a latent class approach to fitting the weighted euclidean model clascal a weighted euclidean distance model for analyzing three way proximity data is proposed that incorporates a latent class approach in this latent class weighted euclidean model the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class this model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions and drastically reduces the number of parameters in the traditional indscal model the probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities the maximum likelihood function is optimized by means of an em algorithm a modified fisher scoring method is used to update the parameters in the m step a model selection strategy is proposed and illustrated on both real and artificial data

linear latent variable models and covariance structures abstract the observed vector is taken as a linear combination of latent unobservable vector variables the loading matrices are functions of a vector parameter the covariance matrix of one latent vector may depend on another vector parameter and the covariance matrices of the other latent vectors are unrestricted positive definite matrices and the different latent vectors are uncorrelated the covariance matrix of the observed vector is a function of the two parameter vectors and the covariance matrices of the latent vectors the maximum likelihood estimator when the latent variables are normally distributed is characterized the asymptotic distribution of the maximum likelihood estimator derived under normality is shown to be valid generally if the different latent variables are independent not just uncorrelated one latent vector is only required to have a sample covariance matrix that has a probability limit tests of the covariance structure are also asymptotically robust

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

random effects diagonal metric multidimensional scaling models by assuming a distribution for the subject weights in a diagonal metric indscal multidimensional scaling model the subject weights become random effects including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the indscal alscal and other multidimensional scaling programs unlike traditional models the number of parameters does not increase with the number of subjects and because the distribution of the subject weights is modeled the construction of linear models of the subject weights and the testing of those models is immediate here we define a random effects diagonal metric multidimensional scaling model give computational algorithms describe our experiences with these algorithms and provide an example illustrating the use of the model and algorithms

a latent class multidimensional scaling model for two way one mode continuous rating dissimilarity data in this paper we propose a cluster mds model for two way one mode continuous rating dissimilarity data the model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low dimensional space under the normal distribution assumption a latent class model is developed in terms of the set of dissimilarities in a maximum likelihood framework in each iteration the probability that a dissimilarity belongs to each of the blocks conforming to a partition of the original dissimilarity matrix and the rest of parameters are estimated in a simulated annealing based algorithm a model selection strategy is used to test the number of latent classes and the dimensionality of the problem both simulated and classical dissimilarity data are analyzed to illustrate the model

an energy conserving method for stochastic maxwell equations with multiplicative noise abstract in this paper it is shown that three dimensional stochastic maxwell equations with multiplicative noise are stochastic hamiltonian partial differential equations possessing a geometric structure i e stochastic multi symplectic conservation law and the energy of system is a conservative quantity almost surely we propose a stochastic multi symplectic energy conserving method for the equations by using the wavelet collocation method in space and stochastic symplectic method in time numerical experiments are performed to verify the excellent abilities of the proposed method in providing accurate solution and preserving energy the mean square convergence result of the method in temporal direction is tested numerically and numerical comparisons with finite difference method are also investigated

iterative methods for subspace and doa estimation in nonuniform noise usually direction of arrival doa estimators are derived under the assumption of uniform white noise whose covariance matrix is a scaled identity matrix however in practice the noise can be nonuniform with an arbitrary unknown diagonal covariance matrix in this situation the performance of doa estimators may be deteriorated considerably if the noise nonuniformity is ignored to tackle this problem iterative approaches to subspace estimation are developed and the corresponding subspace based doa estimators are addressed in our proposed methods the signal subspace and noise covariance matrix are first determined by maximizing the log likelihood ll function or solving a least squares ls minimization problem both of which are accomplished in an iterative manner then the doas are determined from the subspace estimate and or noise covariance matrix estimate with the help of traditional doa estimators as the signal subspace and noise covariance matrix can be computed in closed form in each iteration the proposals are computationally attractive furthermore the signal subspace is directly calculated without the requirement of the exact knowledge of the array manifold enabling us to handle array uncertainties by incorporating conventional subspace based calibration algorithms simulations and experimental results are included to demonstrate the superiority of the proposed approaches

an extension of multiple correspondence analysis for identifying heterogeneous subgroups of respondents an extension of multiple correspondence analysis is proposed that takes into account cluster level heterogeneity in respondents preferences choices the method involves combining multiple correspondence analysis and k means in a unified framework the former is used for uncovering a low dimensional space of multivariate categorical variables while the latter is used for identifying relatively homogeneous clusters of respondents the proposed method offers an integrated graphical display that provides information on cluster based structures inherent in multivariate categorical data as well as the interdependencies among the data an empirical application is presented which demonstrates the usefulness of the proposed method and how it compares to several extant approaches

