a statistical decision rule with incomplete knowledge about classes abstract a statistical decision rule among m classes is presented when the a priori knowledge about classes is not complete either the number of classes is not the true one or it is not possible to obtain samples from all the possible classes the reject option proposed by chow is extended by defining an ambiguity reject option and a distance reject option these two types of reject can be defined in a parametric as well as in a non parametric way an example is given in r in order to illustrate this rule this method has been developed essentially to solve diagnostic problems

some models for stochastic frontiers with endogeneity abstract we consider mostly bayesian estimation of stochastic frontier models where one sided inefficiencies and or the idiosyncratic error term are correlated with the regressors we begin with a model where a chamberlain mundlak device is used to relate a transformation of time invariant effects to the regressors this basic model is then extended in two directions first an extra one sided error term is added to allow for time varying efficiencies second a model with an equation for instrumental variables and a more general error covariance structure is introduced to accommodate correlations between both error terms and the regressors an application of the first and second models to philippines rice data is provided

soft learning vector quantization and clustering algorithms based on non euclidean norms single norm algorithms this paper presents the development of soft clustering and learning vector quantization lvq algorithms that rely on a weighted norm to measure the distance between the feature vectors and their prototypes the development of lvq and clustering algorithms is based on the minimization of a reformulation function under the constraint that the generalized mean of the norm weights be constant according to the proposed formulation the norm weights can be computed from the data in an iterative fashion together with the prototypes an error analysis provides some guidelines for selecting the parameter involved in the definition of the generalized mean in terms of the feature variances the algorithms produced from this formulation are easy to implement and they are almost as fast as clustering algorithms relying on the euclidean norm an experimental evaluation on four data sets indicates that the proposed algorithms outperform consistently clustering algorithms relying on the euclidean norm and they are strong competitors to non euclidean algorithms which are computationally more demanding

analysis of parameter selection for gustafson kessel fuzzy clustering using jacobian matrix in fuzzy clustering the fuzzy c means fcm is the most known algorithm several extensions and variations of fcm had been proposed in the literature the first important extension to fcm was proposed by gustafson and kessel gk in the gk fuzzy clustering they considered the effect of different cluster shapes except for spherical shapes by replacing the euclidean distance of the fcm objective function with the mahalanobis distance the gk algorithm has become one of the most frequently used clustering algorithms just like fcm the fuzziness index m is a parameter in which the value will greatly influence the performance of the gk algorithm however there is no theoretical work on the parameter selection for the fuzziness index m of gk in this paper we reveal the relation between the stable fixed points of the gk algorithm and the datasets using jacobian matrix analysis and then provide a theoretical base for selecting the fuzziness index m in the gk algorithm some experimental results verify the effectiveness of our theoretical results

switching regression models and fuzzy clustering a family of objective functions called fuzzy c regression models which can be used too fit switching regression models to certain types of mixed data is presented minimization of particular objective functions in the family yields simultaneous estimates for the parameters of c regression models together with a fuzzy c partitioning of the data a general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed the approach is illustrated by two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models

general c means clustering model partitional clustering is an important part of cluster analysis based on various theories numerous clustering algorithms have been developed and new clustering algorithms continue to appear in the literature it is known that occam s razor plays a pivotal role in data based models and partitional clustering is categorized as a data based model however no relation had previously been discovered between occam s razor and partitional clustering as we discuss in this paper the three main contributions of this paper can be summarized as follows 1 according to a novel definition of the mean a unifying generative framework for partitional clustering algorithms called a general c means clustering model gcm is presented and studied and 2 based on the local optimality test of the gcm the connection between occam s razor and partitional clustering is established for the first time as its application a comprehensive review of the existing objective function based clustering algorithms is presented based on gcm 3 under a common assumption about partitional clustering a theoretical guide for devising and implementing clustering algorithm is discovered these conclusions are verified by numerical experimental results

