existence of weak solutions for a hyperbolic model of chemosensitive movement a hyperbolic model for chemotaxis and chemosensitive movement in one space dimension is considered in contrast to parabolic models for chemotaxis the hyperbolic model allows us to take the dependence of the particle speed on external stimuli explicitly into account this qualitatively covers recent experiments on chemotaxis in which it has been shown that particles adapt their speed to the surrounding environment the model presented here consists of two hyperbolic differential equations of first order coupled with an elliptic equation we assume that the speed depends on the external stimulus only and not on its gradients in that case solutions with steep gradients are expected which have the interpretation of moving swarms a notion of weak solutions for this hyperbolic chemotaxis model is presented and the global existence of weak solutions is shown the proof relies on the vanishing viscosity method i e we obtain the weak solution as the limit of classical solutions of an associated parabolically regularized problem for vanishing viscosity parameter numerical simulations demonstrate phenomena like swarming behaviour and formation of steep gradients

optimality tests for the fuzzy c means algorithm abstract because of lack of convexity of the fuzzy c means fcm objective functionals the fcm algorithm may converge to a local minimizer or a saddle point in this paper we present a new scheme for testing the optimality of the fixed points of the fcm algorithm one which needs much less computation than kim et al s scheme pattern recognition 21 651 663 1988 we also point out that kim et al s scheme is partly incorrect and propose a repair of it numerical experiments are presented for several sets of data they compare kim et al s scheme the repaired scheme and our scheme

fuzzy clustering for symbolic data most of the techniques used in the literature in clustering symbolic data are based on the hierarchical methodology which utilizes the concept of agglomerative or divisive methods as the core of the algorithm the main contribution of this paper is to show how to apply the concept of fuzziness on a data set of symbolic objects and how to use this concept in formulating the clustering problem of symbolic objects as a partitioning problem finally a fuzzy symbolic c means algorithm is introduced as an application of applying and testing the proposed algorithm on real and synthetic data sets the results of the application of the new algorithm show that the new technique is quite efficient and in many respects superior to traditional methods of hierarchical nature

asymptotic normality of the posterior in relative entropy we show that the relative entropy between a posterior density formed from a smooth likelihood and prior and a limiting normal form tends to zero in the independent and identically distributed case the mode of convergence is in probability and in mean applications to code lengths in stochastic complexity and to sample size selection are discussed

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

inferential models a framework for prior free posterior probabilistic inference posterior probabilistic statistical inference without priors is an important but so far elusive goal fisher s fiducial inference dempster shafer theory of belief functions and bayesian inference with default priors are attempts to achieve this goal but to date none has given a completely satisfactory picture this article presents a new framework for probabilistic inference based on inferential models ims which not only provides data dependent probabilistic measures of uncertainty about the unknown parameter but also does so with an automatic long run frequency calibration property the key to this new approach is the identification of an unobservable auxiliary variable associated with observable data and unknown parameter and the prediction of this auxiliary variable with a random set before conditioning on data here we present a three step im construction and prove a frequency calibration property of the im s belief function under mild conditions a corresponding optimality theory is develo

a generalization of distance functions for fuzzy c means clustering with centroids of arithmetic means fuzzy c means fcm is a widely used fuzzy clustering method which allows an object to belong to two or more clusters with a membership grade between zero and one despite the considerable efforts made by the clustering community the common characteristics of distance functions suitable for fcm remain unclear to fill this crucial void in this paper we first provide a generalized definition of distance functions that fit fcm directly the goal is to provide more flexibility to fcm in the choice of distance functions while preserving the simplicity of fcm by using the centroids of arithmetic means indeed we show that any distance function that fits fcm directly can be derived by a continuously differentiable convex function and thus is an instance of the generalized point to centroid distance p2c d by definition in addition we prove that if the membership grade matrix is nondegenerate any instance of the p2c d fits fcm directly finally extensive experiments have been conducted to demonstrate that the p2c d leads to the global convergence of fcm and that the clustering performances are significantly affected by the choices of distance functions

an approach to the conditional error rate principle with nuisance parameters summary in the presence of nuisance parameters the conditional error rate principle is difficult to apply because of the dependency of the conditional error function of the preplanned test on nuisance parameters to use the conditional error rate principle with nuisance parameters we propose to search among tests that guarantee overall error control for the test that maximizes a weighted combination of the conditional error rates over possible values of the nuisance parameters we show that the optimization problem that defines such a test can be solved efficiently by existing algorithms