an extended discrete gradient formula for oscillatory hamiltonian systems in this paper incorporating the idea of the discrete gradient method into the extended runge kutta nystrom integrator we derive and analyze an extended discrete gradient formula for the oscillatory hamiltonian system with the hamiltonian where represents generalized positions represents generalized momenta and is a symmetric and positive semi definite matrix the solution of this system is a nonlinear oscillator basically many nonlinear oscillatory mechanical systems with a partitioned hamiltonian function lend themselves to this approach the extended discrete gradient formula presented in this paper exactly preserves the energy h p q we derive some properties of the new formula the convergence is analyzed for the implicit schemes based on the discrete gradient formula and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of m which is a significant property for the oscillatory hamiltonian system thus it transpires that a larger step size can be chosen for the new energy preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory hamiltonian system illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature

detection and localization of multiple sources in noise with unknown covariance the authors present a novel technique for the detection and localization of multiple sources in the presence of noise with unknown and arbitrary covariance the technique is applicable to coherent and noncoherent signals and to arbitrary array geometry and is based on rissanen s minimum description length mdl principle 1989 for model selection its computational load is comparable to that of analogous techniques for white noise simulation results demonstrating the performance of this technique are included

numerical solution of damped nonlinear klein gordon equations using variational method and finite element approach numerical treatment for damped nonlinear klein gordon equations based on variational method and finite element approach is studied a semi discrete algorithm is proposed by using quadratic interpolation functions of continuous time and spatial dimension one the gauss legendre quadrature has been utilized for numerical integrations of nonlinear terms and runge kutta method is used for solving ordinary differential equation finally three dimensional graphics of numerical solutions are used to demonstrate the numerical results

complex factor analysis and extensions many subspace based array signal processing algorithms assume that the noise is spatially white in this case the noise covariance matrix is a multiple of the identity and the eigenvectors of the data covariance matrix are not affected by it if the noise covariance is an unknown arbitrary diagonal e g for an uncalibrated array the eigenvalue decomposition leads to incorrect subspace estimates and it has to be replaced by a more general factor analysis decomposition fa which then reveals all relevant information we consider this data model and several extensions where the noise covariance matrix has a more general structure such as banded sparse block diagonal and cases where we have multiple data covariance matrices that share the same noise covariance matrix starting from a nonlinear weighted least squares formulation we propose new estimation algorithms for both classical fa and its extensions the optimization is based on gauss newton gradient descent generally this leads to an iteration involving the inversion of a very large matrix using the structure of the problem we show how this can be reduced to the inversion of a matrix with dimension equal to the number of unknown noise covariance parameters this results in new algorithms that have faster numerical convergence and lower complexity compared to several maximum likelihood based algorithms that could be considered state of the art the new algorithms scale well to large dimensions and can replace eigenvalue decompositions in many applications even if the noise can be assumed to be white

estimation of the directions of arrival of signals in unknown correlated noise i the map approach and its implementation the authors propose a method of direction of arrival doa estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary other than being positive definite they examine the projection of the data onto the noise subspace the conditional probability density function pdf of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed the a posteriori pdf of the signal parameters alone is then obtained by assigning a noninformative a priori pdf to the unknown noise covariance matrix and integrating out this quantity a simple criterion for the maximum a posteriori map estimate of the doas of the signals is established some properties of this criterion are discussed and an efficient numerical algorithm for the implementation of this criterion is developed the advantage of this method is that the noise covariance matrix does not have to be known nor must it be estimated

maximum likelihood estimation for array processing in colored noise direction of arrival estimation of multiple sources using a uniform linear array in noise with unknown covariance is considered the noise is modeled as a spatial autoregressive process with unknown parameters both stochastic and deterministic signal models are considered for the random signal case an approximate maximum likelihood estimator of the signal and noise parameters is derived it requires numerical maximization of a compressed likelihood function over the unknown arrival angles analytical expressions for the mles of the signal covariance and the ar parameters are given similar results for the case of deterministic signals are also presented

application of model selection criteria to some problems in multivariate analysis a review of model selection criteria is presented with a view toward showing their similarities it is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model selection criteria consideration is given to application of model selection criteria to some problems of multivariate analysis especially the clustering of variables factor analysis and more generally describing a complex of variables