an axiomatic approach to soft learning vector quantization and clustering this paper presents an axiomatic approach to soft learning vector quantization lvq and clustering based on reformulation the reformulation of the fuzzy c means fcm algorithm provides the basis for reformulating entropy constrained fuzzy clustering ecfc algorithms according to the proposed approach the development of specific algorithms reduces to the selection of a generator function linear generator functions lead to the fcm and fuzzy learning vector quantization algorithms while exponential generator functions lead to ecfc and entropy constrained learning vector quantization algorithms the reformulation of lvq and clustering algorithms also provides the basis for developing uncertainty measures that can identify feature vectors equidistant from all prototypes these measures are employed by a procedure developed to make soft lvq and clustering algorithms capable of identifying outliers in the data set this procedure is evaluated by testing the algorithms generated by linear and exponential generator functions on speech data

generalized fuzzy c means clustering strategies using l sub p norm distances fuzzy c means fcm is a useful clustering technique modifications of fcm using l sub 1 norm distances increase robustness to outliers object and relational data versions of fcm clustering are defined for the more general case where the l sub p norm p spl ges 1 or semi norm 0 0 in order to facilitate the empirical examination of the object data models both object and relational approaches are included in a numerical study

alternating cluster estimation a new tool for clustering and function approximation many clustering models define good clusters as extrema of objective functions optimization of these models is often done using an alternating optimization ao algorithm driven by necessary conditions for local extrema we abandon the objective function model in favor of a generalized model called alternating cluster estimation ace ace uses an alternating iteration architecture but membership and prototype functions are selected directly by the user virtually every clustering model can be realized as an instance of ace out of a large variety of possible instances of non ao models we present two examples 1 an algorithm with a dynamically changing prototype function that extracts representative data and 2 a computationally efficient algorithm with hyperconic membership functions that allows easy extraction of membership functions we illustrate these non ao instances on three problems a simple clustering of plane data where we show that creating an unmatched ace algorithm overcomes some problems of fuzzy c means fcm ao and possibilistic c means pcm ao b functional approximation by clustering on a simple artificial data set and c functional approximation on a 12 input 1 output real world data set ace models work pretty well in all three cases

possibilistic and probabilistic fuzzy clustering unification within the framework of the non extensive thermostatistics fuzzy clustering algorithms are becoming the major technique in cluster analysis in this paper we consider the fuzzy clustering based on objective functions they can be divided into two categories possibilistic and probabilistic approaches leading to two different function families depending on the conditions required to state that fuzzy clusters are a fuzzy c partition of the input data recently we have presented in menard and eboueya fuzzy sets and systems 27 to be published an axiomatic derivation of the possibilistic and maximum entropy inference mei clustering approaches based upon an unifying principle of physics that of extreme physical information epi defined by frieden physics from fisher information a unification cambridge university press cambridge 1999 here using the same formalism we explicitly give a new criterion in order to provide a theoretical justification of the objective functions constraint terms membership functions and weighting exponent m used in the probabilistic and possibilistic fuzzy clustering moreover we propose an unified framework including the two procedures this approach is inspired by the work of frieden and plastino and plastino and miller physics a 235 577 extending the principle of extremal information in the framework of the non extensive thermostatistics then we show how with the help of epi one can propose extensions of the fcm and possibilistic algorithms

the possibilistic c means algorithm insights and recommendations recently the possibilistic c means algorithm pcm was proposed to address the drawbacks associated with the constrained memberships used in algorithms such as the fuzzy c means fcm in this issue barni et al 1996 report a difficulty they faced while applying the pcm and note that it exhibits an undesirable tendency to converge to coincidental clusters the purpose of this paper is not just to address the issues raised by barni et al but to go further and analytically examines the underlying principles of the pcm and the possibilistic approach in general we analyze the data sets used by barni et al and interpret the results reported by them in the light of our findings

a contribution to convergence theory of fuzzy c means and derivatives in this paper we revisit the convergence and optimization properties of fuzzy clustering algorithms in general and the fuzzy c means fcm algorithm in particular our investigation includes probabilistic and a slightly modified implementation of possibilistic memberships which will be discussed under a unified view we give a convergence proof for the axis parallel variant of the algorithm by gustafson and kessel that can be generalized to other algorithms more easily than in the usual approach using reformulated fuzzy clustering algorithms we apply banach s classical contraction principle and establish a relationship between saddle points and attractive fixed points for the special case of fcm we derive a sufficient condition for fixed points to be attractive allowing identification of them as local minima of the objective function excluding the possibility of a saddle point