marginal inferential models prior free probabilistic inference on interest parameters the inferential models im framework provides prior free frequency calibrated and posterior probabilistic inference the key is the use of random sets to predict unobservable auxiliary variables connected to the observable data and unknown parameters when nuisance parameters are present a marginalization step can reduce the dimension of the auxiliary variable which in turn leads to more efficient inference for regular problems exact marginalization can be achieved and we give conditions for marginal im validity we show that our approach provides exact and efficient marginal inference in several challenging problems including a many normal means problem in nonregular problems we propose a generalized marginalization technique and prove its validity details are given for two benchmark examples namely the behrens fisher and gamma mean problems

a fast and stable well balanced scheme with hydrostatic reconstruction for shallow water flows we consider the saint venant system for shallow water flows with nonflat bottom it is a hyperbolic system of conservation laws that approximately describes various geophysical flows such as rivers coastal areas and oceans when completed with a coriolis term or granular flows when completed with friction numerical approximate solutions to this system may be generated using conservative finite volume methods which are known to properly handle shocks and contact discontinuities however in general these schemes are known to be quite inaccurate for near steady states as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions this difficulty can be overcome by using the so called well balanced schemes we describe a general strategy based on a local hydrostatic reconstruction that allows us to derive a well balanced scheme from any given numerical flux for the homogeneous problem whenever the initial solver satisfies some classical stability properties it yields a simple and fast well balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality

a well balanced flux vector splitting scheme designed for hyperbolic systems of conservation laws with source terms abstract we propose a way to construct robust numerical schemes for the computations of numerical solutions of one and two dimensional hyperbolic systems of balance laws in order to reduce the computational cost we selected the family of flux vector splitting schemes we reformulate the source terms as nonconservative products and treat them directly in the definition of the numerical fluxes by means of generalized jump relations this is applied to a 1d shallow water system with topography and to a 2d simplified model of two phase flows with damping effects numerical results and comparisons with a classical centered discretizations scheme are supplied

on parameter estimation for normal mixtures based on fuzzy clustering algorithms described here are three approaches to estimate the parameters of a mixture of normal distributions one approach is based on a modification of the expectation maximization algorithm to compute maximum likelihood estimates another makes use of the fuzzy c means clustering algorithms and the third is based on the penalized fuzzy c means clustering algorithms the accuracy and computational efficiency of algorithms of these three types to estimate parameters of normal mixtures are compared with samples drawn from univariate normal mixtures of two classes

global convergence and empirical consistency of the generalized lloyd algorithm the generalized lloyd algorithm for vector quantizer design is analyzed as a descent algorithm for nonlinear programming a broad class of convex distortion functions is considered and any input distribution that has no singular continuous part is allowed a well known convergence theorem is applied to show that iterative applications of the algorithm produce a sequence of quantizers that approaches the set of fixed point quantizers the methods of the theorem are extended to sequences of algorithms yielding results on the behavior of the algorithm when an unknown distribution is approximated by a training sequence of observations it is shown that as the length of the training sequence grows large that 1 fixed point quantizers for the training sequence approach the set of fixed point quantizers for the true distribution and 2 limiting quantizers produced by the algorithm with the training sequence distribution perform no worse than limiting quantizers produced by the algorithm with the true distribution

efficient asymptotic preserving ap schemes for some multiscale kinetic equations many kinetic models of the boltzmann equation have a diffusive scaling that leads to the navier stokes type parabolic equations as the small scaling parameter approaches zero in practical applications it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter from the rarefied kinetic regimes to the hydrodynamic diffusive regimes an earlier approach in s jin l pareschi and g toscani siam j numer anal 35 1998 pp 2405 2439 reformulates such systems into the common hyperbolic relaxation system by jin and xin for hyperbolic conservation laws used to construct the relaxation schemes and then uses a multistep time splitting method to solve the relaxation system here we observe that the combination of the two time split steps may yield hyperbolic parabolic systems that are more advantageous in both stability and efficiency for numerical computations we show that such an approach yields a class of asymptotic preserving ap schemes which are suitable for the computation of multiscale kinetic problems we use the goldstein taylor and carleman models to illustrate this approach

penalization bias reduction and default priors in logistic and related categorical and survival regressions penalization is a very general method of stabilizing or regularizing estimates which has both frequentist and bayesian rationales we consider some questions that arise when considering alternative penalties for logistic regression and related models the most widely programmed penalty appears to be the firth small sample bias reduction method albeit with small differences among implementations and the results they provide which corresponds to using the log density of the jeffreys invariant prior distribution as a penalty function the latter representation raises some serious contextual objections to the firth reduction which also apply to alternative penalties based on t distributions including cauchy priors taking simplicity of implementation and interpretation as our chief criteria we propose that the log f 1 1 prior provides a better default penalty than other proposals penalization based on more general log f priors is trivial to implement and facilitates mean squared error reduction and sensitivity analyses of penalty strength by varying the number of prior degrees of freedom we caution however against penalization of intercepts which are unduly sensitive to covariate coding and design idiosyncrasies copyright 2015 john wiley sons ltd