bearing estimation for a distributed source of nonconstant modulus ounds and analysis the paper considers the problem of estimating the bearing of a single far field source surrounded by local scatterers using passive sensor array measurements an associated source bearing estimation problem is formulated and the crame spl acute r rao lower bound is evaluated in addition a comprehensive analysis is performed of the maximum likelihood estimates that due to mismodeling assume a constant modulus source and the degradation in performance is quantified as a function of the source s empirical variance it is shown that for a limited price in terms of mean square error the constant modulus maximum likelihood estimator can replace the optimal nonconstant modulus estimator

a bayesian multidimensional scaling procedure for the spatial analysis of revealed choice data we present a new bayesian formulation of a vector multidimensional scaling procedure for the spatial analysis of binary choice data the gibbs sampler is gainfully employed to estimate the posterior distribution of the specified scalar products bilinear model parameters the computational procedure allows for the explicit estimation of a covariance matrix which can accommodate violations of iia due to context effects in addition posterior standard errors can be estimated which reflect differential degrees of consumer choice uncertainty and or brand position instability a marketing application concerning the analysis of consumers consideration sets for luxury automobiles is provided to illustrate the use of the proposed methodology

application of the conditional population mixture model to image segmentation the problem of image segmentation is considered in the context of a mixture of probability distributions the segments fall into classes a probability distribution is associated with each class of segment parametric families of distributions are considered a set of parameter values being associated with each class with each observation is associated an unobservable label indicating from which class the observation arose segmentation algorithms are obtained by applying a method of iterated maximum likelihood to the resulting likelihood function a numerical example is given choice of the number of classes using akaike s information criterion aic for model identification is illustrated

stochastic conformal schemes for damped stochastic klein gordon equation with additive noise abstract in this article stochastic conformal schemes of the damped stochastic klein gordon equation with additive noise are studied it is shown that this equation possesses the stochastic conformal multi symplectic conservation law under appropriate boundary conditions the global momentum evolution law and the global energy evolution law are proposed we chiefly develop the stochastic conformal preissman scheme the stochastic conformal discrete gradient scheme and the stochastic conformal euler box scheme to preserve the geometric structures of the original system specifically we make theoretical discussions on the three proposed schemes to obtain corresponding discrete conservation laws or discrete evolution laws then the damped stochastic linear klein gordon equation and the damped stochastic nonlinear klein gordon equation with cubic nonlinearity are taken as examples to demonstrate the validity of the proposed schemes through numerical experiments and comparisons the superiorities of the proposed schemes are fully shown which are consistent with our theoretical analysis moreover the mean square convergence orders of the three stochastic conformal schemes in time direction and space direction are tested numerically

direction finding in the presence of colored noise by candidate identification a method is developed for identifying correct angles of arrivals from a set of candidate angles that contains spurious angles and the true ones under the assumption that the colored noise is an autoregressive process and that a uniform linear array of sensors is used the procedure is based on a relation derived for the higher order reflection coefficients corresponding to the autocorrelation sequence of the signal plus noise it is shown that the higher order reflection coefficients of a set of plane waves impinging on a uniform linear array of sensors in the presence of an unknown spatially autoregressive colored noise process are equal to an order independent linear combination of the values of the fourier transform of the corresponding optimal linear least squares normalized prediction error filter at the electric phase angles of the plane waves the magnitudes of the coefficients are then used to decide whether a given candidate direction of arrival corresponds to an actual plane wave or not the estimation of candidate angles is also briefly discussed

multi conformal symplectic pdes and discretizations past work on integration methods that preserve a conformal symplectic structure focuses on hamiltonian systems with weak linear damping in this work systems of pdes that have conformal symplectic structure in time and space are considered meaning conformal symplecticity is fully generalized for pdes using multiple examples it is shown that pdes with this particular structure have interesting applications what it means to preserve a multi conformal symplectic conservation law numerically is explained along with presentation of two numerical methods that preserve such properties then the advantages of the methods are briefly explored through applications to linear equations consideration of momentum and energy dissipation and backward error analysis numerical simulations for two pdes illustrate the properties of the methods as well as the advantages over other standard methods

bayesian multidimensional scaling and choice of dimension multidimensional scaling is widely used to handle data that consist of similarity or dissimilarity measures between pairs of objects we deal with two major problems in metric multidimensional scaling configuration of objects and determination of the dimension of object configuration within a bayesian framework a markov chain monte carlo algorithm is proposed for object configuration along with a simple bayesian criterion called mdsic for choosing their dimension simulation results are presented as are real data our method provides better results than does classical multidimensional scaling and alscal for object configuration and mdsic seems to work well for dimension choice in the examples considered