a methodology for constructing fuzzy algorithms for learning vector quantization this paper presents a general methodology for the development of fuzzy algorithms for learning vector quantization falvq the design of specific falvq algorithms according to existing approaches reduces to the selection of the membership function assigned to the weight vectors of an lvq competitive neural network which represent the prototypes the development of a broad variety of falvq algorithms can be accomplished by selecting the form of the interference function that determines the effect of the nonwinning prototypes on the attraction between the winning prototype and the input of the network the proposed methodology provides the basis for extending the existing falvq 1 falvq 2 and falvq 3 families of algorithms this paper also introduces two quantitative measures which establish a relationship between the formulation that led to falvq algorithms and the competition between the prototypes during the learning process the proposed algorithms and competition measures are tested and evaluated using the iris data set the significance of the proposed competition measure is illustrated using falvq algorithms to perform segmentation of magnetic resonance images of the brain

adaptive fuzzy c shells clustering and detection of ellipses several generalizations of the fuzzy c shells fcs algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells an earlier generalization the adaptive fuzzy c shells afcs algorithm is examined in detail and is found to have global convergence problems when the shapes to be detected are partial new formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the afcs algorithm the resulting algorithm called the afcs u algorithm performs better for partial shapes another formulation based on the second order quadrics equation is considered these algorithms can detect ellipses and circles in 2d data they are compared with the hough transform ht based methods for ellipse detection existing ht based methods for ellipse detection are evaluated and a multistage method incorporating the good features of all the methods is used for comparison numerical examples of real image data show that the afcs algorithm requires less memory than the ht based methods and it is at least an order of magnitude faster than the ht approach

convergence of the single pass and online fuzzy c means algorithms scalable versions of the widely used fuzzy c means clustering algorithm called single pass fuzzy c means and online fuzzy c means have been recently introduced both algorithms facilitate scaling to very large numbers of examples while providing partitions that very closely approximate those one would obtain using fuzzy c means both algorithms have been successfully applied to a number of datasets most notably magnetic resonance image volumes of the human brain in this letter we show that weighting examples in the fuzzy c means algorithm does not cause a violation in its convergence proof and we provide a separate proof of convergence that holds for any dataset

unsupervised minor prototype detection using an adaptive population partitioning algorithm this paper presents a new partitioning algorithm designated as the adaptive c populations acp clustering algorithm capable of identifying natural subgroups and influential minor prototypes in an unlabeled dataset in contrast to traditional fuzzy c means clustering algorithms which partition the whole dataset equally adaptive clustering algorithms such as that presented in this study identify the natural subgroups in unlabeled datasets in this paper data points within a small dense region located at a relatively large distance from any of the major cluster centers are considered to form a minor prototype the aim of acp is to adaptively separate these isolated minor clusters from the major clusters in the dataset the study commences by introducing the mathematical model of the proposed acp algorithm and demonstrates its convergence to a stable solution the ability of acp to detect minor prototypes is confirmed via its application to the clustering of three different datasets with different sizes and characteristics

an integrated approach to fuzzy learning vector quantization and fuzzy c means clustering derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c means and fuzzy learning vector quantization these algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent a close relationship between the resulting algorithms and fuzzy c means is revealed by investigating the functionals involved it is also shown that the fuzzy c means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition

fuzzy algorithms for learning vector quantization this paper presents the development of fuzzy algorithms for learning vector quantization falvq these algorithms are derived by minimizing the weighted sum of the squared euclidean distances between an input vector which represents a feature vector and the weight vectors of a competitive learning vector quantization lvq network which represent the prototypes this formulation leads to competitive algorithms which allow each input vector to attract all prototypes the strength of attraction between each input and the prototypes is determined by a set of membership functions which can be selected on the basis of specific criteria a gradient descent based learning rule is derived for a general class of admissible membership functions which satisfy certain properties the falvq 1 falvq 2 and falvq 3 families of algorithms are developed by selecting admissible membership functions with different properties the proposed algorithms are tested and evaluated using the iris data set the efficiency of the proposed algorithms is also illustrated by their use in codebook design required for image compression based on vector quantization

