on some convergence properties of the subspace constrained mean shift abstract subspace constrained mean shift scms is a non parametric iterative algorithm that has recently been proposed to find principal curves and surfaces based on a new definition involving the gradient and hessian of a kernel probability density estimate although simulation results using synthetic and real data have demonstrated the usefulness of the scms algorithm a rigorous study of its convergence is still missing this paper aims to take initial steps in this direction by showing that the scms algorithm inherits some important convergence properties of the mean shift ms algorithm in particular the monotonicity and convergence of the density estimate values along the sequence of output values of the algorithm is shown also it is shown that the distance between consecutive points of the output sequence converges to zero as does the projection of the gradient vector onto the subspace spanned by the d d eigenvectors corresponding to the d d largest eigenvalues of the local inverse covariance matrix these last two properties provide theoretical guarantees for stopping criteria by modifying the projection step three variations of the scms algorithm are proposed and the running times and performance of the resulting algorithms are compared

the geometry of nonparametric filament estimation we consider the problem of estimating filamentary structure from d dimensional point process data we make some connections with computational geometry and develop nonparametric methods for estimating the filaments we show that under weak conditions the filaments have a simple geometric representation as the medial axis of the data distribution s support our methods convert an estimator of the support s boundary into an estimator of the filaments we also find the rates of convergence of our estimators proofs of all results are in the supplementary material available online

principal curve time warping time warping finds use in many fields of time series analysis and it has been effectively implemented in many different application areas rather than focusing on a particular application area we approach the general problem definition and employ principal curves a powerful machine learning tool to improve the noise robustness of existing time warping methods the increasing noise level is the most important problem that leads to unnatural alignments therefore we tested our approach in low signal to noise ratio snr signals and obtained satisfactory results moreover for the signals denoised by principal curve projections we propose a differential equation based time warping method which has a comparable performance with lower computational complexity than the existing techniques

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

learning nonlinear image manifolds by global alignment of local linear models appearance based methods based on statistical models of the pixel values in an image region rather than geometrical object models are increasingly popular in computer vision in many applications the number of degrees of freedom dof in the image generating process is much lower than the number of pixels in the image if there is a smooth function that maps the dof to the pixel values then the images are confined to a low dimensional manifold embedded in the image space we propose a method based on probabilistic mixtures of factor analyzers to 1 model the density of images sampled from such manifolds and 2 recover global parameterizations of the manifold a globally nonlinear probabilistic two way mapping between coordinates on the manifold and images is obtained by combining several locally valid linear mappings we propose a parameter estimation scheme that improves upon an existing scheme and experimentally compare the presented approach to self organizing maps generative topographic mapping and mixtures of factor analyzers in addition we show that the approach also applies to finding mappings between different embeddings of the same manifold

a global structure based algorithm for detecting the principal graph from complex data principal curves arising as an essential construct in dimensionality reduction and pattern recognition have recently attracted much attention from theoretical as well as practical perspective existing methods usually employ the first principal component of the data as an initial estimate of principal curves however they may be ineffective when dealing with complex data with self intersecting characteristics high curvature and significant dispersion in this paper a new method based on global structure is proposed to detect the principal graph a set of principal curves from complex data first the global structure of the data called an initial principal graph is extracted based on a thinning technique which captures the approximate topological features of the complex data in terms of the characteristics of the data vertex merge step and the improved fitting and smoothing phase are then proposed to control the deviation of the principal graph and improve the process of optimizing the principal graph finally the restructuring step introduced by kegl is used to rectify imperfections of the principal graph by using synthetic and real world data sets the proposed method is compared with other existing algorithms experimental results show the effectiveness of the global structure based method

piecewise linear skeletonization using principal curves proposes an algorithm to find piecewise linear skeletons of handwritten characters by using principal curves the development of the method was inspired by the apparent similarity between the definition of principal curves smooth curves which pass through the middle of a cloud of points and medial axes smooth curves that run equidistantly from the contours of a character image the central fitting and smoothing step of the algorithm is an extension of the polygonal line algorithm which approximates principal curves of data sets by piecewise linear curves the polygonal line algorithm is extended to find principal graphs and complemented with two steps specific to the task of skeletonization an initialization method to capture the approximate topology of the character and a collection of restructuring operations to improve the structural quality of the skeleton produced by the initialization method an advantage of our approach over existing methods is that we optimize the skeleton graph by minimizing an intuitive and explicit objective function that captures the two competing criteria of smoothing the skeleton and fitting it closely to the pixels of the character image we tested the algorithm on isolated handwritten digits and images of continuous handwriting the results indicated that the proposed algorithm can find a smooth medial axis in the great majority of a wide variety of character templates and that it substantially improves the pixel wise skeleton obtained by traditional thinning methods

fractional differential equations and lyapunov functionals abstract we consider a scalar fractional differential equation write it as an integral equation and construct several lyapunov functionals yielding qualitative results about the solution it turns out that the kernel is convex with a singularity and it is also completely monotone as is the resolvent kernel while the kernel is not integrable the resolvent kernel is positive and integrable with an integral value of one these kernels give rise to essentially different types of lyapunov functionals it is to be stressed that the lyapunov functionals are explicitly given in terms of known functions and they are differentiated using leibniz s rule the results are readily accessible to anyone with a background of elementary calculus

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

on model selection criteria in multimodel analysis 1 hydrologic systems are open and complex rendering them prone to multiple conceptualizations and mathematical descriptions there has been a growing tendency to postulate several alternative hydrologic models for a site and use model selection criteria to 1 rank these models 2 eliminate some of them and or 3 weigh and average predictions and statistics generated by multiple models this has led to some debate among hydrogeologists about the merits and demerits of common model selection also known as model discrimination or information criteria such as aic aicc bic and kic and some lack of clarity about the proper interpretation and mathematical representation of each criterion we examine the model selection literature to find that 1 all published rigorous derivations of aic and aicc require that the true model having generated the observational data be in the set of candidate models 2 though bic and kic were originally derived by assuming that such a model is in the set bic has been rederived by cavanaugh and neath 1999 without the need for such an assumption and 3 kic reduces to bic as the number of observations becomes large relative to the number of adjustable model parameters implying that it likewise does not require the existence of a true model in the set of alternatives we explain why kic is the only criterion accounting validly for the likelihood of prior parameter estimates elucidate the unique role that the fisher information matrix plays in kic and demonstrate through an example that it imbues kic with desirable model selection properties not shared by aic aicc or bic our example appears to provide the first comprehensive test of how aic aicc bic and kic weigh and rank alternative models in light of the models predictive performance under cross validation with real hydrologic data

