next we show two methods for deriving nonlinear fuzzy models from the interval model determined by the proposed algorithms nonlinear fuzzy models whose h level sets approximately include all the given patterns can be derived last we show an application of the proposed methods to a real problem

estimation of improper complex valued random signals in colored noise by using the hilbert space theory in this paper the problem of estimating an improper complex valued random signal in colored noise with an additive white part is addressed we tackle the problem from a mathematical perspective and emphasize the advantages of this rigorous treatment the formulation considered is very general in the sense that it permits us to estimate any functional of the signal of interest finally the superiority of the widely linear estimation with respect to the conventional estimation techniques is both theoretically and experimentally illustrated

quantum neural networks qnns inherently fuzzy feedforward neural networks this paper introduces quantum neural networks qnns a class of feedforward neural networks ffnns inherently capable of estimating the structure of a feature space in the form of fuzzy sets the hidden units of these networks develop quantized representations of the sample information provided by the training data set in various graded levels of certainty unlike other approaches attempting to merge fuzzy logic and neural networks qnns can be used in pattern classification problems without any restricting assumptions such as the availability of a priori knowledge or desired membership profile convexity of classes a limited number of classes etc experimental results presented here show that qnns are capable of recognizing structures in data a property that conventional ffnns with sigmoidal hidden units lack

fuzzy regression by fuzzy number neural networks in this paper we describe a method for nonlinear fuzzy regression using neural network models in earlier work strong assumptions were made on the form of the fuzzy number parameters symmetric triangular asymmetric triangular quadratic trapezoidal and so on our goal here is to substantially generalize both linear and nonlinear fuzzy regression using models with general fuzzy number inputs weights biases and outputs this is accomplished through a special training technique for fuzzy number neural networks the technique is demonstrated with data from an industrial quality control problem

power harmonics pattern recognition by solving fuzzy equations abstract the aim of this paper is to introduce an approach to solve equations involving fuzzy numbers by optimisation the technique is illustrated by an application in power system harmonics pattern recognition subject to the intrinsic uncertainty associated with the harmonics spectrum of different loads of the same type and the errors of the measuring equipment fuzzy approach becomes a necessity to handle such a problem a method to identify the patterns of harmonics distribution of each type of common customer load by fuzzy numbers is described a set of linear equations involving fuzzy constants and crisp variables is formulated for an electric power system furthermore power system harmonics pattern recognition by cost function optimisation is presented as a solution to the set of linear equations such analysis leads to the definition of a fuzzy logic based indicator that can truly reveal the degree of seriousness of harmonics pollution at any utilisation point of electric power the methodology described in this paper can be extended to similar problems in other areas

second order statistics of complex signals the second order statistical properties of complex signals are usually characterized by the covariance function however this is not sufficient for a complete second order description and it is necessary to introduce another moment called the relation function its properties and especially the conditions that it must satisfy are analyzed both for stationary and nonstationary signals this leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise finally this is applied to complex autoregressive signals and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration

improper signaling for symbol error rate minimization in k user interference channel the rate maximization for the k user interference channels ics has been investigated extensively in the literature however the practical problem of minimizing the error probability with given signal modulations and or data rates of the users is less studied in this paper by utilizing additional degrees of freedom from the improper signaling versus the conventional proper signaling we seek to optimize the precoding matrices for the k user single input single output siso ics to minimize pair wise error probability pep and symbol error rate ser with two proposed algorithms respectively compared with conventional proper signaling and other state of the art improper signaling designs our proposed improper signaling schemes achieve notable error rate improvement in siso ics under both the additive white gaussian noise awgn and cellular system setups with or without channel coding our study provides another viewpoint for optimizing transmissions in ics and further justifies the practical benefit of improper signaling in interference limited communication systems

improper complex valued multiple model adaptive estimation motivated by the problem of estimating the discrete and continuous states of an improper complex valued stochastic hybrid system the paper proposes a class of widely linear augmented multiple model adaptive estimation algorithms referred to as the c mmae we show that for an improper complex valued signal pseudo covariance of the innovation sequence is not zero and therefore carries useful statistical information regarding the unknown behaviour mode of the hybrid system a new bayesian law is therefore derived as a function of the pseudo covariance of the innovation sequence and used to compute the probability that a hypothesized model is in effect at a certain time we show that the c mmae which uses the new bayesian law and utilizes the complete second order statistical characterization of the complex valued innovation sequence convergences faster than its counterpart which only uses the conventional covariance of the innovation sequence in order to simplify the computational complexity we develop two circularized versions of the c mmae using a preprocessing step referred to as the circularizing filter cf the cf is incorporated to convert the improper observations innovations into the proper ones in order to reduce the computational complexity of the hypothesis testing step finally an interacting version of the c mmae referred to as c imm is developed for improper complex valued systems with markovian switching coefficients simulation results indicate that the proposed hybrid estimators provide improved performance and convergence properties over their traditional counterparts

