the graded witt group kernel of biquadratic extensions in characteristic two baeza showed that when char f 2 if e f is the separable biquadratic extension e f 1 b1 1 b2 then ker wq f wq e wf 1 b1 wf 1 b2 here we give the analogous result for the graded witt group specifically we obtain an exact sequence f n 1 f n 1 h2n 1f h2n 1e from which the result for gwqf follows by the isomorphisms of kato applications to 2 algebras of exponent and index 4 are also given

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

on the brauer group complex for a multiquadratic field extension abstract let f be a field of characteristic not 2 a 1 a n f m f a 1 a n let further g be the subgroup of f f 2 generated by a 1 a n for any i 1 n put a i i i a i a 1 consider the complex i k i k i 2 g f f 2 br 2 f res br 2 m n m e f e m m e 2 br 2 e where k i f a i are all the quadratic extensions of f containing in m w i i a i n k i f w i a i z a i z the homology group of this complex at i 1 th term from the left is denoted by h i m f independently of char f we give examples of these complexes with nontrivial h 3 m f and prescribed n 3 and a 1 a n 1 also similar examples concerning the group h 1 m f are constructed

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

random calibration with many measurements an application of stein estimation in the problem considered a vector of many imprecise measurements e g spectroscopic is used to linearly predict a quantity whose precise measurement is difficult or expensive the regression vector is estimated from a calibration experiment having both types of measurements for a random sample most previous approaches to this problem adjust for approximate multicollinearity which often results from the correlations among the imprecise measurements by inverting an approximation e g factor analytic to their covariance matrix in the approach here it is argued that the regression vector should lie in a lower dimensional suhspace determined by the principal components of the covariance matrix it is then estimated by applying a stein contraction of the least squares estimator to the principal components regression estimator examples using real data are presented in which the proposed estimator substantially improves on the ordinary least squares estimation

witt rings and brauer groups under multiquadratic extensions ii let f be a field of characteristic not 2 and suppose m is a multiquadratic extension of f that is m f is a finite abelian extension of exponent 2 so that m f for some finite subgroup g e f f where f 0 in studying brauer groups and products of quaternion algebras the second author was led to consider the homology groups n m f of a certain complex gm f associated to the extension m f this complex appears in 11 3 1 301 and in 1 1 below the purpose of the present work is to investigate the first homology group n m f and to exhibit its close connections with quadratic form theory the higher homology groups are examined in 11 301 the field f is said to have property pi n if n m f 1 for every multiquadratic extension m f with m f q 2 properties p l and p 2 always hold but there are examples 29 of fields f for which p 3 fails these examples are generalized in section 5

rigid and articulated point registration with expectation conditional maximization this paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration the problem is recast into a missing data framework where unknown correspondences are handled via mixture models adopting a maximum likelihood principle we introduce an innovative em like algorithm namely the expectation conditional maximization for point registration ecmpr algorithm the algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case we analyze in detail the associated consequences in terms of estimation of the registration parameters and propose an optimal method for estimating the rotational and translational parameters based on semidefinite positive relaxation we extend rigid registration to articulated registration robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the gaussian mixture model at hand we provide an in depth analysis of our method and compare it both theoretically and experimentally with other robust methods for point registration

hausdorff s moment problem and expansions in legendre polynomials abstract a new proof is given for hausdorff s condition on a set of moments which determines when the function generating these moments is in l2 the proof uses legendre polynomials and their discrete extensions found by tchebychef then an extension is given to a weighted l2 space using jacobi polynomials and their discrete extensions author

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter

discriminative feature selection for on line signature verification abstract on line handwritten signatures are collected as real time dynamical signals which are written on collective devices by users since individuals have different writing habits consistent and discriminative features should be selected to distinguish genuine signatures from forged signatures in this paper two methods which are based on full factorial experiment design and optimal orthogonal experiment design are proposed for selecting discriminative features among candidates to improve the robustness consistency of feature is analyzed at first and more consistent features are selected as candidates for discriminative feature selection to reduce the influences of fluctuations caused by internal and external writing environments changes before verification signatures are effectively aligned to their reference templates based on gaussian mixture model a modified dynamic time warping with signature curve constraint is presented for verification to improve the efficiency comprehensive experiments are implemented based on the data of the open access databases mcyt and svc2004 task2 experimental results verify the effectiveness and robustness of our proposed methods

