pattern clustering based on noise modeling in wavelet space we describe an effective approach to object or feature detection in point patterns via noise modeling this is based on use of a redundant or non pyramidal wavelet transform noise modeling is based on a poisson process we illustrate this new method with a range of examples we use the close relationship between image pixelated and point representations to achieve the result of a clustering method with constant time computational cost

a note on bayes factors for log linear contingency table models with vague prior information spiegelhalter and smith 1982 hereafter ssproposed an approximate method for calculating the bayes factor for a log linear model mo for a contingency table against the saturated model m1 with vague prior information we adopt their notation and denote by ss n equation n of ss suppose x1 xk have a multinomial distribution with parameters 014 4k where xi 0 0 x4i 1 we write yt log x1 log xk 01 log 01 log dk and y diag x1 xk then if m1 is the saturated model and mo is the nested log linear model defined by setting the contrasts co1 0 where c is an s x k matrix with rank s and rows summing to zero the approximate bayes factor bo1 for mo against m1 is given by ss 32 this however is indeterminate if any of the cell frequencies in the table is zero this is because of the use by ss of a prior density proportional to h i if however we use instead the standard jeffreys prior density proportional to i1i 1 2 the problem no longer arises then by the arguments of ss and lindley 1964 the resulting bayes factor is still given by ss 32 with xi replaced by xi 2 in the definitions of y and y i 1 k and ss 33 replaced by c 1 2 s2 1 cct i 1 2 if this solution is adopted the prior is proper and so in principle the problem of assigning an arbitrary multiplicative constant for which the ss approach was primarily devised need not arise one could in theory simply apply bayes theorem directly and so obtain the bayes factor exactly however in practice this is difficult to do and i know of no general solution to the problem even for simpler more specific contingency table and related models such as those of independence or equiprobability finding the bayes factor exactly is not too easy see for example crook and good 1982 altham 1971 gunel and dickey 1974 gunel 1982 broniatowski 1981 and references therein the second purpose of this note is to point out that conditionally on mo

behavior of solutions of burgers equation with nonlocal boundary conditions in this paper we discuss the long time behavior of positive solutions of burgers equation ut uxx uux 0 0 t 0 with the nonlocal boundary condition u 0 t 0 ux 1 t 12 u2 1 t aup 1 t 10u x t dx q where 0 p 0 q criteria for stability are given blowup in finite time for some solutions is shown general results are discussed

discriminant analysis with common principal components summary zhu hastie 2003 presented a general criterion for finding discriminant directions to optimise their criterion iterative methods are needed unless each class has a gaussian distribution with a common covariance matrix in this short paper we present a slightly more general case where iterative methods can also be avoided

rates of convergence for bayes and maximum likelihood estimation for mixture of normal densities we study the rates of convergence of the maximum likelihood estimator mle and posterior distribution in density estimation problems where the densities are location or location scale mixtures of normal distributions with the scale parameter lying between two positive numbers the true density is also assumed to lie in this class with the true mixing distribution either compactly supported or having sub gaussian tails we obtain bounds for hellinger bracketing entropies for this class and from these bounds we deduce the convergence rates of sieve mles in hellinger distance the rate turns out to be log n n where k 1 is a constant that depends on the type of mixtures and the choice of the sieve next we consider a dirichlet mixture of normals as a prior on the unknown density we estimate the prior probability of a certain kullback leibler type neighborhood and then invoke a general theorem that computes the posterior convergence rate in terms the growth rate of the hellinger entropy and the concentration rate of the prior the posterior distribution is also seen to converge at the rate log n n in where k now depends on the tail behavior of the base measure of the dirichlet process

selection of variables in cluster analysis an empirical comparison of eight procedures eight different variable selection techniques for model based and non model based clustering are evaluated across a wide range of cluster structures it is shown that several methods have difficulties when non informative variables i e random noise are included in the model furthermore the distribution of the random noise greatly impacts the performance of nearly all of the variable selection procedures overall a variable selection technique based on a variance to range weighting procedure coupled with the largest decreases in within cluster sums of squares error performed the best on the other hand variable selection methods used in conjunction with finite mixture models performed the worst