generalized fiducial inference for ultrahigh dimensional regression in recent years the ultrahigh dimensional linear regression problem has attracted enormous attention from the research community under the sparsity assumption most of the published work is devoted to the selection and estimation of the predictor variables with nonzero coefficients this article studies a different but fundamentally important aspect of this problem uncertainty quantification for parameter estimates and model choices to be more specific this article proposes methods for deriving a probability density function on the set of all possible models and also for constructing confidence intervals for the corresponding parameters these proposed methods are developed using the generalized fiducial methodology which is a variant of fisher s controversial fiducial idea theoretical properties of the proposed methods are studied and in particular it is shown that statistical inference based on the proposed methods will have correct asymptotic frequentist property in terms of empirical perform

upwinding of the source term at interfaces for euler equations with high friction we consider euler equations with a friction term that describe an isentropic gas flow in a porous domain more precisely we consider the transition between low and high friction regions in the high friction region the system is reduced to a parabolic equation the porous media equation in this paper we present a hyperbolic approach based on a finite volume technique to compute numerical solutions for the system in both regimes the upwind source at interfaces usi scheme that we propose satisfies the following properties firstly it preserves the nonnegativity of gas density secondly and this is the motivation the scheme is asymptotically consistent with the limit model porous media equation when the friction coefficient goes to infinity we show analytically and through numerical results that the above properties are satisfied we shall also compare results given with the use of usi hyperbolic parabolic coupling and classical centered sources schemes

stability results for a diffusion equation with functional drift approximating a chemotaxis model a hyperbolic parabolic chemotaxis system modelling aggre gation of motile cells by production of a diffusible chemoattractant is ap proximated by a scalar diffusion equation for the cell density where the drift term is an explicit functional of the current density profile we prove the unique existence and using the hopf cole transformation the local stability of an equilibrium i e a steady aggregation state we also discuss the limit ing hyperbolic case of vanishing random motility with the formation of shocks describing cell clumps 1 introduction and development of the model in this note we shall de velop and explore the behavior of a simple two speed one dimensional model which describes the motion of chemosensitive cells that is cells whose motions are influ enced by a chemical gradient dp dx where p p x t denotes the concentration of a diffusible substance produced by each cell a well known example is the mor phogenetic aggregation of slime mold ceils 5 which previously has been modelled by keller and segel 6 using a coupled system of two equations for p and the cell density n u x t the so called chemotaxis system for a recent mathematical analysis see 4 12 in most cases as in slime molds however parameter estimations reveal that the diffusion coefficient of the chemoattractant dp 10 7cm2 sec is about ten times larger than the motility of the cells du 10 8 cm2 sec compare for example 3 if also the production rate of the chemoattractant is relatively large then the quasi stationary gradient of the rapidly diffusing substance approx imately determines the chemotactic drift of the cells this finally leads to a scalar diffusion equation for the cell density u of type

stationary solutions of chemotaxis systems the keller segel model is a system of partial differential equations modelling a mutual attraction of amoebae caused by releasing a chemical substance chemotaxis this paper analyzes the stationary solutions of the system with general nonlinearities via bifurcation techniques and gives a criterion for bifurcation of stable nonhomogeneous aggregation patterns examples are discussed with various kinds of nonlinearities modelling the sensitivity of the chemotaxis response

functional uniform priors for nonlinear modeling summary this article considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function using results on how to construct uniform distributions in general metric spaces we propose a prior distribution that is uniform in the space of functional shapes of the underlying nonlinear function and then back transform to obtain a prior distribution for the original model parameters the primary application considered in this article is nonlinear regression but the idea might be of interest beyond this case for nonlinear regression the so constructed priors have the advantage that they are parametrization invariant and do not violate the likelihood principle as opposed to uniform distributions on the parameters or the jeffrey s prior respectively the utility of the proposed priors is demonstrated in the context of design and analysis of nonlinear regression modeling in clinical dose finding trials through a real data example and simulation

clustering of clusters abstract an algorithm for the clustering of existing clusters is introduced in this paper the algorithm was adopted from fuzzy c mean and modifications made to take into account the extra information i e some data samples already form clusters partition coefficients together with some other criteria are used for testing cluster validity the method was applied on chinese character recognition and an encouraging result was obtained

