a variable selection heuristic for k means clustering one of the most vexing problems in cluster analysis is the selection and or weighting of variables in order to include those that truly define cluster structure while eliminating those that might mask such structure this paper presents a variable selection heuristic for nonhierarchical k means cluster analysis based on the adjusted rand index for measuring cluster recovery the heuristic was subjected to monte carlo testing across more than 2200 datasets with known cluster structure the results indicate the heuristic is extremely effective at eliminating masking variables a cluster analysis of real world financial services data revealed that using the variable selection heuristic prior to the k means algorithm resulted in greater cluster stability

bayesian analysis of mixture models with an unknown number of components an alternative to reversible jump methods richardson and green present a method of performing a bayesian analysis of data from a finite mixture distribution with an unknown number of components their method is a markov chain monte carlo mcmc approach which makes use of the reversible jump methodology described by green we describe an alternative mcmc method which views the parameters of the model as a marked point process extending methods suggested by ripley to create a markov birth death process with an appropriate stationary distribution our method is easy to implement even in the case of data in more than one dimension and we illustrate it on both univariate and bivariate data there appears to be considerable potential for applying these ideas to other contexts as an alternative to more general reversible jump methods and we conclude with a brief discussion of how this might be achieved

dealing with label switching in mixture models summary in a bayesian analysis of finite mixture models parameter estimation and clustering are sometimes less straightforward than might be expected in particular the common practice of estimating parameters by their posterior mean and summarizing joint posterior distributions by marginal distributions often leads to nonsensical answers this is due to the so called label switching problem which is caused by symmetry in the likelihood of the model parameters a frequent response to this problem is to remove the symmetry by using artificial identifiability constraints we demonstrate that this fails in general to solve the problem and we describe an alternative class of approaches relabelling algorithms which arise from attempting to minimize the posterior expected loss under a class of loss functions we describe in detail one particularly simple and general relabelling algorithm and illustrate its success in dealing with the label switching problem on two examples

model based gaussian and non gaussian clustering abstract the classification maximum likelihood approach is sufficiently general to encompass many current clustering algorithms including those based on the sum of squares criterion and on the criterion of friedman and rubin 1967 however as currently implemented it does not allow the specification of which features orientation size and shape are to be common to all clusters and which may differ between clusters also it is restricted to gaussian distributions and it does not allow for noise we propose ways of overcoming these limitations a reparameterization of the covariance matrix allows us to specify that some features but not all be the same for all clusters a practical framework for non gaussian clustering is outlined and a means of incorporating noise in the form of a poisson process is described an approximate bayesian method for choosing the number of clusters is given the performance of the proposed methods is studied by simulation with encouraging results the methods are applied to the analysis of a data set arising in the study of diabetes and the results seem better than those of previous analyses rh

prediction of strongly curved turbulent duct flows with reynolds stress model the effects of strong convex and concave curvature on turbulent duct flows are investigated a compressible navier stokes code incorporating reynolds stress models has been developed using a four stage runge kutta scheme numerical computations have been carried out for strongly curved 180 deg turnaround duct flows with a reynolds stress model an algebraic reynolds stress model and a nonlinear e model a detailed assessment of the models capability in predicting the effects of strong streamline curvature has been carried out the effect of curvature parameter r on the development of mean flow and turbulence has been examined by numerical simulations with the reynolds stress model

development of curvature sensitive nonlinear eddy viscosity model current widely used turbulence closures except the full second moment closure cannot properly account for the suppression of turbulence by convex curvature and the enhancing effect by concave curvature particularly the failure of the explicit algebraic stress model easm to capture the curvature strain effects in curved flows can be attributed to the equilibrium assumption embodied in easm thus the algebraic stress model asm approach is reexamined in the framework of a generalized curvilinear coordinate system in the approach the equilibrium assumption applies only to the gradient part of convective transport while the curvature related algebraic terms in the reynolds stress convection process are retained in this way a curvature sensitive asm is derived and is further transformed into an explicit nonlinear eddy viscosity model in an orthogonal coordinate system with this newly developed explicit asm to predict the curved flow in a two dimensional u duct it is observed that the turbulence suppression at the convex wall is successfully captured

consistent order estimation for linear stochastic feedback control systems carma model abstract a new criterion cic is introduced to estimate orders p0 q0 r0 of the linear stochastic feedback control system with correlated noise described by a carma model it is proved that the estimate is strongly consistent when the upper bounds for p0 q0 and r0 are available but neither the stability condition nor the ergodicity of the input and output are imposed on the system

oblique shock wave boundary layer interaction using near wall reynolds stress models a synthesis is presented of the predictive capability of a family of near wall wall normal free reynolds stress models which are completely independent of wall topology i e of the distance fromthe wall and the normal to thewall orientation for oblique shock wave turbulent boundary layer interactions for the purpose of comparison results are also presented using a standard low turbulence reynolds number k e closure and a reynolds stress model that uses geometric wall normals and wall distances studied shock wave mach numbers are in the range msw 2 85 2 9 and incoming boundary layer thickness reynolds numbers are in the range re 0 1 2 106 computations were carefully checked for grid convergence comparison with measurements shows satisfactory agreement improving on results obtained using a k e model and highlights the relative importance of redistribution and diffusion closures indicating directions for future modeling work