blow up of solutions of semilinear euler poisson darboux equations with nonlocal boundary conditions this article studies the hyperbolic initial nonlocal boundary value problem u t t k t u t u x x u 0 0 u x 0 u 0 x u t x 0 0 0 0 u a t 0 an y u y t q dy t 0 where k is a real number p and q are nonnegative constants and u 0 m and n are given functions criteria for u to blow up in finite time are given

exponential stabilization of the semilinear heat equation with nonlocal boundary conditions abstract the present work is devoted to the problem of boundary stabilization of the semilinear 1 d heat equation with nonlocal boundary conditions the stabilizing controller is finite dimensional linear given in an explicit form involving only the eigenfunctions of the laplace operator with nonlocal boundary conditions

hidden markov models for longitudinal comparisons medical researchers interested in temporal multivariate measurements of complex diseases have recently begun developing health state models which divide the space of patient characteristics into medically distinct clusters the current state of the art in health services research uses k means clustering to form the health states and a first order markov chain to describe transitions between the states this fitting procedure ignores information from temporally adjacent observations and prevents uncertainty from parameter estimation and cluster assignments from being incorporated into the analysis a natural way to address these issues is to combine clustering and longitudinal analyses using a hidden markov model we fit hidden markov models to longitudinal data using bayesian methods that account for all of the uncertainty in the parameters conditional only on the underlying correctness of the model potential lack of time homogeneity in the markov chain is accounted for by embedding transition probabi

a new approach to cluster analysis the clustering function based method the purpose of the paper is to present a new statistical approach to hierarchical cluster analysis with n objects measured on p variables motivated by the model of multivariate analysis of variance and the method of maximum likelihood a clustering problem is formulated as a least squares optimization problem simultaneously solving for both an n vector of unknown group membership of objects and a linear clustering function this formulation is shown to be linked to linear regression analysis and fisher linear discriminant analysis and includes principal component regression for tackling multicollinearity or rank deficiency polynomial or b splines regression for handling non linearity and various variable selection methods to eliminate irrelevant variables from data analysis algorithmic issues are investigated by using sign eigenanalysis

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

detecting features in spatial point processes with clutter via model based clustering abstract we consider the problem of detecting features such as minefields or seismic faults in spatial point processes when there is substantial clutter we use model based clustering based on a mixture model for the process in which features are assumed to generate points according to highly linear multivariate normal densities and the clutter arises according to a spatial poisson process nonlinear features are represented by several densities giving a piecewise linear representation hierarchical model based clustering provides a first estimate of the features and this is then refined using the em algorithm the number of features is estimated from an approximation to its posterior distribution the method gives good results for the minefield and seismic fault problems software to implement it is available on the world wide web

blow up of solutions for nonlinear parabolic equation with nonlocal source and nonlocal boundary condition this paper is devoted to a nonlinear parabolic equation subject to nonlocal boundary condition and with nonlocal reaction source some criteria on this problem which determine whether the solutions blow up in a finite time or exist globally are given moreover the blow up rate estimates are also obtained

the blow up rate for a degenerate parabolic equation with a non local source abstract in this paper we establish the local existence of the solution and the finite time blow up result for the equation v v m xx a l l v q dx x l l 0 moreover it is proved that the solution has global blow up and there exist constants c 1 c 2 such that c 1 t 1 1 q 1 max x l l v x c 2 t 1 1 q 1 where t 1 is the blow up time

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

asymptotic theory for a class of nonautonomous delay differential equations this paper deals with asymptotic behavior of solutions of the nonlinear nonautonomous delay differential equation x t t r t t f t x s d t s su where xf t x 0 f t 0 0 t r t nondecreasing t s is nondecreasing and of bounded variation general sufficient conditions which are easy to verify are obtained for the solutions to be bounded and asymptotically stable locally and globally these results improve many existing ones principally by allowing i r t to be unbounded ii both discrete and distributed delays and iii the equation to be strongly nonlinear and nonautonomous various examples are given in the form of corollaries with a highly flexible integrand

a mixture model with random effects components for classifying sibling pairs in healthy aging research typically multiple health outcomes are measured representing health status the aim of this paper was to develop a model based clustering approach to identify homogeneous sibling pairs according to their health status model based clustering approaches will be considered on the basis of linear mixed effect model for the mixture components class memberships of siblings within pairs are allowed to be correlated and within a class the correlation between siblings is modeled using random sibling pair effects we propose an expectation maximization algorithm for maximum likelihood estimation model performance is evaluated via simulations in terms of estimating the correct parameters degree of agreement and the ability to detect the correct number of clusters the performance of our model is compared with the performance of standard model based clustering approaches the methods are used to classify sibling pairs from the leiden longevity study according to their health status our results suggest that homogeneous healthy sibling pairs are associated with a longer life span software is available for fitting the new models copyright 2011 john wiley sons ltd