robust bayesian variable selection in linear models with spherically symmetric errors this paper studies bayesian variable selection in linear models with general spherically symmetric error distributions we construct the posterior odds based on a separable prior which arises as a class of mixtures of gaussian densities the posterior odds for comparing among nonnull models are shown to be independent of the error distribution if this is spherically symmetric because of this invariance we refer to our method as a robust bayesian variable selection method we demonstrate that our posterior odds have model selection consistency and that our class of prior functions are the only ones within a large class which are robust in our sense

objective bayesian analysis of spatially correlated data spatially varying phenomena are often modeled using gaussian random fields specified by their mean function and covariance function the spatial correlation structure of these models is commonly specified to be of a certain form e g spherical power exponential rational quadratic or matern with a small number of unknown parameters we consider objective bayesian analysis of such spatial models when the mean function of the gaussian random field is specified as in a linear model it is thus necessary to determine an objective or default prior distribution for the unknown mean and covariance parameters of the random field we first show that common choices of default prior distributions such as the constant prior and the independent jeffreys prior typically result in improper posterior distributions for this model next the reference prior for the model is developed and is shown to yield a proper posterior distribution a further attractive property of the reference prior is that it can be used

convergence properties of the generalized fuzzy c means clustering algorithms fuzzy c means fcm clustering algorithms have been widely used to solve clustering problems yang and yu 1 extended these to optimization procedures with respect to any probability distribution they showed that the optimal cluster centers are the fixed points of these generalized fcm clustering algorithms the convergence properties of algorithms are the important theoretical issue in this paper we present convergence properties of the generalized fcm clustering algorithms these are global convergence local convergence and its rate of convergence

maxwellian decay for well balanced approximations of a super characteristic chemotaxis model we focus on the numerical simulation of a one dimensional model of chemotaxis dynamics proposed by greenberg and alt trans amer math soc 300 1987 pp 235 258 in a bounded domain by means of a previously introduced well balanced wb and asymptotic preserving ap scheme l gosse j math anal appl 2011 we are especially interested in studying the decay onto numerical steady states for two reasons 1 conventional upwind schemes have been shown to stabilize onto spurious non maxwellian states with a very big mass flux see e g f guarguaglini et al discrete contin dyn syst ser b 12 2009 pp 39 76 and 2 the initial data lead to a dynamic which is mostly super characteristic in the sense of s jin and m katsoulakis siam j appl math 61 2000 pp 273 292 thus the stability results of gosse do not apply a reflecting boundary condition which is compatible with the well balanced character is presented a mass preservation property is proved and some results on super characteristic relaxation are recalled numerical experiments with coarse computational grids are presented in detail they illustrate the bifurcation diagrams of guarguaglini et al which relate the total initial mass of cells with the time asymptotic values of the chemoattractant substance on each side of the domain it is shown that the wb scheme stabilizes correctly onto zero mass flow rate hence maxwellian steady states which agree with the aforementioned bifurcation diagrams the evolution in time of residues is commented for every considered test case

on a class of fuzzy classification maximum likelihood procedures classification maximum likelihood cml procedure is a remarkable mixture of maximum likelihood approach to clustering this has been well documented in the book of mclachlan and basford in this paper we make the fuzzy extension of the cml procedure based on this class of fuzzy cml procedures we extend the fuzzy clustering algorithms of trauwaert kaufman and rousseeuw by adding a penalty term especially we derive a generalized type of fuzzy c means fcm clustering algorithms called the penalized fcm clustering algorithms then we create some asymptotic behaviors of these penalized fcm procedures by doing some numerical examples we find that the penalized fcm is more meaningful and effective than fcm

optimal design of radial basis function neural networks for fuzzy rule extraction in high dimensional data abstract the design of an optimal radial basis function neural network rbfnf is not a straightforward procedure in this paper we take advantage of the functional equivalence between rbfn and fuzzy inference systems to propose a novel efficient approach to rbfn design for fuzzy rule extraction the method is based on advanced fuzzy clustering techniques solutions to practical problems are proposed by combining these different solutions a general methodology is derived the efficiency of our method is demonstrated on challenging synthetic and real world data sets

bayesian duality and risk analysis on the statistical manifold of exponential family with censored data abstract information geometry has been attracted wide attentions in the past few decades this paper focuses on the bayesian duality on a statistical manifold derived from the exponential family with data from life tests based on life testing data the statistical manifold is constructed with a new cumulant generating function the bregman divergence between two parameter points is studied the dual coordinate system and dual function are obtained then the dualistic structure on the manifold is discussed the results show that the maximum likelihood estimate can be obtained by minimizing the bregman divergence induced from the dual function the bayesian analysis and prediction are investigated based on informative and non informative priors consider the gamma distribution as an example the closed form representations of the dual coordinate system and dual function are obtained a real data set is employed to illustrate the methodologies and experimental designs developed in this paper