probabilistic dimensionality reduction via structure learning we propose an alternative probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data based on this framework we present a new model which is able to learn a set of embedding points in a low dimensional space by retaining the inherent structure from high dimensional data the objective function of this new model can be equivalently interpreted as two coupled learning problems i e structure learning and the learning of projection matrix inspired by this interesting interpretation we propose another model which finds a set of embedding points that can directly form an explicit graph structure we proved that the model by learning explicit graphs generalizes the reversed graph embedding method but leads to a natural interpretation from bayesian perspective this can greatly facilitate data visualization and scientific discovery in downstream analysis extensive experiments are performed that demonstrate that the proposed framework is able to retain the inherent structure of datasets and achieve competitive quantitative results in terms of various performance evaluation criteria

estimating latent distributions in recurrent choice data this paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data these choice models are derived by specifying elements of the choice process at the individual level probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior due to the explicit consideration of random effect sources the choice models are parsimonious and readily interpretable an easy to implement em algorithm is presented for parameter estimation two applications illustrate the proposed approach

a nonparametric approach for assessing latent trait unidimensionality assuming a nonparametric family of item response theory models a theory based procedure for testing the hypothesis of unidimensionality of the latent space is proposed the asymptotic distribution of the test statistic is derived assuming unidimensionality thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait based upon a new notion of dimensionality the test is shown to have asymptotic power 1 a 6300 trial monte carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice

singular integral equations liapunov functionals and resolvents abstract this paper together with a recent paper by the second author on convex singular kernels establishes a base for further investigation of mildly singular equations with liapunov theory we study the two nonlinear scalar integral equations x t a t 0 t d t s x s g s x s d s and z t a t 0 t d t s g s z s d s where d has a singularity at t s the first equation is decomposed into three other simpler equations we then construct a liapunov functional for each of the equations which will yield l p properties of the solutions

principal curve algorithms for partitioning high dimensional data spaces most partitioning algorithms iteratively partition a space into cells that contain underlying linear or nonlinear structures using linear partitioning strategies the compactness of each cell depends on how well the locally linear partitioning strategy approximates the intrinsic structure to partition a compact structure for complex data in a nonlinear context this paper proposes a nonlinear partition strategy this is a principal curve tree pc tree which is implemented iteratively given that a pc passes through the middle of the data distribution it allows for partitioning based on the arc length of the pc to enhance the partitioning of a given space a residual version of the pc tree algorithm is developed denoted here as the principal component analysis tree pcr tree algorithm because of its residual property the pcr tree can yield the intrinsic dimension of high dimensional data comparisons presented in this paper confirm that the proposed pc tree and pcr tree approaches show a better performance than several other competing partitioning algorithms in terms of vector quantization error and nearest neighbor search the comparison also shows that the proposed algorithms outperform competing linear methods in total average coverage which measures the nonlinear compactness of partitioning algorithms

model selection principles in misspecified models summary model selection is of fundamental importance to high dimensional modelling featured in many contemporary applications classical principles of model selection include the bayesian principle and the kullback leibler divergence principle which lead to the bayesian information criterion and akaike information criterion respectively when models are correctly specified yet model misspecification is unavoidable in practice we derive novel asymptotic expansions of the two well known principles in misspecified generalized linear models which give the generalized bayesian information criterion and generalized akaike information criterion a specific form of prior probabilities motivated by the kullback leibler divergence principle leads to the generalized bayesian information criterion with prior probability gbicp which can be naturally decomposed as the sum of the negative maximum quasi log likelihood a penalty on model dimensionality and a penalty on model misspecification directly numerical studies demonstrate the advantage of the new methods for model selection in both correctly specified and misspecified models

hierarchical classes models for three way three mode binary data interrelations and model selection several hierarchical classes models can be considered for the modeling of three way three mode binary data including the indclas model leenen van mechelen de boeck and rosenberg 1999 the tucker3 hiclas model ceulemans van mechelen and leenen 2003 the tucker2 hiclas model ceulemans and van mechelen 2004 and the tucker1 hiclas model that is introduced in this paper two questions then may be raised 1 how are these models interrelated and 2 given a specific data set which of these models should be selected and in which rank in the present paper we deal with these questions by 1 showing that the distinct hierarchical classes models for three way three mode binary data can be organized into a partially ordered hierarchy and 2 by presenting model selection strategies based on extensions of the well known scree test and on the akaike information criterion the latter strategies are evaluated by means of an extensive simulation study and are illustrated with an application to interpersonal emotion data finally the presented hierarchy and model selection strategies are related to corresponding work by kiers 1991 for principal component models for three way three mode real valued data

constraint local principal curve existing principal curve algorithms have some drawbacks such as time consuming and narrow application scope in practice since these algorithms are mainly based on global optimization in this paper we present the concept of constraint local principal curve clpc which uses local optimization methods and restricts the principal curve with two fixed endpoints to reduce the computational complexity in addition we propose three clpc algorithms by local optimization and adaptive radius to expand the range of applications and increase the solution quality the first algorithm i e clpcg is based on greedy thinking the second algorithm i e clpcs uses one dimensional search and the last algorithm clpcc combines the greedy thinking and one dimensional search then we define six performance indices to evaluate the performance of the clpc algorithms finally we present some numerical experiments with three simulation data sets and two gps measured data sets in both highway and railway the results indicate that all of the three clpc algorithms can obtain high accuracy data from multiple low accuracy data efficiently the clpc algorithms can improve the accuracy and computational speed compared with the existing k segment principal curve kpc algorithm in addition clpcc outperforms clpcg and clpcs according to the comprehensive experiments while clpcg runs much faster than other ones we present the concept of constraint local principal curve clpc to reduce the computational complexity we propose three clpc algorithms that combine local optimization and adaptive radius to expand the range of applications and increase the solution quality we present some numerical experiments with three simulation data sets and two measured gps data sets in highway and railway the clpc algorithms can improve the accuracy and computational speed compared with the existing kpc algorithms the features of the each clpc algorithm are analyzed according to the comprehensive experiments