global attractivity for scalar differential equations with small delay abstract for scalar functional differential equations x t f t x t we refine the method of yorke and 3 2 type conditions to prove the global attractivity of the trivial solution the results are applied to establish sufficient conditions for the global attractivity of the positive equilibrium of scalar delayed population models of the form x t x t f t x t and illustrated with the study of two food limited population models with delay for which several criteria for their global attractivity are given

variable selection in clustering via dirichlet process mixture models summary the increased collection of high dimensional data in various fields has raised a strong interest in clustering algorithms and variable selection procedures in this paper we pro pose a model based method that addresses the two problems simultaneously we introduce a latent binary vector to identify discriminating variables and use dirichlet process mixture models to define the cluster structure we update the variable selection index using a metropolis algorithm and obtain inference on the cluster structure via a split merge markov chain monte carlo technique we explore the performance of the methodology on simulated data and illustrate an application with a dna microarray study

the impact of covariance misspecification in multivariate gaussian mixtures on estimation and inference an application to longitudinal modeling multivariate gaussian mixtures are a class of models that provide a flexible parametric approach for the representation of heterogeneous multivariate outcomes when the outcome is a vector of repeated measurements taken on the same subject there is often inherent dependence between observations however a common covariance assumption is conditional independence that is given the mixture component label the outcomes for subjects are independent in this paper we study through asymptotic bias calculations and simulation the impact of covariance misspecification in multivariate gaussian mixtures although maximum likelihood estimators of regression and mixing probability parameters are not consistent under misspecification they have little asymptotic bias when mixture components are well separated or if the assumed correlation is close to the truth even when the covariance is misspecified we also present a robust standard error estimator and show that it outperforms conventional estimators in simulations and can indicate that the model is misspecified body mass index data from a national longitudinal study are used to demonstrate the effects of misspecification on potential inferences made in practice copyright 2013 john wiley sons ltd

triplet markov fields for the classification of complex structure data we address the issue of classifying complex data we focus on three main sources of complexity namely the high dimensionality of the observed data the dependencies between these observations and the general nature of the noise model underlying their distribution we investigate the recent triplet markov fields and propose new models in this class designed for such data and in particular allowing very general noise models in addition our models can handle the inclusion of a learning step in a consistent way so that they can be used in a supervised framework one advantage of our models is that whatever the initial complexity of the noise model parameter estimation can be carried out using state of the art bayesian clustering techniques under the usual simplifying assumptions as generative models they can be seen as an alternative in the supervised case to discriminative conditional random fields identifiability issues underlying the models in the nonsupervised case are discussed while the models performance is illustrated on simulated and real data exhibiting the mentioned various sources of complexity

bayes factors for non homogeneous poisson processes with vague prior information on developpe une approche bayesienne au probleme de la comparaison de modeles pour des processus de poisson non homogenes

a model based approach for clustering of multivariate semicontinuous data with application to dietary pattern analysis and intervention semicontinuous data characterized by a sizable number of zeros and observations from a continuous distribution are frequently encountered in health research concerning food consumptions physical activities medical and pharmacy claims expenditures and many others in analyzing such semicontinuous data it is imperative that the excessive zeros be adequately accounted for to obtain unbiased and efficient inference although many methods have been proposed in the literature for the modeling and analysis of semicontinuous data little attention has been given to clustering of semicontinuous data to identify important patterns that could be indicative of certain health outcomes or intervention effects we propose a bernoulli normal mixture model for clustering of multivariate semicontinuous data and demonstrate its accuracy as compared to the well known clustering method with the conventional normal mixture model the proposed method is illustrated with data from a dietary intervention trial to promote healthy eating behavior among children with type 1 diabetes in the trial certain diabetes friendly foods eg total fruit whole fruit dark green and orange vegetables and legumes whole grain were only consumed by a proportion of study participants yielding excessive zero values due to nonconsumption of the foods baseline foods consumptions data in the trial are used to explore preintervention dietary patterns among study participants while the conventional normal mixture model approach fails to do so the proposed bernoulli normal mixture model approach has shown to be able to identify a dietary profile that significantly differentiates the intervention effects from others as measured by the popular healthy eating index at the end of the trial