inference from intrinsic bayes procedures under model selection and uncertainty in this article we present a fully coherent and consistent objective bayesian analysis of the linear regression model using intrinsic priors the intrinsic prior is a scaled mixture of g priors and promotes shrinkage toward the subspace defined by a base or null model while it has been established that the intrinsic prior provides consistent model selectors across a range of models the posterior distribution of the model parameters has not previously been investigated we prove that the posterior distribution of the model parameters is consistent under both model selection and model averaging when the number of regressors is fixed further we derive tractable expressions for the intrinsic posterior distribution as well as sampling algorithms for both a selected model and model averaging we compare the intrinsic prior to other mixtures of g priors and provide details on the consistency properties of modified versions of the zellner siow prior and hyper g priors supplementary materials for this arti

ncm neutrosophic c means clustering algorithm abstract in this paper a new clustering algorithm neutrosophic c means ncm is introduced for uncertain data clustering which is inspired from fuzzy c means and the neutrosophic set framework to derive such a structure a novel suitable objective function is defined and minimized and the clustering problem is formulated as a constrained minimization problem whose solution depends on the objective function in the objective function two new types of rejection have been introduced the ambiguity rejection which concerns the patterns lying near the cluster boundaries and the distance rejection dealing with patterns that are far away from all the clusters these measures are able to manage uncertainty due to imprecise and or incomplete definition of the clusters we conducted several experiments with synthetic and real data sets the results are encouraging and compared favorably with results from other methods as fcm pcm and fpcm algorithms on the same data sets finally the proposed method was applied into image segmentation algorithm the experimental results show that the proposed algorithm can be considered as a promising tool for data clustering and image processing

a well balanced scheme for the numerical processing of source terms in hyperbolic equations in a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable typical of these are gravity driven flows such as those described by the shallow water equations over a nonuniform ocean bottom 1 10 qquad h t hu x 0 text and hu t left hu 2 frac gh 2 2 right x ga x x h 0 many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper balance between the source terms and internal forces we propose here a numerical scheme adapted to a scalar conservation law that preserves this balance and that can it is hoped be extended to more general hyperbolic systems the proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported

generalized fiducial inference a review and new results abstractr a fisher the father of modern statistics proposed the idea of fiducial inference during the first half of the 20th century while his proposal led to interesting methods for quantifying uncertainty other prominent statisticians of the time did not accept fisher s approach as it became apparent that some of fisher s bold claims about the properties of fiducial distribution did not hold up for multi parameter problems beginning around the year 2000 the authors and collaborators started to reinvestigate the idea of fiducial inference and discovered that fisher s approach when properly generalized would open doors to solve many important and difficult inference problems they termed their generalization of fisher s idea as generalized fiducial inference gfi the main idea of gfi is to carefully transfer randomness from the data to the parameter space using an inverse of a data generating equation without the use of bayes theorem the resulting generalized fiducial distribution gfd can

an objective approach to prior mass functions for discrete parameter spaces we present a novel approach to constructing objective prior distributions for discrete parameter spaces these types of parameter spaces are particularly problematic as it appears that common objective procedures to design prior distributions are problem specific we propose an objective criterion based on loss functions instead of trying to define objective probabilities directly we systematically apply this criterion to a series of discrete scenarios previously considered in the literature and compare the priors the proposed approach applies to any discrete parameter space making it appealing as it does not involve different concepts according to the model supplementary materials for this article are available online

the formal definition of reference priors reference analysis produces objective bayesian inference in the sense that inferential statements depend only on the assumed model and the available data and the prior distribution used to make an inference is least informative in a certain information theoretic sense reference priors have been rigorously defined in specific contexts and heuristically defined in general but a rigorous general definition has been lacking we produce a rigorous general definition here and then show how an explicit expression for the reference prior can be obtained under very weak regularity conditions the explicit expression can be used to derive new reference priors both analytically and numerically