efficient and robust reynolds stress model computation of three dimensional compressible flows thepurposeofthiswork isthedevelopmentofanefe cientand robustimplicitmethodology fortheintegration of the three dimensional compressible favre reynolds averaged navier stokes equations with near wall reynoldsstressclosure thee vemean e owandseventurbulencetransportequationsarediscretizedinspace ona structured multiblock grid using an o x 3 e nitevolumeupwind biased muscl schemewithvanleere ux vectorsplitting and van albada limiters time integration is based on an implicit dual time stepping procedure with alternating direction implicit subiterations a particular treatment of the approximate jacobians used in the subiterations substantiallydiminishesthecomputing timerequirementsoftheimplicitphase sothatthecomputationaloverhead of the reynolds stress seven equation closure compared to a two equation closure is less than 30 per iteration for steady e ow computations local time steps are used for both the subiterations and the time marching with courant friedrichs lewynumbersof o 10 20 fortheo 1 20 subiterationsneededand o 100 500 forthetime marching the robustness of the method is ensured by appropriate positivity boundedness and reynolds stress realizability constraints the numerical method is illustrated by computing and conducting numerical studies for a high subsonic m 0 7 three dimensional e ow with large separation and for a transonic three dimensional shock wave boundary layer interaction

the aastrom wittenmark self tuning regulator revisited and els based adaptive trackers although considerable progress has been made in stochastic adaptive control the problem concerning the convergence of the original self tuning regulator proposed by k j aastrom and b wittenmark 1973 is still open since it is attractive in theory and important in applications this problem is examined and a rigorous proof of its stability and optimality is given related problems such as convergence of the extended least squares els based adaptive tracker are also considered

identification and adaptive control for systems with unknown orders delay and coefficients an analysis that gives recursive estimates for time delay system orders and coefficients of single input single output linear discrete time deterministic and stochastic systems with uncorrelated noise is presented it is assumed that a lower bound for the time delay and upper bounds for system order are known the optimal adaptive control is designed for both tracking and linear quadratic regulation when the system parameters including time delay orders and coefficients are unknown the rates of convergence are derived the coefficient estimates to their true values and the loss functions to their minima

prediction of high lift flows using turbulent closure models the flow over two different multi element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model a subset of recently measured transition locations using hot film on a mcdonnell douglas configuration is presented and the effect of transition location on the computed solutions is explored deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element and not necessarily inadequate turbulence modeling in the wake using measured transition locations for the main element improves the prediction of its boundary layer thickness skin friction and wake profile shape however using measured transition locations on the slat still yields poor slat wake predictions the computation of the slat flow field represents a key roadblock to successful predictions of multi element flows in general the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models

consistent estimation of the order of stochastic control systems a consistent estimate of the order of feedback control systems with unknown matrix coefficients estimated by the least squares method is derived by minimizing a modified version of the bayesian information criterion

variable selection for fisher linear discriminant analysis using the modified sequential backward selection algorithm for the microarray data abstract one of the major challenges is small sample size as compared to large features number for microarray data variable selection is an important step for improving diagnostics of cancer or the classification according to the phenotypes via gene expression data in this study we propose a modified sequential backward selection sbs algorithm to deal with the case where the covariance matrix is singular then we propose a variable selection algorithm based on the weighted mahalanobis distance and modified sbs methods furthermore based on the proposed variable selection algorithm a fisher linear discriminant method is proposed to improve the accuracy of tumor classification through simultaneously taking into account genes joint discriminatory power to validate the efficiency we apply the proposed discriminant method to two different dna microarray data sets for experiment investigation the empirical results show that our method for tumor classification can obtain better classification effectiveness than markov random field method and independent variable group analysis i methods which demonstrates that the proposed variable selection method can obtain more correct and informative gene subset if taking into account the joint discriminatory power of genes for tumor classification

turbulence model predictions of strongly curved flow in a u duct the ability of three types of turbulence models to accurately predict the effects of curvature on the flow in a u duct is studied an explicit algebraic stress model performs slightly better than one or two equation linear eddy viscosity models although it is necessary to fully account for the variation of the production to dissipation rate ratio in the algebraic stress model formulation in their original formulations none of these turbulence models fully captures the suppressed turbulence near the convex wall whereas a full reynolds stress model does some of the underlying assumptions used in the development of algebraic stress models are investigated and compared with the computed flowfield from the full reynolds stress model through this analysis the assumption of reynolds stress anisotropy equilibrium used in the algebraic stress model formulation is found to be incorrect in regions of strong curvature by the accounting for the local variation of the principal axes of the strain rate tensor the explicit algebraic stress model correctly predicts the suppressed turbulence in the outer part of the boundary layer near the convex wall