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

model based clustering for integrated circuit yield enhancement this paper studies the defect data analysis method for semiconductor yield enhancement given the defect locations on a wafer the local defects generated from the assignable causes are classified from the global defects generated from the random causes by model based clustering and the clustering methods can identify the characteristics of local defect clusters the information obtained from this method can facilitate process control particularly root cause analysis the global defects are modeled by the spatial non homogeneous poisson process and the local defects are modeled by the bivariate normal distribution or by the principal curve

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

joint modeling and clustering paired generalized longitudinal trajectories with application to cocaine abuse treatment data in a cocaine dependence treatment study we have paired binary longitudinal trajectories that record the cocaine use patterns of each patient before and after a treatment to better understand the drug using behaviors among the patients we propose a general framework based on functional data analysis to jointly model and cluster these paired non gaussian longitudinal trajectories our approach assumes that the response variables follow distributions from the exponential family with the canonical parameters determined by some latent gaussian processes to reduce the dimensionality of the latent processes we express them by a truncated karhunen loeve kl expansion allowing the mean and covariance functions to be different across clusters we further represent the mean and eigenfunctions functions by flexible spline bases and determine the orders of the truncated kl expansions using data driven methods by treating the cluster membership as a missing value we cluster the cocaine use trajectories by a l

stability analysis of the zero solution for two class evolution equations abstract by constructing some suitable lyapunov type functionals and applying the theory of the definite quadratic form we obtain the stability of the zero solution of two classes of evolution equations with delays including reaction diffusion equations and damped wave equations our criteria depend on the derivatives of delays consequently when the delays are constants these criteria are independent of the magnitudes of the delays so the delays are harmless for the stability of the zero solution

feature selection based on a modified fuzzy c means algorithm with supervision in this paper we propose a new approach to feature selection based on a modified fuzzy c means algorithm with supervision mfcms mfcms completes the unsupervised learning of classical fuzzy c means with labeled patterns the labeled patterns allow mfcms to accurately model the shape of each cluster and consequently to highlight the features which result to be particularly effective to characterize a cluster these features are distinguished by a low variance of their values for the patterns with a high membership degree to the cluster if with respect to these features the distance between the prototype of the cluster and the prototypes of the other clusters is high then these features have the property of discriminating between the cluster and the other clusters to take these two aspects into account for each cluster and each feature we introduce a purposely defined index the higher the value of the index the higher the discrimination capability of the feature for the cluster we execute mfcms on the training set considering all patterns as labeled then we retain the features which are associated at least for one cluster with an index larger than a threshold we applied mfcms to several real world pattern classification benchmarks we used the well known k nearest neighbors as learning algorithm we show that feature selection performed by mfcms achieved an improvement in generalization on all data sets

mixtures of multivariate power exponential distributions summary an expanded family of mixtures of multivariate power exponential distributions is introduced while fitting heavy tails and skewness have received much attention in the model based clustering literature recently we investigate the use of a distribution that can deal with both varying tail weight and peakedness of data a family of parsimonious models is proposed using an eigen decomposition of the scale matrix a generalized expectation maximization algorithm is presented that combines convex optimization via a minorization maximization approach and optimization based on accelerated line search algorithms on the stiefel manifold lastly the utility of this family of models is illustrated using both toy and benchmark data

statistical significance of clustering for high dimension low sample size data clustering methods provide a powerful tool for the exploratory analysis of high dimension low sample size hdlss data sets such as gene expression microarray data a fundamental statistical issue in clustering is which clusters are really there as opposed to being artifacts of the natural sampling variation we propose sigclust as a simple and natural approach to this fundamental statistical problem in particular we define a cluster as data coming from a single gaussian distribution and formulate the problem of assessing statistical significance of clustering as a testing procedure this gaussian null assumption allows direct formulation of p values that effectively quantify the significance of a given clustering hdlss covariance estimation for sigclust is achieved by a combination of invariance principles together with a factor analysis model the properties of sigclust are studied simulated examples as well as an application to a real cancer microarray data set show that the proposed method