bayesian variable selection in linear regression abstract this article is concerned with the selection of subsets of predictor variables in a linear regression model for the prediction of a dependent variable it is based on a bayesian approach intended to be as objective as possible a probability distribution is first assigned to the dependent variable through the specification of a family of prior distributions for the unknown parameters in the regression model the method is not fully bayesian however because the ultimate choice of prior distribution from this family is affected by the data it is assumed that the predictors represent distinct observables the corresponding regression coefficients are assigned independent prior distributions for each regression coefficient subject to deletion from the model the prior distribution is a mixture of a point mass at 0 and a diffuse uniform distribution elsewhere that is a spike and slab distribution the random error component is assigned a normal distribution with mean 0 and standard deviation

inverse groundwater modeling for hydraulic conductivity estimation using bayesian model averaging and variance window 1 this study proposes a bayesian model averaging bma method to address parameter estimation uncertainty arising from nonuniqueness in parameterization methods bma is able to incorporate multiple parameterization methods for prediction through the law of total probability and to obtain an ensemble average of hydraulic conductivity estimates two major issues in applying bma to hydraulic conductivity estimation are discussed the first problem is using occam s window in usual bma applications to measure approximated posterior model probabilities occam s window only accepts models in a very narrow range tending to single out the best method and discard other good methods we propose a variance window to replace occam s window to cope with this problem the second problem is the kashyap information criterion kic in the approximated posterior model probabilities which tends to prefer highly uncertain parameterization methods by considering the fisher information matrix with sufficient amounts of observation data the bayesian information criterion bic is a good approximation and is able to avoid controversial results from using kic this study adopts multiple generalized parameterization gp methods such as the bma models to estimate spatially correlated hydraulic conductivity numerical examples illustrate the issues of using kic and occam s window and show the advantages of using bic and the variance window in bma application finally we apply bma to the hydraulic conductivity estimation of the 1500 foot sand in east baton rouge parish louisiana

better subset regression using the nonnegative garrote a new method called the nonnegative nn garrote is proposed for doing subset regression it both shrinks and zeroes coefficients in tests on real and simulated data it produces lower prediction error than ordinary subset selection it is also compared to ridge regression if the regression equations generated by a procedure do not change drastically with small changes in the data the procedure is called stable subset selection is unstable ridge is very stable and the nn garrote is intermediate simulation results illustrate the effects of instability on prediction error

on the structure of pythagorean fields abstract in this paper we study in detail the relationship between fans and valuations first uncovered by brocker see 2 our techniques are somewhat different as our valuations are constructed by brute force from the properties of the fields involved this approach has the advantage in that the valuation theory it yields can be directly related to the structure theory for spaces of orderings as developed by murray marshall see 11 14 we also discuss several applications which include results in k theory

examples of non rational varieties of adjoint groups let k be a field of characteristic 2 and k a separable closure of k s we say that an algebraic variety xrk is stably k rational if there exist two m n m n w x affine spaces a a and a k rational map a x f a merkurjev 9 k k gave a criterion of stable k rationality for the adjoint classical groups with absolute rank f 3 which covers the case of the variety pso q for any quadratic form qrk of rank f 6 this criterion gives examples of field k and quadratic form q of rank 6 with non trivial signed discriminant such that the variety pso q is not stably k rational the main result of this paper is the following

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

numerical solution of the finite moment problem in a reproducing kernel hilbert space in this work we present a method for evaluating the normal solution of the finite moment problem in the hypothesis that the solution satisfies two linear boundary conditions and the moments are noisy numerical results are presented to illustrate the stability and obtainable accuracy of the method

predictive model selection we consider the problem of selecting one model from a large class of plausible models a predictive bayesian viewpoint is advocated to avoid the specification of prior probabilities for the candidate models and the detailed interpretation of the parameters in each model using criteria derived from a certain predictive density and a prior specification that emphasizes the observables we implement the proposed methodology for three common problems arising in normal linear models variable subset selection selection of a transformation of predictor variables and estimation of a parametric variance function interpretation of the relative magnitudes of the criterion values for various models is facilitated by a calibration of the criteria relationships between the proposed criteria and other well known criteria are examined