generalized fuzzy c shells clustering and detection of circular and elliptical boundaries abstract the fuzzy c shells fcs algorithm and its adaptive generalization called the adaptive fuzzy c shells afcs algorithm are considered for detection of curved boundaries specifically circular and elliptical the fcs algorithms utilize hyper spherical shells as cluster prototypes thus in two dimensions the prototypes are circles the afcs algorithms consider hyper ellipsoidal shells as prototypes hence the ability to characterize elliptical boundaries the generalization is achieved by allowing the distances to be measured through a norm inducing matrix that is symmetric positive definite each cluster is allowed to have a different matrix which is made a variable of optimization the ability of the algorithms to detect circular and elliptical boundaries in two dimensional data is illustrated through several examples

extreme physical information and objective function in fuzzy clustering fuzzy clustering algorithms have been widely studied and applied in a variety of areas they become the major techniques in cluster analysis in this paper we focus on objective function models whose aim is to assign the data to clusters so that a given objective function is optimized we propose a new approach in fuzzy clustering and show how it can be used to obtain a systematic method deriving objective functions this approach is based on a unifying principle of physics that of extreme physical information epi defined by frieden physics from fisher information a unification 1999 the information in question is the trace of the fisher information matrix for the estimation procedure this information is shown to be a physical measure of disorder we use the epi approach for finding the effective and minimal constraint terms in objective functions with the proposed approach we justify the constraint terms defined a priori in the fuzzy c means fcm algorithm and possibilistic and maximum entropy inference approaches indeed these algorithms by contrast offer no such systematic method of finding its constraints moreover in this context the epi approach derives the reason for the extremization of objective functions the resulting formulae have a clearer physical meaning than those obtained by means of classical algorithms the updated equations of our algorithm are identical to those of the possibilistic mei and fcm with regularization approaches

global optimization in clustering using hyperbolic cross points erich novak and klaus ritter developed in 1996 a global optimization algorithm that uses hyperbolic cross points hcps in this paper we develop a hybrid algorithm for clustering called cmhcp that uses a modified version of this hcp algorithm for global search and the alternating optimization for local search the program has been tested extensively with very promising results and high efficiency this provides a nice addition to the arsenal of global optimization in clustering in the process we also analyze the smoothness of some reformulated objective functions

endogeneity in stochastic frontier models abstract stochastic frontier models are typically estimated by maximum likelihood mle or corrected ordinary least squares the consistency of either estimator depends on exogeneity of the explanatory variables inputs in the production frontier setting we will investigate the case that one or more of the inputs is endogenous in the simultaneous equation sense of endogeneity that is we worry that there is correlation between the inputs and statistical noise or inefficiency in a standard regression setting simultaneity is handled by a number of procedures that are numerically or asymptotically equivalent these include 2sls using the residual from the reduced form equations for the endogenous variables as a control function and mle of the system that contains the equation of interest plus the unrestricted reduced form equations for the endogenous variables liml we will consider modifications of these standard procedures for the stochastic frontier setting the paper is mostly a survey and combination of existing results from the stochastic frontier literature and the classic simultaneous equations literature but it also contains some new results

fuzzy clustering and switching regression models using ambiguity and distance rejects abstract this paper examines how reject options can be used in performing fuzzy clustering and switching regression models we define an objective function in which reject options are introduced to optimization of certain clustering models this approach can be directly applied to any clustering model which can be represented as a functional dependent upon a set of cluster centers the approach can be further generalized for models that require parameters other than the cluster centers two types of reject have been included 1 the ambiguity reject which concerns patterns lying near the cluster boundaries or in the case of switching regression problems the data points which fit several models equally well 2 the distance or error reject dealing with patterns that are far away from all the clusters clustering and fuzzy c regression algorithms such as fcm fuzzy c means and fcrm fuzzy c regression models which use calculus based optimization methods suffer from several drawbacks they are very sensitive to the presence of noise moreover the memberships are relative numbers the membership of a point in a cluster depends on the membership of the point in all other clusters so the cluster centers or estimates for the parameters are poor this can be a serious problem in situations where one wishes to generate membership functions from training data this paper provides answers to these problems to avoid the memberships to be spread across the clusters and to allow the distinction between equally likely and unknown we define partial ambiguity rejects which introduce a discounting process between the classical fcm or fcrm membership functions to improve the performance of our algorithm in the presence of noise we use an amorphous noise cluster defined in demko et al actes des sixiemes rencontres del la societe francophone de classification montpellier france september 1998 to compute these rejects we propose an extension of fcrm algorithm hathaway and bezdek ieee trans fuzzy systems 1 3 1993 195 203 this algorithm is called the fuzzy c 2 regression model fc 2rm preliminary computational experiences on the developed algorithm are encouraging and compare favorably with results from other methods as fcrm and afc algorithms on the same data sets