asymptotic preserving and well balanced schemes for the 1d cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes abstract the original well balanced wb framework of greenberg and leroux 1996 24 and gosse 2002 18 relying on non conservative nc products see lefoch and tzavaras 1999 41 is set up in order to efficiently treat the so called cattaneo model of chemotaxis in 1d see hillen and stevens 2000 29 it proceeds by concentrating the source terms onto dirac masses this allows to handle them by nc jump relations based on steady state equations which can be integrated explicitly a riemann solver is deduced and the corresponding wb godunov scheme completed with the standard hoff smoller theory see hillen and stevens 2000 29 for the diffusion reaction equation ruling the evolution of the chemoattractant concentration is studied in detail later following former results of gosse and toscani 2002 2003 21 22 a simple rewriting of the nc jump relations allows to generate another version of the same godunov scheme which is well adapted to the parabolic scaling involving a small parameter e the standard bv framework is used to study the uniform stability of this asymptotic preserving ap scheme with respect to e allows to pass to the limit and derive a simple centered discretization of the keller segel model finally results by filbet 2006 14 permit to pass to the complementary limit when the space step h is sent to zero numerical results are included to illustrate the feasibility and the efficiency of the method

asymptotic high order mass preserving schemes for a hyperbolic model of chemotaxis we introduce a new class of finite difference schemes for approximating the solutions to an initial boundary value problem on a bounded interval for a one dimensional dissipative hyperbolic system with an external source term which arises as a simple model of chemotaxis since the solutions to this problem may converge to nonconstant asymptotic states for large times standard schemes usually fail to yield a good approximation therefore we propose a new class of schemes which use an asymptotic higher order correction second and third order in our examples to balance the effects of the source term and the influence of the asymptotic solutions special care is needed to deal with boundary conditions to avoid harmful loss of mass convergence results are proved for these new schemes and several numerical tests are presented and discussed to verify the effectiveness of their behavior

quantization and the method of k means asymptotic results from the statistical theory of k means clustering are applied to problems of vector quantization the behavior of quantizers constructed from long training sequences of data is analyzed by relating it to the consistency problem for k means

local convergence of the fuzzy c means algorithms abstract much understanding has recently been gained concerning global convergence properties of the fuzzy c means fcm family of clustering algorithms these global convergence properties which hold for all iteration sequences guarantee that every fcm iteration sequence converges at least along a subsequence to a stationary point of an fcm objective function in this paper we prove a local convergence property that is a property pertaining to iteration sequences started near a solution specifically a simple result is proved which shows that whenever an fcm algorithm is started sufficiently near a minimizer of the corresponding objective function then the iteration sequence must converge to that particular minimizer the result guarantees that once captured by the local neighborhood of a minimizer the succeeding iterate sequence will not escape thus infinite oscillation of such a sequence cannot occur the rate of convergence of the sequence to such a point is also discussed

information geometry of generalized bayesian prediction using alpha divergences as loss functions in this paper the methods of information geometry are employed to investigate a generalized bayes rule for prediction taking alpha divergences as the loss functions optimality and asymptotic properties of the generalized bayesian predictive densities are considered we show that the bayesian predictive densities minimize a generalized bayes risk we also find that the asymptotic expansions of the densities are related to the coefficients of the alpha connections of a statistical manifold in addition we discuss the difference between two risk functions of the generalized bayesian predictions based on different priors finally using the non informative priors i e jeffreys and reference priors uniform prior and conjugate prior two examples are presented to illustrate the main results

3d simulations of early blood vessel formation blood vessel networks form by spontaneous aggregation of individual cells migrating toward vascularization sites vasculogenesis a successful theoretical model of two dimensional experimental vasculogenesis has been recently proposed showing the relevance of percolation concepts and of cell cross talk chemotactic autocrine loop to the understanding of this self aggregation process here we study the natural 3d extension of the computational model proposed earlier which is relevant for the investigation of the genuinely three dimensional process of vasculogenesis in vertebrate embryos the computational model is based on a multidimensional burgers equation coupled with a reaction diffusion equation for a chemotactic factor and a mass conservation law the numerical approximation of the computational model is obtained by high order relaxed schemes space and time discretization are performed by using tvd schemes and respectively imex schemes due to the computational costs of realistic simulations we have implemented the numerical algorithm on a cluster for parallel computation starting from initial conditions mimicking the experimentally observed ones numerical simulations produce network like structures qualitatively similar to those observed in the early stages of in vivo vasculogenesis we develop the computation of critical percolative indices as a robust measure of the network geometry as a first step towards the comparison of computational and experimental data

space localization and well balanced schemes for discrete kinetic models in diffusive regimes we derive and study well balanced schemes for quasi monotone discrete kinetic models by means of a rigorous localization procedure we reformulate the collision terms as nonconservative products and solve the resulting riemann problem whose solution is self similar the construction of an asymptotic preserving ap godunov scheme is straightforward and various compactness properties are established within different scalings finally some computational results are supplied to show that this approach is realizable and efficient on concrete 2 2 models