class of widely linear complex kalman filters recently a class of widely linear augmented complex valued kalman filters kfs that make use of augmented complex statistics have been proposed for sequential state space estimation of the generality of complex signals this was achieved in the context of neural network training and has allowed for a unified treatment of both second order circular and noncircular signals that is both those with rotation invariant and rotation dependent distributions in this paper we revisit the augmented complex kf augmented complex extended kf and augmented complex unscented kf in a more general context and analyze their performances for different degrees of noncircularity of input and the state and measurement noises for rigor a theoretical bound for the performance advantage of widely linear kfs over their strictly linear counterparts is provided the analysis also addresses the duality with bivariate real valued kfs together with several issues of implementation simulations using both synthetic and real world proper and improper signals support the analysis

least squares model fitting to fuzzy vector data abstract we consider model fitting problems in which the mathematical model of an observed event is a system of equations involving model parameters and observables and in which the data are fuzzy vectors such problems naturally arise in applications when data are scarce and information is vague about distributions of variances that are contained in the observations then it may only be possible to obtain estimates of membership functions of the data a model can be fitted to such data by maximizing the membership values of the adjusted observations we achieve this by minimizing the sum of squares of the deviations of the membership values from one the optimization problem simplifies significantly if the membership functions of the fuzzy vectors belong to a class of conical functions which are defined in terms of an elliptic norm properties of these functions are discussed and a membership propagation formula derived which component wise obeys the extension principle the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares one obtains as a solution a fuzzy model parameter vector and a number of indicators which describe the quality of the fit viz the grade of compatibility between data and model their discord and dilators of model and data membership functions these new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem

a widely linear complex autoregressive process of order one we propose a simple stochastic process for modeling improper or noncircular complex valued signals the process is a natural extension of a complex valued autoregressive process extended to include a widely linear autoregressive term this process can then capture elliptical as opposed to circular stochastic oscillations in a bivariate signal the process is order one and is more parsimonious than alternative stochastic modeling approaches in the literature we provide conditions for stationarity and derive the form of the covariance and relation sequence of this model we describe how parameter estimation can be efficiently performed both in the time and frequency domain we demonstrate the practical utility of the process in capturing elliptical oscillations that are naturally present in seismic signals

a fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution in a regression analysis it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model y f x email protected however a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters when faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions this regression model has been termed the switching regression model and it is expressed with y l f l x email protected l email protected i 1 pl i here l i indicates the class number of each independent variable and p is indicative of the number of independent variables j r jang anfis adaptive network based fuzzy inference system ieee transaction on systems man and cybernetics 23 3 1993 665 685 m michel fuzzy clustering and switching regression models using ambiguity and distance rejects fuzzy sets and systems 122 2001 363 399 e q richard a new approach to estimating switching regressions journal of the american statistical association 67 338 1972 306 310 in this study adaptive networks have been used to construct a model that has been formed by gathering obtained models there are methods that suggest the class numbers of independent variables heuristically alternatively in defining the optimal class number of independent variables the use of suggested validity criterion for fuzzy clustering has been aimed in the case that independent variables have an exponential distribution an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function which is suitable for exponential distribution

development of a cost function for wastewater treatment systems with fuzzy regression abstract a fuzzy linear regression analysis is performed to study the cost function of wastewater that is developed by using a pool of data from 26 municipal wastewater treatment systems in taiwan the choice of a primary or more higher wastewater treatment process is intimately related to financial land availability effluent standards and managerial factors especially financial consideration plays an important role in the planning stage in addition cost estimation is difficult to precisely evaluate in an uncertain environment in the conventional regression model deviations between the observed values and the estimated values are supposed to be due to measurement errors here taking a different perspective these deviations are regarded as the fuzziness of the system s parameters thus these deviations are reflected in a linear function with fuzzy parameters using linear programming algorithm this fuzzy linear regression model might be very convenient and useful for finding a fuzzy structure in an evaluation system in this paper the details of the fuzzy linear regression concept and its applications to the cost function in an uncertain environment are shown and discussed