differences in spiking patterns among cortical neurons spike sequences recorded from four cortical areas of an awake behaving monkey were examined to explore characteristics that vary among neurons we found that a measure of the local variation of interspike intervals lv is nearly the same for every spike sequence for any given neuron while it varies significantly among neurons the distributions of lv values for neuron ensembles in three of the four areas were found to be distinctly bimodal two groups of neurons classified according to the spiking irregularity exhibit different responses to the same stimulus this suggests that neurons in each area can be classified into different groups possessing unique spiking statistics and corresponding functional properties

mixtures of shifted asymmetriclaplace distributions a mixture of shifted asymmetric laplace distributions is introduced and used for clustering and classification a variant of the em algorithm is developed for parameter estimation by exploiting the relationship with the generalized inverse gaussian distribution this approach is mathematically elegant and relatively computationally straightforward our novel mixture modelling approach is demonstrated on both simulated and real data to illustrate clustering and classification applications in these analyses our mixture of shifted asymmetric laplace distributions performs favourably when compared to the popular gaussian approach this work which marks an important step in the non gaussian model based clustering and classification direction concludes with discussion as well as suggestions for future work

mixtures of factor analyzers with common factor loadings applications to the clustering and visualization of high dimensional data mixtures of factor analyzers enable model based density estimation to be undertaken for high dimensional data where the number of observations n is not very large relative to their dimension p in practice there is often the need to further reduce the number of parameters in the specification of the component covariance matrices to this end we propose the use of common component factor loadings which considerably reduces further the number of parameters moreover it allows the data to be displayed in low dimensional plots

uniform blow up profiles and boundary behavior for diffusion equations with nonlocal nonlinear source in this paper we introduce a new method for investigating the rate and profile of blow up of solutions of diffusion equations with nonlocal nonlinear reaction terms for large classes of equations we prove that the solutions have global blow up and that the rate of blow up is uniform in all compact subsets of the domain this results in a flat blow up profile except for a boundary layer whose thickness vanishes astapproaches the blow up timet in each case the blow up rate of u t is precisely determined furthermore in many cases we derive sharp estimates on the size of the boundary layer and on the asymptotic behavior of the solution in the boundary layer the size of the boundary layer then decays liket t and the solutionu t x behaves like u t d x t tin the boundary layer wheredis the distance to the boundary some fujita type critical exponents results are also given for the cauchy problem

regularized parameter estimation in high dimensional gaussian mixture models finite gaussian mixture models are widely used in statistics thanks to their great flexibility however parameter estimation for gaussian mixture models with high dimensionality can be challenging because of the large number of parameters that need to be estimated in this letter we propose a penalized likelihood estimator to address this difficulty the type penalty we impose on the inverse covariance matrices encourages sparsity on its entries and therefore helps to reduce the effective dimensionality of the problem we show that the proposed estimate can be efficiently computed using an expectation maximization algorithm to illustrate the practical merits of the proposed method we consider its applications in model based clustering and mixture discriminant analysis numerical experiments with both simulated and real data show that the new method is a valuable tool for high dimensional data analysis

a concave pairwise fusion approach to subgroup analysis abstractan important step in developing individualized treatment strategies is correct identification of subgroups of a heterogeneous population to allow specific treatment for each subgroup this article considers the problem using samples drawn from a population consisting of subgroups with different mean values along with certain covariates we propose a penalized approach for subgroup analysis based on a regression model in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject specific intercepts we apply concave penalty functions to pairwise differences of the intercepts this procedure automatically divides the observations into subgroups to implement the proposed approach we develop an alternating direction method of multipliers algorithm with concave penalties and demonstrate its convergence we also establish the theoretical properties of our proposed estimator and determine the order requirement of the minimal difference of signals between g

testing a point null hypothesis the irreconcilability of p values and evidence abstract the problem of testing a point null hypothesis or a small interval null hypothesis is considered of interest is the relationship between the p value or observed significance level and conditional and bayesian measures of evidence against the null hypothesis although one might presume that a small p value indicates the presence of strong evidence against the null such is not necessarily the case expanding on earlier work especially edwards lindman and savage 1963 and dickey 1977 it is shown that actual evidence against a null as measured say by posterior probability or comparative likelihood can differ by an order of magnitude from the p value for instance data that yield a p value of 05 when testing a normal mean result in a posterior probability of the null of at least 30 for any objective prior distribution objective here means that equal prior weight is given the two hypotheses and that the prior is symmetric and nonincreasing away from the null other definiti