asymptotic inference for mixture models by using data dependent priors for certain mixture models improper priors are undesirable because they yield improper posteriors however proper priors may be undesirable because they require subjective input we propose the use of specially chosen data dependent priors we show that in some cases data dependent priors are the only priors that produce intervals with second order correct frequentist coverage the resulting posterior also has another interpretation it is the product of a fixed prior and a pseudolikelihood

a micro macro decomposition based asymptotic preserving scheme for the multispecies boltzmann equation in this paper we extend the micro macro decomposition based asymptotic preserving scheme developed by bennoune lemou and mieussens j comput phys 227 2008 pp 3781 3803 for the single species boltzmann equation to the multispecies problems an asymptotic preserving scheme for the kinetic equation is very efficient in the fluid regime where the knudsen number is small and the collision term becomes stiff it allows a coarse independent of the knudsen number mesh size and a large time step in the fluid regime the difficulty associated with multispecies problems is that there are no local conservation laws for each species resulting in extra stiff nonlinear source terms that need to be discretized properly in order to 1 avoid newton type solvers for nonlinear algebraic systems and 2 to be asymptotic preserving we show that these extra nonlinear source terms can be solved using only linear system solvers and the scheme preserves the correct euler and navier stokes limits numerical examples are used to demonstrate the efficiency and applicability of the schemes for both euler and navier stokes regimes

asymptotic high order schemes for 2 times2 dissipative hyperbolic systems we investigate finite difference schemes which approximate 2 times 2 one dimensional linear dissipative hyperbolic systems we show that it is possible to introduce some suitable modifications in standard upwinding schemes which keep into account the long time behavior of the solutions to yield numerical approximations which are increasingly accurate for large times when computing small perturbations of stable asymptotic states respectively around stationary solutions and in the diffusion chapman enskog limit

parameter estimation for finite mixture distributions abstract in this paper we compare numerically two approaches to the estimation of the parameters of the component densities in a univariate mixture of normal distributions one approach is based on a constrained maximum likelihood ml algorithm the other on the fuzzy c means fcm clustering algorithm our study indicates that i the ml method produces superior estimates when the component densities are well mixed while either algorithm provides good estimates for well separated distributions ii the fcm approach is almost always faster than the ml method and iii initialization of the ml method with the output of fcm almost always improves both the run time and accuracy of the statistical estimates

conditional inferential models combining information for prior free probabilistic inference summary the inferential model im framework provides valid prior free probabilistic inference by focusing on predicting unobserved auxiliary variables but efficient im based inference can be challenging when the auxiliary variable is of higher dimension than the parameter here we show that features of the auxiliary variable are often fully observed and in such cases a simultaneous dimension reduction and information aggregation can be achieved by conditioning this proposed conditioning strategy leads to efficient im inference and casts new light on fisher s notions of sufficiency conditioning and also bayesian inference a differential equation driven selection of a conditional association is developed and validity of the conditional im is proved under some conditions for problems that do not admit a conditional im of the standard form we propose a more flexible class of conditional ims based on localization examples of local conditional ims in a bivariate normal model and a normal variance components model are also given

a new convergence proof of fuzzy c means in this letter we give a new more direct derivation of the convergence properties of the fuzzy c means fcm algorithm using the equivalence between the original and reduced fcm criterion from the point of view of the reduced criterion the fcm algorithm is simply a steepest descent algorithm with variable steplength we prove that steplength adjustment follows from the majorization principle for steplength by applying the majorization principle we give a straightforward proof of global convergence further convergence properties follow immediately using known results of optimization theory

on a class of fuzzy c numbers clustering procedures for fuzzy data this paper describes a class of fuzzy clustering procedures for fuzzy data most fuzzy clustering techniques are designed for handling crisp data with their class memberships using the idea of fuzzy set theory here we derive new types of fuzzy clustering procedures in dealing with fuzzy data these procedures are called fuzzy c numbers fcn clusterings specially we construct these fcns for u type triangular trapezoidal and normal fuzzy numbers k jwoy s cluster analysis fuzzy clustering fuzzy data analysis fuzzy numbers fuzzy intervals fuzzy c means clustering fuzzy c numbers clustering

ordered group reference priors with application to the multinomial problem summary noninformative priors are developed using the reference prior approach for multiparameter problems in which there may be parameters of interest and nuisance parameters for a given grouping of parameters and ordering of the groups intuitively according to inferential importance an algorithm for determining the associated reference prior is presented the algorithm is illustrated on the multinomial problem with discussion of the variety and success of various groupings and ordering strategies