a neural fuzzy network for word information processing a neural fuzzy system learning with fuzzy training data is proposed in this study the system is able to process and learn numerical information as well as word information at first we propose a basic structure of five layered neural network for the connectionist realization of a fuzzy inference system the connectionist structure can house fuzzy logic rules and membership functions for fuzzy inference the inputs outputs and weights of the proposed network can be fuzzy numbers of any shape also they can be hybrid of fuzzy numbers and numerical numbers through the use of fuzzy singletons based on interval arithmetics a fuzzy supervised learning algorithm is developed for the proposed system it extends the normal supervised learning techniques to the learning problems where only word teaching signals are available the fuzzy supervised learning scheme can train the proposed system with desired fuzzy input output pairs an experimental system is constructed to illustrate the performance and applicability of the proposed scheme

incorporating fuzzy membership functions into the perceptron algorithm the perceptron algorithm one of the class of gradient descent techniques has been widely used in pattern recognition to determine linear decision boundaries while this algorithm is guaranteed to converge to a separating hyperplane if the data are linearly separable it exhibits erratic behavior if the data are not linearly separable fuzzy set theory is introduced into the perceptron algorithm to produce a fuzzy algorithm which ameliorates the convergence problem in the nonseparable case it is shown that the fuzzy perceptron like its crisp counterpart converges in the separable case a method of generating membership functions is developed and experimental results comparing the crisp to the fuzzy perceptron are presented

detection and estimation of improper complex random signals nonstationary complex random signals are in general improper not circularly symmetric which means that their complementary covariance is nonzero since the karhunen loeve k l expansion in its known form is only valid for proper processes we derive the improper version of this expansion it produces two sets of eigenvalues and improper observable coordinates we then use the k l expansion to solve the problems of detection and estimation of improper complex random signals in additive white gaussian noise we derive a general result comparing the performance of conventional processing which ignores complementary covariances with processing that takes these into account in particular for the detection and estimation problems considered we find that the performance gain as measured by deflection and mean squared error mse respectively can be as large as a factor of 2 in a communications example we show how this finding generalizes the result that coherent processing enjoys a 3 db gain over noncoherent processing

complex support vector machines for regression and quaternary classification the paper presents a new framework for complex support vector regression svr as well as support vector machines svm for quaternary classification the method exploits the notion of widely linear estimation to model the input out relation for complex valued data and considers two cases 1 the complex data are split into their real and imaginary parts and a typical real kernel is employed to map the complex data to a complexified feature space and 2 a pure complex kernel is used to directly map the data to the induced complex feature space the recently developed wirtinger s calculus on complex reproducing kernel hilbert spaces is employed to compute the lagrangian and derive the dual optimization problem as one of our major results we prove that any complex svm svr task is equivalent with solving two real svm svr tasks exploiting a specific real kernel which is generated by the chosen complex kernel in particular the case of pure complex kernels leads to the generation of new kernels which have not been considered before in the classification case the proposed framework inherently splits the complex space into four parts this leads naturally to solving the four class task quaternary classification instead of the typical two classes of the real svm in turn this rationale can be used in a multiclass problem as a split class scenario based on four classes as opposed to the one versus all method this can lead to significant computational savings experiments demonstrate the effectiveness of the proposed framework for regression and classification tasks that involve complex data

widely linear versus linear blind multiuser detection with subspace based channel estimation finite sample size effects in a recent paper a s cacciapuoti et al ldquofinite sample performance analysis of widely linear multiuser receivers in ds cdma systems ieee transactions on signal processing vol 56 no 4 pp 1572 1588 apr 2008 we presented the finite sample theoretical performance comparison between linear l and widely linear wl minimum output energy moe receivers for direct sequence code division multiple access ds cdma systems worked out under the assumption that the channel impulse response of the desired user is exactly known the main scope of this paper is to extend such an analysis taking into account not only autocorrelation matrix acm estimation effects but also the accuracy of subspace based blind channel estimation ce we aim to answer the two following questions which of the two estimation processes acm or ce is the main source of degradation when implementing the receivers on the basis of a finite sample size compared with the l moe one is the finite sample wl moe receiver with blind ce capable of achieving the performance gains predicted by the theory to this goal simple and easily interpretable formulas are developed for the signal to interference plus noise ratio sinr at the output of the l and wl moe receivers with blind ce when they are implemented using either the sample acm or its eigendecomposition in addition the derived formulas which are validated by simulations allow one to recognize and discuss interesting tradeoffs between the main parameters of the ds cdma system