invariant measures for stochastic nonlinear beam and wave equations existence of an invariant measure for a stochastic extensible beam equation and for a stochastic damped wave equation with polynomial nonlinearities is proved it is shown first that the corresponding transition semigroups map the space of all bounded sequentially weakly continuous functions on the state space into itself and then by a lyapunov functions approach solutions bounded in probability are found

constrained latent class analysis simultaneous classification and scaling of discrete choice data a reparameterization of a latent class model is presented to simultaneously classify and scale nominal and ordered categorical choice data latent class specific probabilities are constrained to be equal to the preference probabilities from a probabilistic ideal point or vector model that yields a graphical multidimensional representation of the classification results in addition background variables can be incorporated as an aid to interpreting the latent class specific response probabilities the analyses of synthetic and real data sets illustrate the proposed method

stochastic nonlinear beam equations an extensible beam equation with a stochastic force of a white noise type is studied lyapunov functions techniques being used to prove existence of global mild solutions and asymptotic stability of the zero solution

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

preservation of physical properties of stochastic maxwell equations with additive noise via stochastic multi symplectic methods stochastic maxwell equations with additive noise are a system of stochastic hamiltonian partial differential equations intrinsically possessing the stochastic multi symplectic conservation law it is shown that the averaged energy increases linearly with respect to the evolution of time and the flow of stochastic maxwell equations with additive noise preserves the divergence in the sense of expectation moreover we propose three novel stochastic multi symplectic methods to discretize stochastic maxwell equations in order to investigate the preservation of these properties numerically we make theoretical discussions and comparisons on all of the three methods to observe that all of them preserve the corresponding discrete version of the averaged divergence meanwhile we obtain the corresponding dissipative property of the discrete averaged energy satisfied by each method especially the evolution rates of the averaged energies for all of the three methods are derived which are in accordance with the continuous case numerical experiments are performed to verify our theoretical results

numerical solution of the nonlinear klein gordon equation using radial basis functions the nonlinear klein gordon equation is used to model many nonlinear phenomena in this paper we propose a numerical scheme to solve the one dimensional nonlinear klein gordon equation with quadratic and cubic nonlinearity our scheme uses the collocation points and approximates the solution using thin plate splines tps radial basis functions rbf the implementation of the method is simple as finite difference methods the results of numerical experiments are presented and are compared with analytical solutions to confirm the good accuracy of the presented scheme

conformal conservation laws and geometric integration for damped hamiltonian pdes conformal conservation laws are defined and derived for a class of multi symplectic equations with added dissipation in particular the conservation laws of energy and momentum are considered along with those that arise from linear symmetries numerical methods that preserve these conformal conservation laws are presented in detail providing a framework for proving a numerical method exactly preserves the dissipative properties considered the conformal methods are compared analytically and numerically to standard conservative methods which includes a thorough inspection of numerical solution behavior for linear equations damped klein gordon and sine gordon equations and a damped nonlinear schrodinger equation are used as examples to demonstrate the results

decoupled local global energy preserving schemes for the n coupled nonlinear schrodinger equations abstract we develop two local energy preserving integrators and a global energy preserving integrator for the general multisymplectic hamiltonian system when applied to the 1d and multi dimensional n coupled nonlinear schrodinger equations the given schemes have the exact preservation of the local global conservation law and are decoupled in the components n n 1 2 n i e each of the components can be solved independently the decoupled feature is significant and helpful for overcoming the computational difficulty of the n coupled n 3 nonlinear schrodinger equations especially of the multi dimensional case the composition method is employed to improve the accuracy of the schemes in time and the discrete fast fourier transform is used to reduce the computational complexity several numerical experiments are carried out to exhibit the behaviors of the wave solutions numerical results confirm the theoretical results

detection and localization in colored noise via generalized least squares a method for detection and localization of multiple signals in spatially colored noise by an arbitrary passive sensor array is presented the method also enables exploitation of prior knowledge that the signals are uncorrelated so as to improve the performance and to allow detection and localization even if the number of signals exceeds the number of sensors the estimation based on the generalized least squares criterion is both consistent and asymptotically efficient the detection is performed via the minimum description length mdl principle and is proved to be consistent simulation results confirming the theoretical results are included