on the path density of a gradient field we consider the problem of reliably finding filaments in point clouds realistic data sets often have numerous filaments of various sizes and shapes statistical techniques exist for finding one or a few filaments but these methods do not handle noisy data sets with many filaments other methods can be found in the astronomy literature but they do not have rigorous statistical guarantees we propose the following method starting at each data point we construct the steepest ascent path along a kernel density estimator we locate filaments by finding regions where these paths are highly concentrated formally we define the density of these paths and we construct a consistent estimator of this path density

similarity preserving principal curve an optimal 1 d feature extractor for data representation this paper discusses the problem of what kind of learning model is suitable for the tasks of feature extraction for data representation and suggests two evaluation criteria for nonlinear feature extractors reconstruction error minimization and similarity preservation based on the suggested evaluation criteria a new type of principal curve similarity preserving principal curve sppc is proposed sppcs minimize the reconstruction error under the condition that the similarity between similar samples are preserved in the extracted features thus giving researchers effective and reliable cognition of the inner structure of data sets the existence and properties of sppcs are analyzed a practical learning algorithm is proposed and high dimensional extensions of sppcs are also discussed experimental results show the virtues of sppcs in preserving inner structures of data sets and discovering manifolds with high nonlinearity

a fast algorithm for the computation of axial moments and its application to the orthogonal fitting of curves this paper describes a fast algorithm to compute local axial moments used in the detection of objects of interest in images the basic idea is the elimination of redundant operations while computing axial moments for two neighboring angles of orientation the main result is that the complexity of the recursive computation of axial moments becomes independent of the total number of computed moments at a given point i e it is of the order o n where n is the size of the data set this result is of great importance in computer vision since many feature extraction methods rely on the computation of axial moments the use of this algorithm for fast object skeletonization in images by orthogonal regression fitting is described in detail with the experimental results confirming the theoretical computational complexity

cluster number selection for a small set of samples using the bayesian ying yang model one major problem in cluster analysis is the determination of the number of clusters in this paper we describe both theoretical and experimental results in determining the cluster number for a small set of samples using the bayesian kullback ying yang byy model selection criterion under the second order approximation we derive a new equation for estimating the smoothing parameter in the cost function finally we propose a gradient descent smoothing parameter estimation approach that avoids complicated integration procedure and gives the same optimal result

learning and design of principal curves principal curves have been defined as self consistent smooth curves which pass through the middle of a d dimensional probability distribution or data cloud they give a summary of the data and also serve as an efficient feature extraction tool we take a new approach by defining principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution the new definition makes it possible to theoretically analyze principal curve learning from training data and it also leads to a new practical construction our theoretical learning scheme chooses a curve from a class of polygonal lines with k segments and with a given total length to minimize the average squared distance over n training points drawn independently convergence properties of this learning scheme are analyzed and a practical version of this theoretical algorithm is implemented in each iteration of the algorithm a new vertex is added to the polygonal line and the positions of the vertices are updated so that they minimize a penalized squared distance criterion simulation results demonstrate that the new algorithm compares favorably with previous methods both in terms of performance and computational complexity and is more robust to varying data models

a response model for multiple choice items in the mid 1960s samejima initiated the development of item response models that involve separate response functions for all of the alternatives in the multiple choice and likert type formats her work in this area began at the educational testing service and continued during a visit to the l l thurstone psychometric laboratory at the university of north carolina both samejima s 1969 this volume original model for graded item responses and bock s 1972 this volume model for nominal responses were originally intended to produce response functions for all of the alternatives of multiple choice items for various reasons neither model has proved entirely satisfactory for that purpose although both have been applied in other contexts using a combination of ideas suggested by bock 1972 and samejima 1968 1979 a multiple choice model was developed that produces response functions that fit unidimensional multiple choice tests better thissen and steinberg 1984 that model is the subject of this chapter

self organization as an iterative kernel smoothing process kohonen s self organizing map when described in a batch processing mode can be interpreted as a statistical kernel smoothing problem the batch som algorithm consists of two steps first the training data are partitioned according to the voronoi regions of the map unit locations second the units are updated by taking weighted centroids of the data falling into the voronoi regions with the weighing function given by the neighborhood then the neighborhood width is decreased and steps 1 2 are repeated the second step can be interpreted as a statistical kernel smoothing problem where the neighborhood function corresponds to the kernel and neighborhood width corresponds to kernel span to determine the new unit locations kernel smoothing is applied to the centroids of the voronoi regions in the topological space this interpretation leads to some new insights concerning the role of the neighborhood and dimensionality reduction it also strengthens the algorithm s connection with the principal curve algorithm a generalized self organizing algorithm is proposed where the kernel smoothing step is replaced with an arbitrary nonparametric regression method

principal surfaces from unsupervised kernel regression we propose a nonparametric approach to learning of principal surfaces based on an unsupervised formulation of the nadaraya watson kernel regression estimator as compared with previous approaches to principal curves and surfaces the new method offers several advantages first it provides a practical solution to the model selection problem because all parameters can be estimated by leave one out cross validation without additional computational cost in addition our approach allows for a convenient incorporation of nonlinear spectral methods for parameter initialization beyond classical initializations based on linear pca furthermore it shows a simple way to fit principal surfaces in general feature spaces beyond the usual data space setup the experimental results illustrate these convenient features on simulated and real data

range image segmentation using surface selection criterion in this paper we address the problem of recovering the true underlying model of a surface while performing the segmentation first and in order to solve the model selection problem we introduce a novel criterion which is based on minimising strain energy of fitted surfaces we then evaluate its performance and compare it with many other existing model selection techniques using this criterion we then present a robust range data segmentation algorithm capable of segmenting complex objects with planar and curved surfaces the presented algorithm simultaneously identifies the type order and geometric shape of each surface and separates all the points that are part of that surface this paper includes the segmentation results of a large collection of range images obtained from objects with planar and curved surfaces the resulting segmentation algorithm successfully segments various possible types of curved objects more importantly the new technique is capable of detecting the association between separated parts of a surface which has the same cartesian equation while segmenting a scene this aspect is very useful in some industrial applications of range data analysis