stabilizability of linear systems with uncertain gains abstract the problem is considered of stabilizing a linear time invariant plant by means of a linear time invariant feed back controller some of the gains of the plant are uncertain it is proved that robust stabilization is possible if and only if every unstable pole of the nominal plant has maximum degree

validity guided re clustering with applications to image segmentation when clustering algorithms are applied to image segmentation the goal is to solve a classification problem however these algorithms do not directly optimize classification duality as a result they are susceptible to two problems 1 the criterion they optimize may not be a good estimator of true classification quality and 2 they often admit many suboptimal solutions this paper introduces an algorithm that uses cluster validity to mitigate problems 1 and 2 the validity guided re clustering vgc algorithm uses cluster validity information to guide a fuzzy re clustering process toward better solutions it starts with a partition generated by a soft or fuzzy clustering algorithm then it iteratively alters the partition by applying novel split and merge operations to the clusters partition modifications that result in improved partition validity are retained vgc is tested on both synthetic and real world data for magnetic resonance image mri segmentation evaluations by radiologists show that vgc outperforms the unsupervised fuzzy c means algorithm and vgc s performance approaches that of the supervised k nearest neighbors algorithm

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators this paper presents the development and investigates the properties of ordered weighted learning vector quantization lvq and clustering algorithms these algorithms are developed by using gradient descent to minimize reformulation functions based on aggregation operators an axiomatic approach provides conditions for selecting aggregation operators that lead to admissible reformulation functions minimization of admissible reformulation functions based on ordered weighted aggregation operators produces a family of soft lvq and clustering algorithms which includes fuzzy lvq and clustering algorithms as special cases the proposed lvq and clustering algorithms are used to perform segmentation of magnetic resonance mr images of the brain the diagnostic value of the segmented mr images provides the basis for evaluating a variety of ordered weighted lvq and clustering algorithms

a study of some fuzzy cluster validity indices genetic clustering and application to pixel classification in this article the effectiveness of variable string length genetic algorithm along with a recently developed fuzzy cluster validity index pbmf has been demonstrated for clustering a data set into an unknown number of clusters the flexibility of a variable string length genetic algorithm vga is utilized in conjunction with the fuzzy indices to determine the number of clusters present in a data set as well as a good fuzzy partition of the data for that number of clusters a comparative study has been performed for different validity indices namely pbmf xb pe and pc the results of the fuzzy vga algorithm are compared with those obtained by the well known fcm algorithm which is applicable only when the number of clusters is fixed a priori moreover another genetic clustering scheme that also requires fixing the value of the number of clusters is implemented the effectiveness of the pbmf index as the optimization criterion along with a genetic fuzzy partitioning technique is demonstrated on a number of artificial and real data sets including a remote sensing image of the city of kolkata

reducing the time complexity of the fuzzy c means algorithm in this paper we present an efficient implementation of the fuzzy c means clustering algorithm the original algorithm alternates between estimating centers of the clusters and the fuzzy membership of the data points the size of the membership matrix is on the order of the original data set a prohibitive size if this technique is to be applied to very large data sets with many clusters our implementation eliminates the storage of this data structure by combining the two updates into a single update of the cluster centers this change significantly affects the asymptotic runtime as the new algorithm is linear with respect to the number of clusters while the original is quadratic elimination of the membership matrix also reduces the overhead associated with repeatedly accessing a large data structure empirical evidence is presented to quantify the savings achieved by this new method

a time varying true individual effects model with endogenous regressors abstract we propose a fairly general individual effects stochastic frontier model which allows both heterogeneity and inefficiency to change over time moreover our model handles the endogeneity problems if either at least one of the regressors or one sided error term is correlated with the two sided error term our monte carlo experiments show that our estimator performs well we employed our methodology to the us banking data and found a negative relationship between return on revenue and cost efficiency estimators ignoring time varying heterogeneity or endogeneity did not perform well and gave very different estimates compared to our estimator