neurofuzzy networks with nonlinear quantum learning nonlinear quantum processing allows the solution of an optimization problem by the exhaustive search on all its possible solutions hence it can replace advantageously the algorithms for learning from a training set in order to pursue this possibility in the case of neurofuzzy networks we propose in this paper to tailor their architectures to the requirements of quantum processing in particular superposition is introduced to pursue parallelism and entanglement to associate the network performance with each solution present in the superposition two aspects of the proposed method are considered in detail the binary structure of membership functions and fuzzy reasoning and the use of a particular nonlinear quantum algorithm for extracting the optimal neurofuzzy network by exhaustive search

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

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

an extension to fuzzy cognitive maps for classification and prediction fuzzy cognitive maps fcms as an illustrative causative representation of modeling and manipulation of complex systems can be used to model the dynamic behavior of the investigated systems however due to defects in expression and architecture the traditional fcms and most of their relevant extensions are not applicable to classification problems to solve this problem this paper presents an approach that directly extends the model by translating the reasoning mechanism of traditional fcms to a set of fuzzy if then rules moreover the proposed approach fully considers the contribution of the inputs to the activation of the fuzzy rules and quantifies the causalities using mutual subsethood which works in conjunction with volume defuzziflcation in a gradient descent learning framework in this manner our approach enhances the capability of the conventional fcms to automatically identify membership functions and quantify causalities despite the increase in the number of tunable parameters experimental results show that the proposed approach efficiently extends the application of the traditional fcms into classification problems while keeping the ability for prediction and approximation

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

an architecture of neural networks with interval weights and its application to fuzzy regression analysis abstract in this paper we first propose an architecture of neural networks that have interval weights and interval biases a neural network with the proposed architecture maps an input vector of real numbers to an output interval the target output is also given as an interval next we define a cost function using the interval output from the neural network and the corresponding target output a learning algorithm is derived from the cost function in a similar manner as the bp back propagation algorithm we also show two variations of the learning algorithm for the proposed architecture which lead to the inclusion relation between the interval output and the interval target last we apply the learning algorithms to fuzzy regression analysis where target outputs are given as fuzzy numbers

fuzzy nonlinear regression analysis using a random weight network modeling a fuzzy in fuzzy out system where both inputs and outputs are uncertain is of practical and theoretical importance fuzzy nonlinear regression fnr is one of the approaches used most widely to model such systems in this study we propose the use of a random weight network rwn to develop a fnr model called fnrrwn where both the inputs and outputs are triangular fuzzy numbers unlike existing fnr models based on back propagation bp and radial basis function rbf networks fnrrwn does not require iterative adjustment of the network weights and biases instead the input layer weights and hidden layer biases of fnrrwn are selected randomly the output layer weights for fnrrwn are calculated analytically based on a derived updating rule which aims to minimize the integrated squared error between cut sets that correspond to the predicted fuzzy outputs and target fuzzy outputs respectively in fnrrwn the integrated squared error is solved approximately by riemann integral theory the experimental results show that the proposed fnrrwn method can effectively approximate a fuzzy in fuzzy out system fnrrwn obtains better prediction accuracy in a lower computational time compared with existing fnr models based on bp and rbf networks

interval regression analysis using support vector networks support vector machines svms have been very successful in pattern classification and function estimation problems for crisp data in this paper the v support vector interval regression network v svirn is proposed to evaluate interval linear and nonlinear regression models for crisp input and output data as it is difficult to select an appropriate value of the insensitive tube width in e support vector regression network the proposed v svirn alleviates this problem by utilizing a new parametric insensitive loss function the proposed v svirn automatically adjusts a flexible parametric insensitive zone of arbitrary shape and minimal size to include the given data besides the proposed method can achieve automatic accuracy control in the interval regression analysis task for a priori chosen v at most a fraction v of the data points lie outside the interval model constructed by the proposed v svirn to be more precise v is an upper bound on the fraction of training errors and a lower bound on the fraction of support vectors hence the selection of v is more intuitive moreover the proposed algorithm here is a model free method in the sense that we do not have to assume the underlying model function experimental results are then presented which show the proposed v svirn is useful in practice especially when the noise is heteroscedastic that is the noise strongly depends on the input value x