a fuzzy k modes algorithm for clustering categorical data this correspondence describes extensions to the fuzzy k means algorithm for clustering categorical data by using a simple matching dissimilarity measure for categorical objects and modes instead of means for clusters a new approach is developed which allows the use of the k means paradigm to efficiently cluster large categorical data sets a fuzzy k modes algorithm is presented and the effectiveness of the algorithm is demonstrated with experimental results

objective priors for discrete parameter spaces this article considers the development of objective prior distributions for discrete parameter spaces formal approaches to such development such as the reference prior approach often result in a constant prior for a discrete parameter which is questionable for problems that exhibit certain types of structure to take advantage of structure this article proposes embedding the original problem in a continuous problem that preserves the structure and then using standard reference prior theory to determine the appropriate objective prior four different possibilities for this embedding are explored and applied to a population size model the hypergeometric distribution the multivariate hypergeometric distribution the binomial beta distribution and the binomial distribution the recommended objective priors for the first third and fourth problems are new

estimating a product of means bayesian analysis with reference priors abstract suppose that we observe x n 1 and independently y n 1 and are concerned with inference mainly estimation and confidence statements about the product of means this problem arises most obviously in situations of determining area based on measurements of length and width it also arises in other practical contexts however for instance in gypsy moth studies the hatching rate of larvae per unit area can be estimated as the product of the mean of egg masses per unit area times the mean number of larvae hatching per egg mass approximately independent samples can be obtained for each mean see southwood 1978 noninformative prior bayesian approaches to the problem are considered in particular the reference prior approach of bernardo 1979 an appropriate reference prior for the problem is developed and relatively easily implementable formulas for posterior moments e g the posterior mean and variance and credible sets are derived comparisons with alternative noninf

adaptive fuzzy segmentation of magnetic resonance images an algorithm is presented for the fuzzy segmentation of two dimensional 2 d and three dimensional 3 d multispectral magnetic resonance mr images that have been corrupted by intensity inhomogeneities also known as shading artifacts the algorithm is an extension of the 2 d adaptive fuzzy c means algorithm 2 d afcm presented in previous work by the authors this algorithm models the intensity inhomogeneities as a gain field that causes image intensities to smoothly and slowly vary through the image space it iteratively adapts to the intensity inhomogeneities and is completely automated in this paper the authors fully generalize 2 d afcm to three dimensional 3 d multispectral images because of the potential size of 3 d image data they also describe a new faster multigrid based algorithm for its implementation they show using simulated mr data that 3 d afcm yields lower error rates than both the standard fuzzy c means fcm algorithm and two other competing methods when segmenting corrupted images its efficacy is further demonstrated using real 3 d scalar and multispectral mr brain images

detection and characterization of cluster substructure i linear structure fuzzy c lines in part i a generalization of the fuzzy c means or fuzzy isodata clustering algorithms is developed necessary conditions for minimization of a generalized total weighted squared orthogonal error objective function lead to a picard iteration scheme which generates simultaneously i c fuzzy clusters in the data ii a set of c prototypical straight lines in feature space which best fit the data in a well defined sense iii a set of c prototpyical centers of mass on the c lines which characterize the core of each linear fuzzy cluster theoretical optimization is achieved using principal components of generalized within cluster fuzzy scatter matrices a convergence theorem for each algorithm in the infinite family is given the algorithms are exemplified by five numerical examples using both real and artificial data sets having essentially linear substructure in part ii the fuzzy c means and fuzzy c lines algorithms are shown to be special cases of a more general class of fuzzy algorithms the

reference priors with partial information summary in this paper reference priors are derived for three cases where partial information is available if a subjective conditional prior is given two reasonable methods are proposed for finding the marginal reference prior if instead a subjective marginal prior is available a method for defining the conditional reference prior is proposed a sufficient condition is then given under which this conditional reference prior agrees with the conditional reference prior derived in the first stage of the reference prior algorithm of berger bernardo 1989 1992 finally under the assumption of independence a method for finding marginal reference priors is also proposed various examples are given to illustrate the methods

default priors for bayesian and frequentist inference summary we investigate the choice of default priors for use with likelihood for bayesian and frequentist inference such a prior is a density or relative density that weights an observed likelihood function leading to the elimination of parameters that are not of interest and then a density type assessment for a parameter of interest for independent responses from a continuous model we develop a prior for the full parameter that is closely linked to the original bayes approach and provides an extension of the right invariant measure to general contexts we then develop a modified prior that is targeted on a component parameter of interest and by targeting avoids the marginalization paradoxes of dawid and co workers this modifies jeffreys s prior and provides extensions to the development of welch and peers these two approaches are combined to explore priors for a vector parameter of interest in the presence of a vector nuisance parameter examples are given to illustrate the computation of the priors