spherical principal curves this paper presents a new approach for dimension reduction of data observed on spherical surfaces several dimension reduction techniques have been developed in recent years for non euclidean data analysis as a pioneer work hauberg 2016 attempted to implement principal curves on riemannian manifolds however this approach uses approximations to process data on riemannian manifolds resulting in distorted results this study proposes a new approach to project data onto a continuous curve to construct principal curves on spherical surfaces our approach lies in the same line of hastie and stuetzle 1989 that proposed principal curves for data on euclidean space we further investigate the stationarity of the proposed principal curves that satisfy the self consistency on spherical surfaces the results on the real data analysis and simulation examples show promising empirical characteristics of the proposed approach

resolvents and solutions of weakly singular linear volterra integral equations abstract the structure of the resolvent r t s for a weakly singular matrix function b t s is determined where b t s is the kernel of the linear volterra vector integral equation e x t a t 0 t b t s x s d s and a t is a given continuous vector function using contraction mappings in a banach space of continuous vector functions with an exponentially weighted norm we show that when b t s satisfies certain integral conditions r t s has the form r t s b t s r 1 t s where r 1 t s is the unique continuous solution of the integral equation r 1 t s b 1 t s s t b t u r 1 u s d u and b 1 t s is defined by b 1 t s s t b t u b u s d u as examples the formulas of resolvents for a couple of weakly singular kernels of practical interest are derived we also obtain conditions under which a weakly singular integral equation e has a unique continuous solution x t and show that it can be expressed in terms of r t s by x t a t 0 t r t s a s d s finally we show that there are parallel results for an alternative resolvent r t s and examine when it and r t s are equivalent

a unification theory of krasnoselskii for differential equations abstract the theory of differential equations is very broad and contains many seemingly unrelated types of problems with markedly different methods of solution it is very difficult to discern any unity in the theory yet sixty years ago one of the foremost investigators krasnoselskii suggested the possibility of finding unity he claimed that the inversion of a perturbed differential operator yields the sum of a contraction and compact map accordingly he proved a general fixed point theorem to cover this situation in this paper we begin a long study with a view to putting his idea to the test we begin with fractional differential equations of caputo type continue to neutral functional differential equations and conclude with a study of an old problem of volterra which continues to describe many important real world problems for these problems there is the perfect unity predicted by krasnoselskii it is an invitation to continue the study by examining other important real world problems

a maximum likelihood method for latent class regression involving a censored dependent variable the standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored this model is generalized by developing a conditional mixture maximum likelihood method for latent class censored regression the proposed method simultaneously estimates separate regression functions and subject membership in k latent classes or groups given a censored dependent variable for a cross section of subjects maximum likelihood estimates are obtained using an em algorithm the proposed method is illustrated via a consumer psychology application

riemannian manifold learning recently manifold learning has been widely exploited in pattern recognition data analysis and machine learning this paper presents a novel framework called riemannian manifold learning rml based on the assumption that the input high dimensional data lie on an intrinsically low dimensional riemannian manifold the main idea is to formulate the dimensionality reduction problem as a classical problem in riemannian geometry that is how to construct coordinate charts for a given riemannian manifold we implement the riemannian normal coordinate chart which has been the most widely used in riemannian geometry for a set of unorganized data points first two input parameters the neighborhood size k and the intrinsic dimension d are estimated based on an efficient simplicial reconstruction of the underlying manifold then the normal coordinates are computed to map the input high dimensional data into a low dimensional space experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data preserve radial geodesic distances and yield regular embeddings

a liapunov functional for a singular integral equation abstract we consider a scalar integral equation x t a t 0 t c t s g s x s d s where a l 2 0 while c t s has a significant singularity but is convex when t s 0 we construct a liapunov functional and show that g t x t a t l 2 0 and that x t a t 0 pointwise as t small perturbations are also added to the kernel in addition we consider both infinite and finite delay problems this paper offers a first step toward treating discontinuous kernels with liapunov functionals

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

deriving ultrametric tree structures from proximity data confounded by differential stimulus familiarity this paper presents a new procedure called treefam for estimating ultrametric tree structures from proximity data confounded by differential stimulus familiarity the objective of the proposed treefam procedure is to quantitatively filter out the effects of stimulus unfamiliarity in the estimation of an ultrametric tree a conditional alternating maximum likelihood procedure is formulated to simultaneously estimate an ultrametric tree under the unobserved condition of complete stimulus familiarity and subject specific parameters capturing the adjustments due to differential unfamiliarity we demonstrate the performance of the treefam procedure under a variety of alternative conditions via a modest monte carlo experimental study an empirical application provides evidence that the treefam outperforms traditional models that ignore the effects of unfamiliarity in terms of superior tree recovery and overall goodness of fit

binomial regression with monotone splines a psychometric application abstract a binomial regression function p x models the probability of rj successes in nj trials as a function of the values of an observed covariate xj and or a latent variable j j 1 j this article explores the use of monotone regression splines to define p and applies them to the representation of test items as functions of examinee ability some illustrative data suggest that the flexibility of monotone splines permits the detection of item characteristics not observable using logistic based or log linear approaches a simulation study indicates that estimates of both item characteristic curves and ability are reasonably precise for numbers of items and examinees typical of large university lectures given a set of such binomial regression functions it can be useful to study the principal components of functional variation the extension of multivariate principal components analysis to permit the analysis of many item characteristic curves is described

a model based approach for visualizing the dimensional structure of ordered successive categories preference data a cyclical conditional maximum likelihood estimation procedure is developed for the multidimensional unfolding of two or three way dominance data e g preference choice consideration measured on ordered successive category rating scales the technical description of the proposed model and estimation procedure are discussed as well as the rather unique joint spaces derived we then conduct a modest monte carlo simulation to demonstrate the parameter recovery of the proposed methodology as well as investigate the performance of various information heuristics for dimension selection a consumer psychology application is provided where the spatial results of the proposed model are compared to solutions derived from various traditional multidimensional unfolding procedures this application deals with consumers intending to buy new luxury sport utility vehicles suvs finally directions for future research are discussed