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

fuzzy order statistics and their application to fuzzy clustering the median and the median absolute deviation mad are robust statistics based on order statistics order statistics are extended to fuzzy sets to define a fuzzy median and a fuzzy mad the fuzzy c means fcm clustering algorithm is defined for any p norm pfcm including the l sub 1 norm 1fcm the 1fcm clustering algorithm is implemented via the alternating optimization ao method and the clustering centers are shown to be the fuzzy median the resulting ao 1fcm clustering algorithm is called the fuzzy c medians fcmed clustering algorithm an example illustrates the robustness of the fcmed

relational duals of cluster validity functions for the c means family clustering aims to identify groups of similar objects to evaluate the results of cluster algorithms an investigator uses cluster validity indices while the theory of cluster validity is well established for vector object data little effort has been made to extend it to relationship based data as such this paper proposes a theory of reformulation for object data validity indices so that they can be used to rank the results produced by the relational means clustering algorithms more specifically we create a class of relational validity indices which is called dual relational indices that are guaranteed under certain but easily met constraints to produce the same results and hence the same cluster counts as their object data counterparts

optimization of clustering criteria by reformulation various hard fuzzy and possibilistic clustering criteria objective functions are useful as bases for a variety of pattern recognition problems at present many of these criteria have customized individual optimization algorithms because of the specialized nature of these algorithms experimentation with new and existing criteria can be very inconvenient and costly in terms of development and implementation time this paper shows how to reformulate some clustering criteria so that specialized algorithms can be replaced by general optimization routines found in commercially available software we prove that the original and reformulated versions of each criterion are fully equivalent finally two numerical examples are given to illustrate reformulation

competitive algorithms for the clustering of noisy data abstract in this paper we consider the issue of clustering when outliers exist the outlier set is defined as the complement of the data set following this concept a specially designed fuzzy membership weighted objective function is proposed and the corresponding optimal membership is derived unlike the membership of fuzzy c means the derived fuzzy membership does not reduce with the increase of the cluster number with the suitable redefinition of the distance metric we demonstrate that the objective function could be used to extract c spherical shells a hard clustering algorithm alleviating the prototype under utilization problem is also derived artificially generated data are used for comparisons

gain margin and time lag tolerance constraints applied to the stabilization problem and robust servomechanism problem definitions of gain margin tolerance and time lag tolerance for a multivariable linear time invariant system are given which correspond to a generalization of the notions of gain and phase margin of classical control system theory existence conditions are then given to solve the stabilization problem and the robust servomechanism problem with gain margin and time lag tolerance constraints in particular the following is shown for a system described in terms of a state state model 1 generically there exists a controller to stabilize an unstable m input r output system so that the resultant closed loop system possesses a nonzero gain margin if and only if min r m 1 2 for stable plants there always exists a controller to solve the robust servomechanism problem so that it has an arbitrary specified gain margin time lag tolerance constraint if and only if there exists a solution to the robust servomechanism problem for the plant a controller synthesis method is then given which solves the robust servomechanism problem so that it has a specified gain margin time lag tolerance various examples of the proposed algorithm are given to illustrate the type of results that may be obtained

rederivation of the fuzzypossibilistic clustering objective function through bayesian inference unsupervised clustering of a set of datums into homogeneous groups is a primitive operation required in many signal and image processing applications in fact different incarnations and hybrids of fuzzy c means fcm and possibilistic c means pcm have been suggested which address additional requirements such as accepting weighted sets and being robust to the presence of outliers nevertheless arriving at a general framework which is independent of the datum model and the notion of homogeneity of a particular problem class is a challenge however this process has not been followed organically and clustering algorithms are generally based on exogenous objective functions which are heuristically engineered and are believed to lead to the satisfaction of a required behavior these techniques also commonly depend on regularization coefficients which are to be set prudently by the user or through separate processes in contrast in this work we utilize bayesian inference and derive a robustified objective function for a fuzzypossibilistic clustering algorithm by assuming a generic datum model and a generic notion of cluster homogeneity we utilize this model for the purpose of cluster validity assessment as well we emphasize the epistemological importance of the theoretical basis on which the developed methodology rests at the end of this paper we present experimental results to exhibit the utilization of the developed framework in the context of four different problem classes