a subspace method for direction of arrival estimation of uncorrelated emitter signals a novel eigenstructure based method for direction estimation is presented the method assumes that the emitter signals are uncorrelated ideas from subspace and covariance matching methods are combined to yield a noniterative estimation algorithm when a uniform linear array is employed the large sample performance of the estimator is analyzed it is shown that the asymptotic variance of the direction estimates coincides with the relevant cramer rao lower bound crb a compact expression for the crb is derived for the ease when it is known that the signals are uncorrelated and it is lower than the crb that is usually used in the array processing literature assuming no particular structure for the signal covariance matrix the difference between the two crbs can be large in difficult scenarios this implies that in such scenarios the proposed methods has significantly better performance than existing subspace methods such as for example wsf music and esprit numerical examples are provided to illustrate the obtained results

multiclus a new method for simultaneously performing multidimensional scaling and cluster analysis this paper develops a maximum likelihood based method for simultaneously performing multidimensional scaling and cluster analysis on two way dominance or profile data this multiclus procedure utilizes mixtures of multivariate conditional normal distributions to estimate a joint space of stimulus coordinates andk vectors one for each cluster or group in at dimensional space the conditional mixture maximum likelihood method is introduced together with an e m algorithm for parameter estimation a monte carlo analysis is presented to investigate the performance of the algorithm as a number of data parameter and error factors are experimentally manipulated finally a consumer psychology application is discussed involving consumer expertise experience with microcomputers

on maximum likelihood localization of coherent signals we consider the problem of localizing multiple signal sources in the special case where all the signals are known a priori to be coherent a maximum likelihood estimator mle is constructed for this special case and its asymptotical performance is analyzed via the cramer rao bound crb it is proved that the crb for this case is identical to the crb for the case that no prior knowledge on coherency is exploited thus establishing a quite surprising result that asymptotically the localization errors are not reduced by exploiting this prior knowledge also we prove that in the coherent case the deterministic signals model and the stochastic signals model yield mle s that are asymptotically identical simulation results confirming these theoretical results are included

source enumeration in array processing using a two step test we investigate the problem of enumerating source signals impinging on an array of sensors given noisy limited observations the assumption of a large sample size is indispensable for most of the existing approaches so that they suffer significant performance degradation when only a small number of samples is available random matrix theory can capture the asymptotic distributions of the eigenvalues accurately and provide good approximations even for a finite sample size in this paper we take into account the relationship and distributions of the noise and signal eigenvalues based on random matrix theory and derive a simple two step test numerical simulations demonstrate that it is capable of correctly determining the number of sources in the case of small sample sizes

sympletic finite difference approximations of the nonlinear klein gordon equation we analyze three finite difference approximations of the nonlinear klein gordon equation and show that they are directly related to symplectic mappings two of the schemes the perring skyrme and ablowitz kruskal ladik are long established and the third is a new higher order accurate scheme we test the schemes on traveling wave and periodic breather problems over long time intervals and compare their accuracy and computational costs with those of symplectic and nonsymplectic method of lines approximations and a nonsymplectic energy conserving method

a bayesian vector multidimensional scaling procedure incorporating dimension reparameterization with variable selection we propose a two way bayesian vector spatial procedure incorporating dimension reparameterization with a variable selection option to determine the dimensionality and simultaneously identify the significant covariates that help interpret the derived dimensions in the joint space map we discuss how we solve identifiability problems in a bayesian context that are associated with the two way vector spatial model and demonstrate through a simulation study how our proposed model outperforms a popular benchmark model in addition an empirical application dealing with consumers ratings of large sport utility vehicles is presented to illustrate the proposed methodology we are able to obtain interpretable and managerially insightful results from our proposed model with variable selection in comparison with the benchmark model

modeling viewpoint shifts in probabilistic choice a number of mathematical models for overcoming intransitive choice have been proposed and tested in the literature of decision theory this article presents the development of a new stochastic choice model based on multidimensional scaling this allows decision makers to have multiple viewpoints whereas current multidimensional scaling models are based on the assumption that a subject or group of subjects has only one viewpoint the implication of our model is that subjects make an intransitive choice because they are able to shift their viewpoint this paper also presents the maximum likelihood estimation of the proposed model and reanalyzes tversky s gamble experiment data

on the achievable localization accuracy of multiple sources at high snr the cramer rao bound crb for the problem of localizing multiple signal sources by an arbitrary passive sensor array is analyzed for the general case where the array is not necessarily simultaneously sampled and where the signals may a priori be known to be uncorrelated it is shown that unlike in the case where the number of samples grows wherein the crb for the localization error always converges to zero in the case where the number of snapshots is kept fixed and the signal to noise ratio snr grows the crb converges to zero only if the number of sensors simultaneously sampled exceeds the signal subspace dimension