stability on nonlinear delay differential equations with impulses abstract in this paper the asymptotic stability for nonlinear delay differential equations with impulses 1 1 x t f t x t t 0 t t k x t k x t k i k x t k k n is studied and 3 2 stability theorems are presented the results here have improved the known results

bayesian morphology fast unsupervised bayesian image analysis abstract we consider the problems of image segmentation and classification and image restoration when the true image is made up of a small number of unordered colors our emphasis is on both performance and speed speed has become increasingly important for analyzing large images and multispectral images with many bands processing large image databases real time or near realtime image analysis and the online analysis of video bayesian image analysis provides an elegant solution to these problems but it is computationally expensive and the solutions it provides may be sensitive to unrealistic global properties of the models on which it is based the icm algorithm is faster and based on the local properties of the models underlying bayesian image analysis parameter estimation is performed iteratively via pseudolikelihood mathematical morphology is faster again and is widely considered to perform well but lacks a statistical basis method selection analogous to parameter estimation is done in a

blow up of solutions for semilinear heat equation with nonlinear nonlocal boundary condition abstract in this paper we consider a semilinear heat equation u t u c x t u p for x t 0 with nonlinear and nonlocal boundary condition u 0 k x y t u l d y and nonnegative initial data where p 0 and l 0 we prove global existence theorem for max p l 1 some criteria on this problem which determine whether the solutions blow up in a finite time for sufficiently large or for all nontrivial initial data or the solutions exist for all time with sufficiently small or with any initial data are also given

a hybrid sem algorithm for high dimensional unsupervised learning using a finite generalized dirichlet mixture this paper applies a robust statistical scheme to the problem of unsupervised learning of high dimensional data we develop analyze and apply a new finite mixture model based on a generalization of the dirichlet distribution the generalized dirichlet distribution has a more general covariance structure than the dirichlet distribution and offers high flexibility and ease of use for the approximation of both symmetric and asymmetric distributions we show that the mathematical properties of this distribution allow high dimensional modeling without requiring dimensionality reduction and thus without a loss of information this makes the generalized dirichlet distribution more practical and useful we propose a hybrid stochastic expectation maximization algorithm hsem to estimate the parameters of the generalized dirichlet mixture the algorithm is called stochastic because it contains a step in which the data elements are assigned randomly to components in order to avoid convergence to a saddle point the adjective hybrid is justified by the introduction of a newton raphson step moreover the hsem algorithm autonomously selects the number of components by the introduction of an agglomerative term the performance of our method is tested by the classification of several pattern recognition data sets the generalized dirichlet mixture is also applied to the problems of image restoration image object recognition and texture image database summarization for efficient retrieval for the texture image summarization problem results are reported for the vistex texture image database from the mit media lab

clustering from categorical data sequences the three parameter cluster model is a combinatorial stochastic process that generates categorical response sequences by randomly perturbing a fixed clustering parameter this clear relationship between the observed data and the underlying clustering is particularly attractive in cluster analysis in which supervised learning is a common goal and missing data is a familiar issue the model is well equipped for this task as it can handle missing data perform out of sample inference and accommodate both independent and dependent data sequences moreover its clustering parameter lies in the unrestricted space of partitions so that the number of clusters need not be specified beforehand we establish these and other theoretical properties and also demonstrate the model on datasets from epidemiology genetics political science and legal studies

algorithms for model based gaussian hierarchical clustering agglomerative hierarchical clustering methods based on gaussian probability models have recently shown promise in a variety of applications in this approach a maximum likelihood pair of clusters is chosen for merging at each stage unlike classical methods model based methods reduce to a recurrence relation only in the simplest case which corresponds to the classical sum of squares method we show how the structure of the gaussian model can be exploited to yield efficient algorithms for agglomerative hierarchical clustering

improving on deterministic approximate bayesian inferences for mixture distributions this paper presents the branching approach which can improve deterministic implementation methods such as variational bayesian inference and expectation propagation method for bayesian mixture distributions this proposed approach utilizes a set of artificial conditions defined by using the latent variables of the mixture distribution this condition set is updated iteratively by branching based on a condition selected from the previous condition set the target approximate bayesian inference is obtained by merging the approximate conditional inferences under each condition in the condition set the proposed approach is compared with several standard implementation methods by using a numerical example and a real world example