possibility and necessity pattern classification using neural networks abstract we propose two learning algorithms of neural networks for two group discriminant problems from the view point of possibility and necessity one algorithm corresponds to the possibility analysis and the other to the necessity analysis the proposed algorithms are similar to the back propagation algorithm and the difference stems from a formulation of a cost function to be minimized in each algorithm each cost function of the proposed algorithms is the weighted sum of squared errors that is the sum of squared errors with different penalties when we discuss the possibility of group 1 the penalty for the squared errors relating to the patterns in group 1 is greater than that of group 2 this means that in the possibility analysis of group 1 we attach greater importance to the patterns in group 1 than to those in group 2 on the other hand when we discuss the necessity of group 1 the penalty for the squared errors relating to the patterns in group 2 is greater than that of group 1

support vector interval regression machine for crisp input and output data support vector regression svr has been very successful in function estimation problems for crisp data in this paper we propose a robust method to evaluate interval regression models for crisp input and output data combining the possibility estimation formulation integrating the property of central tendency with the principle of standard svr the proposed method is robust in the sense that outliers do not affect the resulting interval regression furthermore the proposed method is model free method since we do not have to assume the underlying model function for interval nonlinear regression model with crisp input and output in particular this method performs better and is conceptually simpler than support vector interval regression networks svirns which utilize two radial basis function networks to identify the upper and lower sides of data interval five examples are provided to show the validity and applicability of the proposed method

identification of possibilistic linear systems by quadratic membership functions of fuzzy parameters abstract we have already discussed several models of the possibilities linear regression analysis under the assumption that probabilitioes parameters in the models are non interactive i e the possibilistic distribution of parameters is defined by minimum operators in this paper quadratic membership functions as defined by a celmi s are considered to propose an identification method of interactive fuzzy parameters in possibilistic linear systems our method can be reduced to linear programming so that it is very easy to obtain the posssibilistic distribution of parameters

widely linear equalization and blind channel identification for interference contaminated multicarrier systems this work addresses the problem of designing efficient detection techniques for multicarrier transmission systems operating in the presence of narrowband interference nbi in this case conventional linear receivers such as the zero forcing zf or the minimum mean square error mmse ones usually perform poorly since they are not capable of suppressing satisfactorily the nbi to synthesize interference resistant detection algorithms we resort to widely linear wl filtering which allows one to exploit the noncircularity property of the desired signal constellation by jointly processing the received signal and its complex conjugate version in particular we synthesize new wl zf receivers for multicarrier systems which mitigate in the minimum output energy moe sense the nbi contribution at the receiver output without requiring knowledge of the nbi statistics by exploiting the noncircularity property we also propose a new subspace based blind channel identification algorithm and derive the channel identifiability condition blind identification can be performed satisfactorily also in the presence of nbi requiring only an approximate rank determination of the nbi autocorrelation matrix the performance analysis shows that the proposed moe wl zf receiver even when implemented blindly assures a substantial improvement over the conventional linear zf and mmse ones particularly when the nbi bandwidth is very small in comparison with the intercarrier spacing and the nbi is not exactly located on a subcarrier

generic behavior of master stability functions in coupled nonlinear dynamical systems master stability functions msfs are fundamental to the study of synchronization in complex dynamical systems for example for a coupled oscillator network a necessary condition for synchronization to occur is that the msf at the corresponding normalized coupling parameters be negative to understand the typical behaviors of the msf for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators we address this issue by examining systematically msfs for known chaotic oscillators our computations and analysis indicate that it is generic for msfs being negative in a finite interval of a normalized coupling parameter a general scheme is proposed to classify the typical behaviors of msfs into four categories these results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators

quantum learning for neural associative memories abstract quantum information processing in neural structures results in an exponential increase of patterns storage capacity and can explain the extensive memorization and inferencing capabilities of humans an example can be found in neural associative memories if the synaptic weights are taken to be fuzzy variables in that case the weights update is carried out with the use of a fuzzy learning algorithm which satisfies basic postulates of quantum mechanics the resulting weight matrix can be decomposed into a superposition of associative memories thus the fundamental memory patterns attractors can be mapped into different vector spaces which are related to each other via unitary rotations quantum learning increases the storage capacity of associative memories by a factor of 2 n where n is the number of neurons

