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 general hankel norm approximation scheme for linear recursive filtering let x t and y t be stochastic processes which are weakly stationary and stationarily correlated we consider the problem of finding an approximate recursive low dimensional filter of x t based on the observation of the past of y t using hankel norm techniques several estimation problems have been investigated in the past using these techniques we present here a general framework which includes many of these approaches as special cases we also discuss some new applications the approximate filter so constructed allows for an a priori bound on the estimation error

hankel norm approximation of a rational function using stochastic realizations abstract in this paper we present a new proof of the classical adamyan arov krein theorem on the approximation of rational functions in hankel norm let y t t z be a scalar valued stationary process we define a hankel operator h with singular values which are equal to the canonical correlations between the past and the future of y we approximate this hankel operator by h k using a finite dimensional realization of the process y and show that the singular values of h k coincide with the canonical correlations between two suitably defined subspaces

note on ultrametric hierarchical clustering algorithms milligan presented the conditions that are required for a hierarchical clustering strategy to be monotonic based on a formula by lance and williams in the present paper the statement of the conditions is improved and shown to provide necessary and sufficient conditions

gindclus generalized indclus with external information a generalized indclus model termed gindclus is presented for clustering three way two mode proximity data in order to account for the heterogeneity of the data both a partition of the subjects into homogeneous classes and a covering of the objects into groups are simultaneously determined furthermore the availability of information which is external to the three way data is exploited to better account for such heterogeneity the weights of both classifications are linearly linked to external variables allowing for the identification of meaningful classes of subjects and groups of objects the model is fitted in a least squares framework and an efficient alternating least squares algorithm is provided an extensive simulation study and an application on benchmark data are also presented

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

acausal models and balanced realizations of stationary processes abstract we study acausal realizations of stationary or stationary increment processes in particular we characterize the family of models whose corresponding spectral factors have a fixed zero structure acausal models with a fixed zero structure are related to each other by a certain group of state feedback transformations which is naturally parametrized by the solution set of a homogeneous algebraic riccati equation each feedback transformation reflects some of the eigenvalues of the generator matrix a of the representation to a mirror image with respect to the imaginary axis dually acausal models with a fixed pole structure are parametrized by a dual riccati equation and by a corresponding family of output injection transformations from a general standpoint the results of this study clarify the role played by dual pairs of riccati equations in spectral factorization and may be relevant to other problem areas than stochastic modelling one natural application of the concepts discussed in the paper is to stochastic balancing balancing of models with an essentially arbitrary eigenvalue location can be accomodated very naturally in this framework a balancing algorithm involving the solution of a dual pair of riccati equations is discussed

canonical correlations of past inputs and future outputs for linear stochastic systems the dependence of future outputs on past inputs in a stochastic system is investigated by means of the canonical correlation analysis in particular a classification of minimal stochastic realizations of a given process with respect to the information transmitted from past inputs to future outputs is presented the results are then rephrased in terms of certain block hankel matrices and their relevance for the hankel norm approximation of stochastic systems is discussed

extended similarity trees proximity data can be represented by an extended tree which generalizes traditional trees by including marked segments that correspond to overlapping clusters an extended tree is a graphical representation of the distinctive features model a computer program extree that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data

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

on the distribution of zeros of solutions of first order delay differential equations abstract this paper contains new estimates for the distance between adjacent zeros of solutions of the first order delay differential equation x t p t x t 0 where p is a nonnegative continuous function our results are new and improve some known criteria illustrative examples are given to show the strength of some obtained results over the known ones

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

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

optimal angle reduction a behavioral approach to linear system approximation we investigate the problem of optimal state reduction under minimization of the angle between system behaviors the angle is defined in a worst case sense as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model this problem is analyzed for linear time invariant finite dimensional systems in a behavioral l2 setting without reference to input output decompositions and stability considerations the notion of a weakest past future link is introduced and it is shown how this concept is applied for the purpose of model reduction a method that reduces the state dimension by one is presented and shown to be optimal specific algorithms are provided for the numerical implementation of the approximation method the concepts and results are explicitly translated to an input output setting and related to balancing hankel norm reduction and normalized doubly coprime factorizations

generic oscillations for delay differential equations in this article we study oscillation and nonoscillation of the solutions of linear delay differential equations we define generic oscillation and generic nonoscillation as a topological assessment of the extent of oscillatory or nonoscillatory solutions of a delay differential equation we provide sufficient conditions for both phenomena based on the roots of the characteristic equation and concrete conditions for some special cases

clustering with relational constraint the paper deals with clustering problems where grouping is constrained by a symmetric and reflexive relation for solving clustering problems with relational constraints two methods are adapted the standard hierarchical clustering procedure based on the lance and williams formula and local optimization procedure cludia to illustrate these procedures clusterings of the european countries are given based on the developmental indicators where the relation is determined by the geographical neighbourhoods of countries

the k indscal model for heterogeneous three way dissimilarity data a weighted euclidean distance model for analyzing three way dissimilarity data stimuli by stimuli by subjects for heterogeneous subjects is proposed first it is shown that indscal may fail to identify a common space representative of the observed data structure in presence of heterogeneity a new model that removes the rotational invariance of the classical multidimensional scaling problem and specifies k common homogeneous spaces is proposed the model called mixture indscal in k classes or briefly k indscal still includes individual saliencies however the large number of parameters in k indscal may produce instability of the estimates and therefore a parsimonious model will also be discussed the parameters of the model are estimated in a least squares fitting context and an efficient coordinate descent algorithm is given the usefulness of k indscal is demonstrated by both artificial and real data analyses

a least squares algorithm for fitting additive trees to proximity data a least squares algorithm for fitting additive trees to proximity data is described the algorithm uses a penalty function to enforce the four point condition on the estimated path length distances the algorithm is evaluated in a small monte carlo study finally an illustrative application is presented