principal points and self consistent points of elliptical distributions the k principal points of a p variate random vector x are those points 1 k r p which approximate the distribution of x by minimizing the expected squared distance of x from the nearest of the j any set of k points y 1 y k partitions r p into domains of attraction d 1 d k according to minimal distance following hastie and stuetzle we call y 1 y k self consistent if e xx d j y j for j 1 k principal points are a special case of self consistent points in this paper we study principal points and self consistent points of p variate elliptical distributions the main results are the following 1 if k self consistent points of x span a subspace of dimension q p then this subspace is also spanned by q principal components that is self consistent points of elliptical distributions exist only in principal component subspaces 2 the subspace spanned by k principal points of x is identical with the subspace spanned by the principal components associated with the largest roots this proves a conjecture of flury we also discuss implications of our results for the computation and estimation of principal points

the byy annealing learning algorithm for gaussian mixture with automated model selection bayesian ying yang byy learning has provided a new mechanism that makes parameter learning with automated model selection via maximizing a harmony function on a backward architecture of the byy system for the gaussian mixture however since there are a large number of local maxima for the harmony function any local searching algorithm such as the hard cut em algorithm does not work well in order to overcome this difficulty we propose a simulated annealing learning algorithm to search the global maximum of the harmony function being expressed as a kind of deterministic annealing em procedure it is demonstrated by the simulation experiments that this byy annealing learning algorithm can efficiently and automatically determine the number of clusters or gaussians during the learning process moreover the byy annealing learning algorithm is successfully applied to two real life data sets including iris data classification and unsupervised color image segmentation

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

weighted likelihood estimation of ability in item response theory applications of item response theory which depend upon its parameter invariance property require that parameter estimates be unbiased a new method weighted likelihood estimation wle is derived and proved to be less biased than maximum likelihood estimation mle with the same asymptotic variance and normal distribution wle removes the first order bias term from mle two monte carlo studies compare wle with mle and bayesian modal estimation bme of ability in conventional tests and tailored tests assuming the item parameters are known constants the monte carlo studies favor wle over mle and bme on several criteria over a wide range of the ability scale

a characterization of monotone unidimensional latent variable models recently the problem of characterizing monotone unidimensional latent variable models for binary repeated measures was studied by ellis and van den wollenberg and by junker we generalize their work with a de finetti like characterization of the distribution of repeated measures x x 1 x 2 that can be represented with mixtures of likelihoods of independent but not identically distributed random variables where the data satisfy a stochastic ordering property with respect to the mixing variable the random variables x j may be arbitrary real valued random variables we show that the distribution of x can be given a monotone unidimensional latent variable representation that is useful in the sense of junker if and only if this distribution satisfies conditional association ca and a vanishing conditional dependence vcd condition which asserts that finite subsets of the variables in x become independent as we condition on a larger and larger segment of the remaining variables in x it is also interesting that the mixture representation is in a certain ordinal sense unique when ca and vcd hold the characterization theorem extends and simplifies the main result of junker and generalizes methods of ellis and van den wollenberg to a much broader class of models exchangeable sequences of binary random variables also satisfy both ca and vcd as do exchangeable sequences arising as location mixtures in the same way that de finetti s theorem provides a path toward justifying standard i i d mixture components in hierarchical models on the basis of our intuitions about the exchangeability of observations this theorem justifies one dimensional latent variable components in hierarchical models in terms of our intuitions about positive association and redundancy between observations because these conditions are on the joint distribution of the observable data x they may also be used to construct asymptotically power 1 tests for unidimensional latent variable models

incremental nonlinear dimensionality reduction by manifold learning understanding the structure of multidimensional patterns especially in unsupervised cases is of fundamental importance in data mining pattern recognition and machine learning several algorithms have been proposed to analyze the structure of high dimensional data based on the notion of manifold learning these algorithms have been used to extract the intrinsic characteristics of different types of high dimensional data by performing nonlinear dimensionality reduction most of these algorithms operate in a batch mode and cannot be efficiently applied when data are collected sequentially in this paper we describe an incremental version of isomap one of the key manifold learning algorithms our experiments on synthetic data as well as real world images demonstrate that our modified algorithm can maintain an accurate low dimensional representation of the data in an efficient manner

parameter selection for principal curves principal curves are nonlinear generalizations of the notion of first principal component roughly a principal curve is a parameterized curve in which passes through the middle of a data cloud drawn from some unknown probability distribution depending on the definition a principal curve relies on some unknown parameters number of segments length turn etc which have to be properly chosen to recover the shape of the data without interpolating in this paper we consider the principal curve problem from an empirical risk minimization perspective and address the parameter selection issue using the point of view of model selection via penalization we offer oracle inequalities and implement the proposed approach to recover the hidden structures in both simulated and real life data

data model conclusion doing it again this paper explores the robustness of conclusions from a statistical model against variations in model choice rather than variations in random sampling and random assignment to treatments which are the usual variations covered by inferential statistics after the problem formulation in section 1 section 2 presents an example from box and tiao in which variation in parent distribution is modeled for a one sample location problem an adaptive bayesian procedure permits to use a weighted mixture of parent distributions rather than choosing just one such as a normal or a uniform distribution in section 3 similar considerations are applied to an event history model for the influence of education and gender on age at first marriage but here the conclusions are hardly influenced by the choice of the duration distribution in section 4 a brief discussion of model choice in factor analysis and structural equation models is followed by a more elaborate treatment of the choice of integer valued slopes for item response functions in the oplm model which is an extension of the rasch model a modest simulation study suggests that adaptive bayesian modeling with a mixture of sets of slopes works better than fixing one set of postulated slopes the paper concludes with some remarks on the roles and sources of prior distributions followed by a short epilogue which argues that simultaneous consideration of a class of models for the same data is sometimes superior to exclusively analyzing the data under one specific model chosen from such a class

a similarity based smoothing approach to nondimensional item analysis the probability that an examinee chooses a particular option within an item is estimated by averaging over the responses to that item of examinees with similar response patterns for the whole test the approach does not presume any latent variable structure or any dimensionality but simulated and actual data analyses are presented to show that when the responses are determined by a latent ability variable this similarity based smoothing procedure can reveal the dimensionality of ability very satisfactorily