robust interval regression analysis using neural networks abstract as a very important tool for dealing with both crisp data and fuzzy data fuzzy regression analysis based on interval regression analysis has become an active area of research some neural network related methods for nonlinear interval regression analysis have been proposed on the assumption that given training data are totally good data the performance of these methods will significantly worsen when the training data are spoiled by outliers in this paper we introduce the concepts of polarity and quality of the training data on the basis of which we propose two robust learning algorithms for determining a robust nonlinear interval regression model which makes a feature of a new cost function for reflecting not only the polarity of the training data but also the estimated knowledge about the quality of the training data the two robust algorithms are derived in a manner similar to the back propagation bp algorithm simulation results show that our robust algorithms outperform the existing methods remarkably in two aspects when outliers are present 1 they are robust against outliers 2 their rates of convergence are improved to some extent

widely linear alamouti receiver for the reception of real valued constellations corrupted by interferences the alamouti saic maic concept orthogonal space time block codes stbc and the alamouti scheme in particular are of particular interest in multiple input multiple output mimo systems since they achieve full spatial diversity over fading channels and are decoded from linear processing at the receiver nevertheless due to the expensive spectral resource increasing network capacity requires the development of interference cancellation ic techniques allowing several users to share the same spectral resources without impacting the transmission quality in this context several ic schemes have been developed during this last decade where each user is equipped with multiple antennas and employs stbc at transmission however these ic techniques require multiple antennas at reception which remains a challenge at the handset level due to cost and size limitations for this reason low complexity single antenna interference cancellation saic techniques currently operational in gsm handsets have been developed recently for single antenna users using real valued modulations or complex filtering of real valued modulations by using a widely linear wl filtering at reception extension to multiple antennas at reception is called multiple antenna interference cancellation maic technique the purpose of this paper is to extend the saic maic technology to users using both real valued constellations such as amplitude shift keying ask constellations and the alamouti scheme at transmission a wl minimum mean square error mmse receiver completely new for ic purposes in the context of radio communications systems using the alamouti scheme is proposed and analyzed this receiver which corresponds to the maximum likelihood ml receiver for synchronous intranetwork interferences is able to separate up to 2 n alamouti users from n antennas at reception hence saic capability for n 1

on circularity circularity is an assumption that was originally introduced for the definition of the probability distribution function of complex normal vectors however this concept can be extended in various ways for nonnormal vectors the first purpose of the paper is to introduce and compare some possible definitions of circularity from these definitions it is also possible to introduce the concept of circular signals and to study whether or not the spectral representation of stationary signals introduces circular components therefore the relationships between circularity and stationarity are analyzed in detail finally the theory of linear mean square estimation for complex signals exhibits some connections with circularity and it is shown that without this assumption the estimation theory must be reformulated

an orderwise polynomial regression procedure for fuzzy data a procedure for polynomial fit with fuzzy data is presented as in real case studies there is often dependence between modes and spreads we propose a regression polynomial model capable to take into account possible interactions between the estimated spreads and modes this method finds applications in several fields such as reliability quality control psychometrics marketing image processing etc an application to a software reliability problem is also presented

reformulated radial basis neural networks trained by gradient descent this paper presents an axiomatic approach for constructing radial basis function rbf neural networks this approach results in a broad variety of admissible rbf models including those employing gaussian rbfs the form of the rbfs is determined by a generator function new rbf models can be developed according to the proposed approach by selecting generator functions other than exponential ones which lead to gaussian rbfs this paper also proposes a supervised learning algorithm based on gradient descent for training reformulated rbf neural networks constructed using the proposed approach a sensitivity analysis of the proposed algorithm relates the properties of rbfs with the convergence of gradient descent learning experiments involving a variety of reformulated rbf networks generated by linear and exponential generator functions indicate that gradient descent learning is simple easily implementable and produces rbf networks that perform considerably better than conventional rbf models trained by existing algorithms

fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks in this paper first we explain several versions of fuzzy regression methods based on linear fuzzy models with symmetric triangular fuzzy coefficients next we point out some limitations of such fuzzy regression methods then we extend the symmetric triangular fuzzy coefficients to asymmetric triangular and trapezoidal fuzzy numbers we show that the limitations of the fuzzy regression methods with the symmetric triangular fuzzy coefficients are remedied by such extension several formulations of linear programming problems are proposed for determining asymmetric fuzzy coefficients from numerical data finally we show how fuzzified neural networks can be utilized as nonlinear fuzzy models in fuzzy regression in the fuzzified neural networks asymmetric fuzzy numbers are used as connection weights the fuzzy connection weights of the fuzzified neural networks correspond to the fuzzy coefficients of the linear fuzzy models nonlinear fuzzy regression based on the fuzzified neural networks is illustrated by computer simulations where type i and type ii membership functions are determined from numerical data