blow up problem for semilinear heat equation with absorption and a nonlocal boundary condition abstract in this paper we consider a semilinear parabolic equation u t u c x t u p for x t 0 with nonlinear and nonlocal boundary condition u 0 k x y t u l d y and nonnegative initial data where p 0 and l 0 we prove some global existence results criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given

inference and prediction for a general order statistic model with unknown population size abstract suppose that the first n order statistics from a random sample of n positive random variables are observed where n is unknown this the general order statistic model has been applied to the study of market penetration capture recapture burn in in repairable systems software reliability growth the estimation of the number of individuals exposed to radiation and the estimation of the number of unseen species inference is to be made about the unknown parameters especially n and future observations are to be predicted a bayes empirical bayes approach to inference is presented this permits the comparison of competing perhaps nonnested models for the distribution of the random variables in a natural way it also provides easily implemented inference and prediction procedures that avoid the difficulties of non bayesian methods one such difficulty is that the maximum likelihood estimator of n may be infinite results are given for the case in which vague prior information about the model

biclustering models for two mode ordinal data the work in this paper introduces finite mixture models that can be used to simultaneously cluster the rows and columns of two mode ordinal categorical response data such as those resulting from likert scale responses we use the popular proportional odds parameterisation and propose models which provide insights into major patterns in the data model fitting is performed using the em algorithm and a fuzzy allocation of rows and columns to corresponding clusters is obtained the clustering ability of the models is evaluated in a simulation study and demonstrated using two real data sets

stability theorems for nonlinear scalar delay differential equations in this paper the stability on nonlinear scalar delay differential equations is studied and improved 3 2 stability theorems are presented

global attractivity results for nonlinear delay differential equations abstract the aim of this paper is to give sufficient conditions for global attractivity of the zero solution of the nonlinear delay differential equationx t p t f x t an example which guarantees that our 3 2 stability condition is the best possible is also given

on structure testing for component covariance matrices of a high dimensional mixture summary by studying the family of p dimensional scale mixtures the paper shows for the first time a non trivial example where the eigenvalue distribution of the corresponding sample covariance matrix does not converge to the celebrated marcenko pastur law a different and new limit is found and characterized the reasons for failure of the marcenko pastur limit in this situation are found to be a strong dependence between the p co ordinates of the mixture next we address the problem of testing whether the mixture has a spherical covariance matrix to analyse the traditional john s type test we establish a novel and general central limit theorem for linear statistics of eigenvalues of the sample covariance matrix it is shown that john s test and its recent high dimensional extensions both fail for high dimensional mixtures precisely because of the different spectral limit above as a remedy a new test procedure is constructed afterwards for the sphericity hypothesis this test is then applied to identify the covariance structure in model based clustering it is shown that the test has much higher power than the widely used integrated classification likelihood and bayesian information criteria in detecting non spherical component covariance matrices of a high dimensional mixture

a dirichlet problem under integral boundary condition abstract in this paper we establish some results concerning existence and multiplicity of solution for a elliptic problem under integral dirichlet boundary condition we mainly use a lower and upper solution method and a result due to rabinowitz 11 related to the existence of a continuum of solutions of an abstract nonlinear eigenvalue problem

kernel methods for point symmetry based clustering this paper deals with the point symmetry based clustering task that consists in retrieving from a data set clusters having a point symmetric shape prototype based algorithms are considered and a non trivial generalization to kernel methods is proposed thanks to the geometric properties satisfied by the point symmetry distances proposed until now the proposed kernelized framework offers new opportunities to deal with non euclidean symmetries and to reconsider any intractable examples by means of implicit feature spaces a deep experimental study is proposed that brings out on artificial data sets the capabilities and the limits of the current point symmetry based clustering methods it reveals that kernel methods are quite capable of stretching the current limits for the considered task and encourages new research on the kernel selection issue in order to design a fully unsupervised symmetric pattern recognition process highlightsgeneralization by kernelization of a family of point symmetry distances kernelized sbkm that offers new possibilities for point symmetry based clustering empirical recognition of symmetric clusters using any proximity measure highlighting new simple examples hard to manage by original methods new complex examples well managed with ksbkm by using implicit projections