the fuzzy c 2 means solving the ambiguity rejection in clustering abstract in this paper we deal with the clustering problem whose goal consists of computing a partition of a family of patterns into disjoint classes the method that we propose is formulated as a constrained minimization problem whose solution depends on a fuzzy objective function in which reject options are introduced two types of rejection have been included the ambiguity rejection which concerns patterns lying near the class boundaries and the distance rejection dealing with patterns that are far away from all the classes to compute these rejections we propose an extension of the fuzzy c means fcm algorithm of bezdek pattern recognition with fuzzy objective function algorithms plenum press new york 1981 this algorithm is called the fuzzy c 2 means fc 2m these measures allow to manage uncertainty due both to imprecise and incomplete definition of the classes the advantages of our method are 1 the degree of membership to the reject classes for a pattern xk are learned in the iterative clustering problem 2 it is not necessary to compute other characteristics to determine the reject and ambiguity degrees 3 the partial ambiguity rejections introduce a discounting process between the classical fcm membership functions in order to avoid the memberships to be spread across the classes 4 the membership functions are more immune to noise and correspond more closely to the notion of compatibility preliminary computational experiences on the developed algorithm are encouraging and compared favorably with results from other methods as fcm fpcm and f c 1 m fuzzy c 1 means clustering with solely distance rejection algorithms on the same data sets the differences in the performance can be attributed to the fact that ambiguous patterns are less accounted in for the computing of the centers

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

production frontiers with cross sectional and time series variation in efficiency levels abstract in this paper we consider the efficient instrumental variables estimation of a panel data model with heterogeneity in slopes as well as intercepts using a panel of u s airlines we apply our methodology to a frontier production function with cross sectional and temporal variation in levels of technical efficiency our approach allows us to estimate time varying efficiency levels for individual firms without invoking strong distributional assumptions for technical inefficiency or random noise we do so by including in the production function a flexible function of time whose parameterization depends on the firm we also generalize the results of hausman and taylor 1981 to exploit assumptions about the uncorrelatedness of certain exogenous variables with the temporal pattern of the firm s technical inefficiency our empirical analysis of the airline industry over two periods of regulation yields believable evidence on the pattern of changes in efficiency across regulatory environments

fuzzy j means a new heuristic for fuzzy clustering abstract a fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership in order to solve it we first propose a new local search heuristic called fuzzy j means where the neighbourhood is defined by all possible centroid to pattern relocations the integer solution is then moved to a continuous one by an alternate step i e by finding centroids and membership degrees for all patterns and clusters to alleviate the difficulty of being stuck in local minima of poor value this local search is then embedded into the variable neighbourhood search metaheuristic results on five standard test problems from the literature are reported and compared with those obtained with the well known fuzzy c means heuristic it appears that solutions of substantially better quality are obtained with the proposed methods than with this former one

a spatial autoregressive stochastic frontier model for panel data with asymmetric efficiency spillovers abstract by blending seminal literature on non spatial stochastic frontier models with key contributions to spatial econometrics we develop a spatial autoregressive sar stochastic frontier for panel data the specification of the sar frontier allows efficiency to vary over time and across the cross sections efficiency is calculated from a composed error structure by assuming a half normal distribution for inefficiency the sar frontier is estimated using maximum likelihood methods taking into account the endogenous sar variable the application of the estimator to an aggregate production frontier for european countries highlights among other things the asymmetry between efficiency spillovers to and from a country

a spatial stochastic frontier model with endogenous frontier and environmental variables abstract we propose a spatial autoregressive stochastic frontier model which allows for the endogeneity in both the frontier and environmental variables i e endogeneity due to correlation of inefficiency term and two sided error term the model parameters are estimated using a single stage control function approach monte carlo simulations show that our proposed model and approach perform well in finite samples we employed our methodology to the chinese chemicals firm data and found evidence for both spatial effects and endogeneity