shrinkage linear and widely linear complex valued least mean squares algorithms for adaptive beamforming in this paper shrinkage linear complex valued least mean squares sl clms and shrinkage widely linear complex valued least mean squares swl clms algorithms are devised for adaptive beamforming by exploiting the relationship between the noise free a posteriori and a priori error signals the sl clms method is able to provide a variable step size to update the weight vector for the adaptive beamformer significantly enhancing the convergence speed and decreasing the steady state misadjustment on the other hand besides adopting a variable step size determined by minimizing the square of the augmented noise free a posteriori errors the swl clms approach exploits the noncircular properties of the signal of interest which considerably improves the steady state performance simulation results are presented to illustrate their superiority over the clms complex valued normalized lms variable step size recursive least squares rls algorithms and their corresponding widely linear based schemes additionally our proposed algorithms are more computationally efficient than the rls solutions though they may have a slightly slower convergence rate

complex valued filtering based on the minimization of complex error entropy in this paper we consider the training of complex valued filter based on the information theoretic method we first generalize the error entropy criterion to complex domain to present the complex error entropy criterion ceec due to the difficulty in estimating the entropy of complex valued error directly the entropy bound minimization ebm method is used to compute the upper bounds of the entropy of the complex valued error and the tightest bound selected by the ebm algorithm is used as the estimator of the complex error entropy then based on the minimization of complex error entropy mcee and the complex gradient descent approach complex valued learning algorithms for both the linear transverse filter and the nonlinear neural network are derived the algorithms are applied to complex valued linear filtering and complex valued nonlinear channel equalization to demonstrate their effectiveness and advantages

fuzzy regression wiht radial basis function network radial basis function network is used in fuzzy regression analysis without predefined functional relationship between the input and the output the proposed approach is a fuzzification of the connection weights between the hidden and the output layers this fuzzy network is trained by a hybrid learning algorithm where self organized learning is used for training the parameters of the hidden units and supervised learning is used for updating the weights between the hidden and the output layers the c mean clustering method and the k nearest neighbor heuristics are used for the self organized learning the supervised learning is carried out by solving a linear possibilistic programming problem techniques for the generalization of the network are also proposed numerical examples are used to illustrate and to test the performances of the approach

unitary events in multiple single neuron spiking activity i detection and significance it has been proposed that cortical neurons organize dynamically into functional groups cell assemblies by the temporal structure of their joint spiking activity here we describe a novel method to detect conspicuous patterns of coincident joint spike activity among simultaneously recorded single neurons the statistical significance of these unitary events of coincident joint spike activity is evaluated by the joint surprise the method is tested and calibrated on the basis of simulated stationary spike trains of independently firing neurons into which coincident joint spike events were inserted under controlled conditions the sensitivity and specificity of the method are investigated for their dependence on physiological parameters firing rate coincidence precision coincidence pattern complexity and temporal resolution of the analysis in the companion article in this issue we describe an extension of the method designed to deal with nonstationary firing rates

a unifying discussion of correlation analysis for complex random vectors the assessment of multivariate association between two complex random vectors is considered a number of correlation coefficients based on three popular correlation analysis techniques namely canonical correlation analysis multivariate linear regression and partial least squares are reviewed and connected to performance measures in signal processing and communications such as mean squared estimation error mutual information and signal to noise ratio snr for complex data there are three types of correlation coefficients which account for rotational reflectional and total i e rotational and reflectional dependencies between two random vectors these three types are defined and analyzed for different correlation coefficients and a numerical example is given it is often required to compare two complex random vectors in a lower dimensional subspace for the large class of increasing schur convex correlation coefficients it is shown that the low rank approximations of two random vectors maximizing a particular correlation coefficient are determined only by the constraints imposed on the correlation analysis technique in this context the correlation spread is defined as a normalized measure of how much of the overall correlation is contained in a low dimensional subspace

cyclic wiener filtering theory and method conventional time and space filtering of stationary random signals which amounts to forming linear combinations of time translates and space translates exploits the temporal and spatial coherence of the signals by including frequency translates as well the spectral coherence that is characteristic of cyclostationary signals can also be exploited some of the theoretical concepts underlying this generalized type of filtering called frequency shift fresh filtering are developed the theory of optimum fresh filtering which is a generalization of wiener filtering called cyclic wiener filtering is summarized and the theory is illustrated with specific examples of separating temporally and spectrally overlapping communications signals including am bpsk and qpsk the structures and performances of optimum fresh filters are presented and adaptive adjustment of the weights in these structures is discussed also specific results on the number of digital qam signals that can be separated as a function of excess bandwidth are obtained