convergence rate of least squares identification and adaptive control for stochastic systems the strong consistency and the convergence rate of least squares identification for the multidimensional armax model are established under some decaying excitation conditions which are satisfied if both input and output do not grow too fast and the attenuating excitation technique is applied the parameter identification results are applied to adaptive control systems with a quadratic loss function the rate of convergence of the loss function to its minimum is also obtained

bayesian variable selection in clustering high dimensional data over the last decade technological advances have generated an explosion of data with substantially smaller sample size relative to the number of covariates p n a common goal in the analysis of such data involves uncovering the group structure of the observations and identifying the discriminating variables in this article we propose a methodology for addressing these problems simultaneously given a set of variables we formulate the clustering problem in terms of a multivariate normal mixture model with an unknown number of components and use the reversible jump markov chain monte carlo technique to define a sampler that moves between different dimensional spaces we handle the problem of selecting a few predictors among the prohibitively vast number of variable subsets by introducing a binary exclusion inclusion latent vector which gets updated via stochastic search techniques we specify conjugate priors and exploit the conjugacy by integrating out some of the parameters we describe strategies

reversible jump markov chain monte carlo computation and bayesian model determination markov chain monte carlo methods for bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some fixed standard underlying measure they have therefore not been available for application to bayesian model determination where the dimensionality of the parameter vector is typically not fixed this paper proposes a new framework for the construction of reversible markov chain samplers that jump between parameter subspaces of differing dimensionality which is flexible and entirely constructive it should therefore have wide applicability in model determination problems the methodology is illustrated with applications to multiple change point analysis in one and two dimensions and to a bayesian comparison of binomial experiments

multivariate bayesian variable selection and prediction the multivariate regression model is considered with p regressors a latent vector with p binary entries serves to identify one of two types of regression coefficients those close to 0 and those not specializing our general distributional setting to the linear model with gaussian errors and using natural conjugate prior distributions we derive the marginal posterior distribution of the binary latent vector fast algorithms aid its direct computation and in high dimensions these are supplemented by a markov chain monte carlo approach to sampling from the known posterior distribution problems with hundreds of regressor variables become quite feasible we give a simple method of assigning the hyperparameters of the prior distribution the posterior predictive distribution is derived and the approach illustrated on compositional analysis of data involving three sugars with 160 near infra red absorbances as regressors

brief on line order estimation and parameter identification for linear stochastic feedback control systems carma model this paper presents a new recursive estimate method for orders and coefficients of linear stochastic feedback control systems carma model under the assumption that the upper bounds of system orders are known the strong consistency of the estimates for orders and coefficients is proved and the convergence rate of coefficient estimates to their true values is also obtained the estimate algorithm is applied to adaptive tracking of the systems with unknown orders and unknown coefficients the resulting closed loop systems are then globally stable and the tracking sample mean square error is minimized as well simultaneously the estimates of the adaptive tracking for orders and coefficients are also strongly consistent the simulation results given here show that the new developed algorithms of both system identification and adaptive tracking are effective

on bayesian analysis of mixtures with an unknown number of components with discussion new methodology for fully bayesian mixture analysis is developed making use of reversible jump markov chain monte carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture a sample from the full joint distribution of all unknown variables is thereby generated and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution the methodology is applied here to the analysis of univariate normal mixtures using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context

analysis of streamline curvature effects on wall bounded turbulent flows we deal with numerical analysis for the effects of surface curvature particularly the concave curvature on turbulent duct flows and boundary layers a compressible navier stokes code incorporating reynolds stress models has been developed using a four stage runge kutta scheme numerical computations have been carried out for curved flows in 180 deg and 90 deg turning ducts and a turbulent boundary layer using reynolds stress models with without modifications to the dissipation rate e equation various modifications to the e equation are discussed a quantitative relationship has been established between two seemingly different modifications to the e equation it is observed that the modeling of concave curvature effect is qualitatively different from the modeling of convex curvature effect detailed comparisons between computations and data indicate that to capture the strong amplification of turbulence near a concave wall the standard e equation needs to be modified

estimation of finite mixture distributions through bayesian sampling summary a formal bayesian analysis of a mixture model usually leads to intractable calculations since the posterior distribution takes into account all the partitions of the sample we present approximation methods which evaluate the posterior distribution and bayes estimators by gibbs sampling relying on the missing data structure of the mixture model the data augmentation method is shown to converge geometrically since a duality principle transfers properties from the discrete missing data chain to the parameters the fully conditional gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case we also consider non informative approximations associated with improper priors assuming that the sample corresponds exactly to a k component mixture

clustering objects on subsets of attributes with discussion read before the royal statistical society at a meeting organized by the research section on wednesday may 5th 2004 professor j t kent in the chair summary a new procedure is proposed for clustering attribute value data when used in conjunction with conventional distance based clustering algorithms this procedure encourages those algorithms to detect automatically subgroups of objects that preferentially cluster on subsets of the attribute variables rather than on all of them simultaneously the relevant attribute subsets for each individual cluster can be different and partially or completely overlap with those of other clusters enhancements for increasing sensitivity for detecting especially low cardinality groups clustering on a small subset of variables are discussed applications in different domains including gene expression arrays are presented