on the choice of a model to fit data from an exponential family let x 1 cdots x n be iid observations coming from an exponential family the problem of interest is this given a finite number of models m j smoothly curved manifolds in mathbb r k choose the best model to fit the observations with some penalty for choosing models with dimensions which are too large a result of schwarz is made more specific and is extended to the case where the models are curved manifolds if s y n j is up to a constant c n independent of the model the log of the posterior probability of the j th model where the sample mean y n 1 n sum n i 1 x i has been replaced by y schwarz suggested an asymptotic expansion of s y n j whose leading terms are gamma y n j n sup psi in m j cap theta y psi b psi frac 1 2 k j log n in the case where the models are affine subspaces of mathbb r k we establish a similar asymptotic expansion including the next term with uniform bounds for y in a compact neighborhood of nabla b theta where theta is the true value of the parameter we suggest a criterion for the choice of the best model that consists of maximizing the three leading terms in the expansion s y n j we show that the criterion gives the correct model with probabilities p n theta rightarrow 1 as n rightarrow infty

facaic model selection algorithm for the orthogonal factor model using aic and caic this paper describes the authors fortran algorithm facaic for choosing the number of factors for an orthogonal factor model using akaike s information criterion facaic utilizes the imsl subroutine ofcomm

tail measurability in monotone latent variable models we consider latent variable models for an infinite sequence or universe of manifest observable variables that may be discrete continuous or some combination of these the main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality monotonicity conditional independence andtail measurability tail measurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed the characterizing necessary and sufficient conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence as one conditions upon successively more other manifest variables our main theorem considerably generalizes and sharpens earlier results of ellis and van den wollenberg 1993 holland and rosenbaum 1986 and junker 1993 it is also related to the work of stout 1990 the main theorem is preceded by many results for latent variable modelsin general not necessarily unidimensional and monotone they pertain to the uniqueness of latent variables and are connected with the conditional independence theorem of suppes and zanotti 1981 we discuss new definitions of the concepts of true score and subpopulation which generalize these notions from the stochastic subject random sampling and domain sampling formulations of latent variable models e g holland 1990 lord novick 1968 these definitions do not require the a priori specification of a latent variable model

locally defined principal curves and surfaces principal curves are defined as self consistent smooth curves passing through the middle of the data and they have been used in many applications of machine learning as a generalization dimensionality reduction and a feature extraction tool we redefine principal curves and surfaces in terms of the gradient and the hessian of the probability density estimate this provides a geometric understanding of the principal curves and surfaces as well as a unifying view for clustering principal curve fitting and manifold learning by regarding those as principal manifolds of different intrinsic dimensionalities the theory does not impose any particular density estimation method can be used with any density estimator that gives continuous first and second derivatives therefore we first present our principal curve surface definition without assuming any particular density estimation method afterwards we develop practical algorithms for the commonly used kernel density estimation kde and gaussian mixture models gmm results of these algorithms are presented in notional data sets as well as real applications with comparisons to other approaches in the principal curve literature all in all we present a novel theoretical understanding of principal curves and surfaces practical algorithms as general purpose machine learning tools and applications of these algorithms to several practical problems

model order selection rules for covariance structure classification in radar the adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper this represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties the considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of model order selection mos is exploited to devise suitable decision rules several mos techniques such as the akaike takeuchi and bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed at the analysis stage illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

principal graph and structure learning based on reversed graph embedding many scientific datasets are of high dimension and the analysis usually requires retaining the most important structures of data principal curve is a widely used approach for this purpose however many existing methods work only for data with structures that are mathematically formulated by curves which is quite restrictive for real applications a few methods can overcome the above problem but they either require complicated human made rules for a specific task with lack of adaption flexibility to different tasks or cannot obtain explicit structures of data to address these issues we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding as showcases models that can learn a spanning tree or a weighted undirected ell 1 graph are proposed and a new learning algorithm is developed that learns a set of principal points and a graph structure from data simultaneously the new algorithm is simple with guaranteed convergence we then extend the proposed framework to deal with large scale data experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly

bootstrap choice of estimators in parametric and semiparametric families an extension of eic ishiguro sakamoto et kitagawa 1997 ont propose le eic comme une extension du critere d akaike aic le eic est construit en corrigeant le biais de la log vraisemblance consideree comme un estimateur de l information de kullback leibler par la technique du bootstrap nous developpons ce critere dans un cadre d estimation semi parametrique multivarie et nous montrons qu il peut etre utilise pour choisir un estimateur parmi une famille d estimateurs parametriques et semi parametriques une etude de simulation basee sur un modele de regression montre que l eic est meilleur que les criteres usuels bien que la validation croisee appliquee a la vraisemblance donne des resulats tres proches sauf dans le cas d echantillons de faible taille nous avons applique le eic afin d estimer l evolution moyenne de la charge virale d enfants infectes par le vih

quasi equilibrium closure hierarchies for the boltzmann equation abstract after boltzmann and gibbs the notion of disorder in statistical physics relates to ensembles not to individual states this disorder is measured by the logarithm of ensemble volume the entropy but recent results about measure concentration effects in analysis and geometry allow us to return from the ensemble based point of view to a state based one at least partially in this paper the order disorder problem is represented as a problem of relation between distance and measure the effect of strong order disorder separation for multiparticle systems is described the phase space could be divided into two subsets one of them set of disordered states has almost zero diameter the second one has almost zero measure the symmetry with respect to permutations of particles is responsible for this type of concentration dynamics of systems with strong order disorder separation has high average acceleration squared which can be interpreted as evolution through a series of collisions acceleration dominated dynamics the time arrow direction from order to disorder follows from the strong order disorder separation but inverse for systems in space of symmetric configurations with sticky boundaries the way back from disorder to order is typical natural selection recommendations for mining of molecular dynamics results are also presented

admissible selection of an accurate and parsimonious normal linear regression model let mo be a normal linear regression model and let m1 mk be distinct proper linear submodels of mo let k e 0 k be a model selection rule based on observed data from the true model given k let the unknown parameters of the selected model ms be fitted by the maximum likelihood method a loss function is introduced which depends additively on two parts i a measure of the difference between the fitted model ms and the true model and ii a measure cs of the complexity of the selected model a natural model selection rule k which minimizes an empirical version of this loss is shown to be admissible and very nearly bayes