generalized likelihood ratios for testing the properness of quaternion gaussian vectors in a recent paper the second order statistical analysis of quaternion random vectors has shown that there exist two different kinds of quaternion widely linear processing which are associated with the two main types of quaternion properness in this paper we consider the problem of determining from a finite number of independent vector observations whether a quaternion gaussian vector is proper or not specifically we derive three generalized likelihood ratio tests glrts for testing the two main kinds of quaternion properness and show that the glrts reduce to the estimation of three previously proposed quaternion improperness measures interestingly the three glrt statistics improperness measures can be interpreted as an estimate of the entropy loss due to the quaternion improperness additionally we analyze the case in which the orthogonal basis for the representation of the quaternion vector is unknown which results in the problem of estimating the principal bbc properness direction i e the pure unit quaternion minimizing the bbc improperness measure although this estimation problem is not convex we propose a technique based on successive convex approximations which can be solved in closed form finally some simulation examples illustrate the performance and practical application of the proposed tests

arma prediction of widely linear systems by using the innovations algorithm a new autoregressive moving average arma predictor for widely linear systems is presented by using the innovations algorithm and under an improper treatment the main characteristics of this predictor are its facility of implementation from a practical standpoint and a better performance with respect to the conventional predictor obtained from a proper processing

interpolation of complex stationary processes the problem of minimum mean square infinite extent interpolation for discrete time stationary complex stochastic processes is studied the interpolator consists of linear combinations of samples of the process and of their complex conjugate the expressions of the interpolator and of the approximation error are derived and various consequences are examined it is shown in particular that the approximation error may be zero while the interpolation error obtained when using only linear combinations of the samples is maximum

applying fuzzy adaptive network to fuzzy regression analysis abstract a fuzzy inference system based on the sugeno inference model is first formulated for fuzzy regression analysis this system is then represented by a fuzzy adaptive network this approach combines the power of representation of fuzzy inference system with the ability of learning of the neural network numerical examples are trained and solved to illustrate the approach the results are compared with other approaches

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

a rank reduced lmmse canceller for narrowband interference suppression in ofdm based systems we present a narrowband interference nbi canceller that suppresses spectral leakage in an orthogonal frequency division multiplexing ofdm based system caused by a narrowband nb signal we assume that the spectrum of the nb signal is within the spectrum of the ofdm signal this can be the case e g on digital subscriber lines dsl and in new unlicensed frequency bands for radio transmission the canceller makes linear minimum mean square error estimates of the spectral leakage by measuring the nbi on a few modulated or unmodulated ofdm subcarriers it uses a model of the nb signal s power spectral density as a priori information using a frequency invariant design it is possible to cancel nbi from signals that are changing their frequency location with significantly reduced complexity overhead the operational complexity of the canceller can be lowered by using the theory of optimal rank reduction and using the time bandwidth product of the nb signal analytical performance evaluations as well as monte carlo simulations show that without perfect a priori information this canceller can suppress the spectral leakage from a strong nb signal e g with equal power as the ofdm signal to well below the background noise floor for typical applications where it causes negligible signal to noise ratio and symbol error rate degradation

a frequency domain test for propriety of complex valued vector time series this paper proposes a frequency domain approach to test the hypothesis that a stationary complex valued vector time series is proper i e for testing whether the vector time series is uncorrelated with its complex conjugate if the hypothesis is rejected frequency bands causing the rejection will be identified and might usefully be related to known properties of the physical processes the test needs the associated spectral matrix that can be estimated by multitaper methods by using say k tapers standard asymptotic distributions for the test statistic are of no use since they would require k rightarrow infty but as k increases so does resolution bandwidth that causes spectral blurring in many analyses k is necessarily kept small and hence our efforts are directed at practical and accurate methodology for hypothesis testing for small k our generalized likelihood ratio statistic combined with exact cumulant matching gives very accurate rejection percentages we also prove that the statistic on which the test is based is comprised of canonical coherencies arising from our complex valued vector time series frequency specific tests are combined by using multiple hypothesis testing to give an overall test our methodology is demonstrated on ocean current data collected at different depths in the labrador sea overall this paper extends results on propriety testing for complex valued vectors to the complex valued vector time series setting

fuzzy neural networks a survey abstract in this paper a fuzzy neural network will be a layered feedforward neural net that has fuzzy signals and or fuzzy weights we survey recent results on learning algorithms and applications for fuzzy neural networks