shared farthest neighbor approach to clustering of high dimensionality low cardinality data clustering algorithms are routinely used in biomedical disciplines and are a basic tool in bioinformatics depending on the task at hand there are two most popular options the central partitional techniques and the agglomerative hierarchical clustering techniques and their derivatives these methods are well studied and well established however both categories have some drawbacks related to data dimensionality for partitional algorithms and to the bottom up structure for hierarchical agglomerative algorithms to overcome these limitations motivated by the problem of gene expression analysis with dna microarrays we present a hierarchical clustering algorithm based on a completely different principle which is the analysis of shared farthest neighbors we present a framework for clustering using ranks and indexes and introduce the shared farthest neighbors sfn clustering criterion we illustrate the properties of the method and present experimental results on different data sets using the strategy of evaluating data clustering by extrinsic knowledge given by class labels

rates of convergence for the gaussian mixture sieve gaussian mixtures provide a convenient method of densityestimation that lies somewhere between parametric models and kernel densityestimators when the number of components of the mixture is allowed to increase as sample size increases the model is called a mixture sieve we establish a bound on the rate of convergence in hellinger distance for densityestimation using the gaussian mixture sieve assuming that the true density is itself a mixture of gaussians the underlying mixing measure of the true densityis not necessarilyassumed to have finite support computing the rate involves some delicate calculations since the size of the sieve as measured bybracketing entropy and the saturation rate cannot be found using standard methods when the mixing measure has compact support using kn n 2 3 log n 1 3 components in the mixture yields a rate of order log n 1 6 n1 6 for every 0 the rates depend heavilyon the tail behavior of the true density the sensitivity to the tail behavior is diminished byusing a robust sieve which includes a long tailed component in the

fitting straight lines to point patterns abstract in many types of point patterns linear features are of greatest interest a very general algorithm is presented here which determines non overlapping clusters of points which have large linearity given a set of points the algorithm successively merges pairs of clusters or of points encompassing in the merging criterion both contiguity and linearity the algorithm is a generalization of the widely used ward s minimum variance hierarchical clustering method the application of this algorithm is illustrated using examples from the literature in biometrics and in character recognition

a nonparametric statistical approach to clustering via mode identification a new clustering approach based on mode identification is developed by applying new optimization techniques to a nonparametric density estimator a cluster is formed by those sample points that ascend to the same local maximum mode of the density function the path from a point to its associated mode is efficiently solved by an em style algorithm namely the modal em mem this method is then extended for hierarchical clustering by recursively locating modes of kernel density estimators with increasing bandwidths without model fitting the mode based clustering yields a density description for every cluster a major advantage of mixture model based clustering moreover it ensures that every cluster corresponds to a bump of the density the issue of diagnosing clustering results is also investigated specifically a pairwise separability measure for clusters is defined using the ridgeline between the density bumps of two clusters the ridgeline is solved for by the ridgeline em rem algorithm an extension of mem based upon this new measure a cluster merging procedure is created to enforce strong separation experiments on simulated and real data demonstrate that the mode based clustering approach tends to combine the strengths of linkage and mixture model based clustering in addition the approach is robust in high dimensions and when clusters deviate substantially from gaussian distributions both of these cases pose difficulty for parametric mixture modeling a c package on the new algorithms is developed for public access at http www stat psu edu jiali hmac

model based learning using a mixture of mixtures of gaussian and uniform distributions we introduce a mixture model whereby each mixture component is itself a mixture of a multivariate gaussian distribution and a multivariate uniform distribution although this model could be used for model based clustering model based unsupervised learning or model based classification model based semi supervised learning we focus on the more general model based classification framework in this setting we fit our mixture models to data where some of the observations have known group memberships and the goal is to predict the memberships of observations with unknown labels we also present a density estimation example a generalized expectation maximization algorithm is used to estimate the parameters and thereby give classifications in this mixture of mixtures model to simplify the model and the associated parameter estimation we suggest holding some parameters fixed this leads to the introduction of more parsimonious models a simulation study is performed to illustrate how the model allows for bursts of probability and locally higher tails two further simulation studies illustrate how the model performs on data simulated from multivariate gaussian distributions and on data from multivariate t distributions this novel approach is also applied to real data and the performance of our approach under the various restrictions is discussed