a case study in pharmacologic colon imaging using principal curves in single photon emission computed tomography in this article we are concerned with functional imaging of the colon to assess the kinetics of microbicide lubricants the overarching goal is to understand the distribution of the lubricants in the colon such information is crucial for understanding the potential impact of microbicides on human immunodeficiency virus transmission the experiment was conducted by imaging a radiolabeled lubricant distributed in the subject s colon the tracer imaging was conducted via single photon emission computed tomography a noninvasive in vivo functional imaging technique we have developed a novel principal curve algorithm to construct a three dimensional curve through the colon images the algorithm was tested and debugged on several difficult two dimensional images of familiar curves where the original principal curve algorithm does not apply the final curve fit to the colon data is compared with experimental sigmoidoscope collection

a unified model for probabilistic principal surfaces principal curves and surfaces are nonlinear generalizations of principal components and subspaces respectively they can provide insightful summary of high dimensional data not typically attainable by classical linear methods solutions to several problems such as proof of existence and convergence faced by the original principal curve formulation have been proposed in the past few years nevertheless these solutions are not generally extensible to principal surfaces the mere computation of which presents a formidable obstacle consequently relatively few studies of principal surfaces are available we previously 2000 proposed the probabilistic principal surface pps to address a number of issues associated with current principal surface algorithms pps uses a manifold oriented covariance noise model based on the generative topographical mapping gtm which can be viewed as a parametric formulation of kohonen s self organizing map building on the pps we introduce a unified covariance model that implements pps 0 1 by varying the clamping parameter spl alpha then we comprehensively evaluate the empirical performance of pps gtm and the manifold aligned gtm on three popular benchmark data sets it is shown in two different comparisons that the pps outperforms the gtm under identical parameter settings convergence of the pps is found to be identical to that of the gtm and the computational overhead incurred by the pps decreases to 40 percent or less for more complex manifolds these results show that the generalized pps provides a flexible and effective way of obtaining principal surfaces

a new item response theory modeling approach with applications to unidimensionality assessment and ability estimation using an infinite item test framework it is argued that the usual assumption of local independence be replaced by a weaker assumption essential independence a fortiori the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriatestatistically testable assumption of essential unidimennsionality essential unidimennsionnality implies the existence of a unique unidimensional latent ability essential unidimensionality is equivalent to the consistent estimation of this latnet ability in an ordinal scaling sense using anybalanced empirical scaling a variation of this estimation approach allows consistent estimation of ability on the given latent ability scale

regularization free principal curve estimation principal curves and manifolds provide a framework to formulate manifold learning within a statistical context principal curves define the notion of a curve passing through the middle of a distribution while the intuition is clear the formal definition leads to some technical and practical difficulties in particular principal curves are saddle points of the mean squared projection distance which poses severe challenges for estimation and model selection this paper demonstrates that the difficulties in model selection associated with the saddle point property of principal curves are intrinsically tied to the minimization of the mean squared projection distance we introduce a new objective function facilitated through a modification of the principal curve estimation approach for which all critical points are principal curves and minima thus the new formulation removes the fundamental issue for model selection in principal curve estimation a gradient descent based estimator demonstrates the effectiveness of the new formulation for controlling model complexity on numerical experiments with synthetic and real data

bayesian estimation in the three parameter logistic model a bayesian procedure is developed for the estimation of parameters in the two parameter logistic item response model joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described through simulation studies it is shown that bayesian estimates of the parameters are superior to maximum likelihood estimates in the sense that they are a more meaningful since they do not drift out of range and b more accurate in that they result in smaller mean squared differences between estimates and true values

filter order selection in adaptive maximum likelihood estimation the choice of the number of parameters is an important problem in adaptive filtering in the general ground of maximum likelihood ml parameter estimation akaike criterion has proved to be a very useful tool significant results and the importance of the kullback information measure as the implicit measure of distance associated with ml estimation are discussed application of these results to adaptive filtering is then considered for time invariant and time varying parametric models the corresponding practical forms of akaike criterion are given in the time varying case this criterion may be used as a way to fit the model into the nonstationarity of an exact filter the possible generalization of the akaike criterion to non ml estimation is discussed and application is made for weighted least squares estimation a more general approach to the nonstationary case is given by assuming a linear stochastic model for the vector of the filter coefficients in which case the ml estimate is computed recursively using the kalman filtering equation then the random sequence of kalman gains is close to a deterministic average sequence this sequence may be precomputed and gives an optimal choice for the gain matrices in an adaptive gradient type filter

identification of piecewise affine systems based on statistical clustering technique this paper is concerned with the identification of a class of piecewise affine systems called a piecewise affine autoregressive exogenous pwarx model the pwarx model is composed of arx sub models each of which corresponds to a polyhedral region of the regression space under the temporary assumption that the number of sub models is known a priori the input output data are collected into several clusters by using a statistical clustering algorithm we utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space in each cluster the parameter vector of the sub model is obtained by the least squares method it turns out that the present statistical clustering approach enables us to estimate the number of sub models based on the information criteria such as caic and mdl the estimate of the number of sub models is performed by applying the identification procedure several times to the same data set after having fixed the number of sub models to different values finally we verify the applicability of the present identification method through a numerical example of a hammerstein model

the mean shift algorithm and its relation to kernel regression we investigate the connection between the asymptotic bias of the well known nadaraya watson kernel regression and the mean shift ms vector with the gaussian kernel we first show that the asymptotic bias for the univariate nadaraya watson kernel regression can be estimated using the ms scalar then we investigate the general d dimensional case d 1 and derive a formula for the asymptotic bias as a function of the ms vector we show that when the regression function is a linear function of its entries then the asymptotic bias can be represented as a linear function of the ms vector the ms algorithm for the univariate and the linear cases can be used to find points where the nadaraya watson kernel regression gives an unbiased estimate furthermore this connection suggests that exploiting the theoretical properties of the asymptotic bias of the nadaraya watson kernel regression may be helpful to show the convergence of the ms algorithm through the simulations we show that how the given theoretical results can be used to estimate the bias of the estimated clean signal by just observing the noisy signal having access to the bias of the estimator enables us to evaluate the accuracy of the estimated clean data which later will be used to design a quantizer

on model selection and the arc sine laws generalizations of the arc sine laws are shown to provide insight into the operating characteristics of certain techniques for selecting models to fit a given data set when the available models are nested as a corollary one sees that a popular technique may be expected to include about one superfluous parameter even if the sample size is large

the derivation of some tests for the rasch model from the multinomial distribution the present paper is concerned with testing the fit of the rasch model it is shown that this can be achieved by constructing functions of the data on which model tests can be based that have power against specific model violations it is shown that the asymptotic distribution of these tests can be derived by using the theoretical framework of testing model fit in general multinomial and product multinomial models the model tests are presented in two versions one that can be used in the context of marginal maximum likelihood estimation and one that can be applied in the context of conditional maximum likelihood estimation

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

the chic model a global model for coupled binary data often problems result in the collection of coupled data which consist of different n way n mode data blocks that have one or more modes in common to reveal the structure underlying such data an integrated modeling strategy with a single set of parameters for the common mode s that is estimated based on the information in all data blocks may be most appropriate such a strategy implies a global model consisting of different n way n mode submodels and a global loss function that is a weighted sum of the partial loss functions associated with the different submodels in this paper such a global model for an integrated analysis of a three way three mode binary data array and a two way two mode binary data matrix that have one mode in common is presented a simulated annealing algorithm to estimate the model parameters is described and evaluated in a simulation study an application of the model to real psychological data is discussed

high snr consistent linear model order selection and subset selection high snr consistency of model order selection criteria in linear regression models has attracted a lot of attention in the signal processing community recently it is now known that exponentially embedded family versions of minimum description length etc are high snr consistent however a general framework for high snr consistency in linear regression is still missing this paper fills this gap by deriving necessary and sufficient conditions nscs for model order selection criteria in both known and unknown noise variance situations to be high snr consistent many popular model order selection criteria are proved to be high snr consistent using these nscs we also provide a convergence rate analysis to discriminate between various high snr consistent model order selection criteria a direct application of model order selection techniques to the very important subset selection problem is computationally infeasible this paper establish the high snr consistency of an existing t statistics based index ordering scheme that allows the conversion of a subset selection problem into a model order selection problem combining this index ordering with high snr consistent model order selection criteria leads to a novel subset selection procedure ssp that is numerically shown to outperform existing high snr consistent ssps

a multidimensional item response model constrained latent class analysis using the gibbs sampler and posterior predictive checks in this paper it will be shown that a certain class of constrained latent class models may be interpreted as a special case of nonparametric multidimensional item response models the parameters of this latent class model will be estimated using an application of the gibbs sampler it will be illustrated that the gibbs sampler is an excellent tool if inequality constraints have to be taken into consideration when making inferences model fit will be investigated using posterior predictive checks checks for manifest monotonicity the agreement between the observed and expected conditional association structure marginal local homogeneity and the number of latent classes will be presented

a bottom up algorithm for finding principal curves with applications to image skeletonization this paper proposes a new method for finding principal curves from data sets motivated by solving the problem of highly curved and self intersecting curves we present a bottom up strategy to construct a graph called a principal graph for representing a principal curve the method initializes a set of vertices based on principal oriented points introduced by delicado and then constructs the principal graph from these vertices through a two layer iteration process in inner iteration the kernel smoother is used to smooth the positions of the vertices in outer iteration the principal graph is spanned by minimum spanning tree and is modified by detecting closed regions and intersectional regions and then new vertices are inserted into some edges in the principal graph we tested the algorithm on simulated data sets and applied it to image skeletonization experimental results show the effectiveness of the proposed algorithm

optimal product positioning based on paired comparison data a new approach for analyzing paired comparison data is proposed which combines a probabilistic ideal point model with product positioning issues unlike traditional approaches based on paired comparison data the same formulation is used for estimating a joint space representation of consumer segments and products as well as for determining optimal new product positioning options in a relevant product market a monte carlo experiment is presented and real world coffee market data are used to show advantages of the new approach

mixtures of constrained ultrametric trees this paper presents a new methodology concerned with the estimation of ultrametric trees calibrated on subjects pairwise proximity judgments of stimuli capturing subject heterogeneity using a finite mixture formulation we assume that a number of unobserved classes of subjects exist each having a different ultrametric tree structure underlying the pairwise proximity judgments a new likelihood based estimation methodology is presented for those finite mixtures of ultrametric trees that accommodates ultrametric as well as other external constraints various assumptions on the correlation of the error of the dissimilarities are accommodated the performance of the method to recover known ultrametric tree structures is investigated on synthetic data an empirical application to published data from schiffman reynolds and young 1981 is provided the ability to deal with external constraints on the tree topology is demonstrated and a comparison with an alternative clustering based method is made

semiparametric estimation of count regression models this paper develops a semiparametric estimation approach for mixed count regression models based on series expansion for the unknown density of the unobserved heterogeneity we use the generalized laguerre series expansion around a gamma baseline density to model unobserved heterogeneity in a poisson mixture model we establish the consistency of the estimator and present a computational strategy to implement the proposed estimation techniques in the standard count model as well as in truncated censored and zero inflated count regression models monte carlo evidence shows that the finite sample behavior of the estimator is quite good the paper applies the method to a model of individual shopping behavior

factor analysis and aic the information criterion aic was introduced to extend the method of maximum likelihood to the multimodel situation it was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis the use of the aic criterion in the factor analysis is particularly interesting when it is viewed as the choice of a bayesian model this observation shows that the area of application of aic can be much wider than the conventional i i d type models on which the original derivation of the criterion was based the observation of the bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings

regularized principal manifolds many settings of unsupervised learning can be viewed as quantization problems the minimization of the expected quantization error subject to some restrictions this allows the use of tools such as regularization from the theory of supervised risk minimization for unsupervised learning this setting turns out to be closely related to principal curves the generative topographic map and robust coding we explore this connection in two ways 1 we propose an algorithm for finding principal manifolds that can be regularized in a variety of ways and 2 we derive uniform convergence bounds and hence bounds on the learning rates of the algorithm in particular we give bounds on the covering numbers which allows us to obtain nearly optimal learning rates for certain types of regularization operators experimental results demonstrate the feasibility of the approach