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

a fast algorithm for generalized hankel matrices arising in finite moment problems abstract consider an n n lower triangular matrix l whose i 1 st row is defined by the coefficients of the real polynomial p i x of degree i such that p i x is a set of orthogonal polynomials satisfying a standard three term recurrence relation if h is an n n real hankel matrix with nonsingular leading principal submatrices then h lhl t will be referred to as a strongly nonsingular hankel matrix with respect to the orthogonal polynomial basis p i x in this paper we develop an efficient o n 2 algorithm for the solution of a system of linear equations with a real symmetric coefficient matrix h which is a hankel matrix with respect to a suitable orthogonal polynomial basis this leads to an efficient method for computing polynomial approximations of an unknown function given its modified moments

signature alignment based on gmm for on line signature verification on line handwritten signatures are collected as real time dynamical signals which are written on collective devices by users since writing environments are always changed fluctuations can be caused by signature size location and rotation angle which being various at each inputting signatures should be effectively aligned before verification which can diminish deviations caused by these fluctuations in this study we propose a method of signature alignment based on gaussian mixture model to obtain the best matching in verification a modified dynamic time warping with signature curve constraint is presented to improve the efficiency weight factors are dynamically assigned to features which depend on coefficient of variation to improve the robustness several experiments are implemente d on the open access on line signature databases mcyt and svc2004 task2 the best performances can be provided with equal error rates 2 15 and 2 63 respectively experimental results indicate the effectiveness and robustness of our proposed method signatures are aligned well to reference template based on gaussian mixture model before verification efficiency of verification is improved by modified dynamic time warping with signature curve constraint distance probability is presented to describe the dissimilarity between test signatures and references a strategy of dynamic weight factors being assigned to features depend on coefficient of variation

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

on the solution of the finite moment problem abstract in this work we propose a method to obtain the normal solution of the finite moment problem both in the absence and in the presence of linear boundary constraints the method gives the normal solution as a linear combination of jacobi polynomials and furnishes its coefficients in terms of the moments a number of examples are given to illustrate the strength of the method

orthogonal involutions on central simple algebras and function fields of severi brauer varieties abstract an orthogonal involution on a central simple algebra a after scalar extension to the function field f a of the severi brauer variety of a is adjoint to a quadratic form q over f a which is uniquely defined up to a scalar factor some properties of the involution such as hyperbolicity and isotropy up to an odd degree extension of the base field are encoded in this quadratic form meaning that they hold for the involution if and only if they hold for q as opposed to this we prove that there exists non totally decomposable orthogonal involutions that become totally decomposable over f a so that the associated form q is a pfister form we also provide examples of nonisomorphic involutions on an index 2 algebra that yield similar quadratic forms thus proving that the form q does not determine the isomorphism class of even when the underlying algebra has index 2 as a consequence we show that the e 3 invariant for orthogonal involutions is not classifying in degree 12 and does not detect totally decomposable involutions in degree 16 as opposed to what happens for quadratic forms

using geometric extrema for segment to segment characteristics comparison in online signature verification abstract a signature verification algorithm based on a segment to segment matching is described in which a new approach for finding segment to segment correspondence is proposed in the proposed method geometric extrema are used as segmenting boundaries with two reasons 1 extrema are reproduced with high stability and 2 the properties of extrema are useful in finding segment to segment correspondence in this paper a set of rules for legitimate correspondence between extrema is defined based on their properties which is utilized for the similarity evaluation between segments dynamic programming is then applied to find an optimal correspondence map through experiments the proposed algorithm is assessed to be effective in improving discriminative ability we also showed that the overall performance is further improved by combining the proposed method with the traditional global parametric algorithm

piecewise polynomial estimation of a regression function we deal with the problem of choosing a piecewise polynomial estimator of a regression function s mapping 0 1 p into r in a first part of this paper we consider some collection of piecewise polynomial models each model is defined by a partition m of 0 1 p and a series of degrees d d j j m nm we propose a penalized least squares criterion which selects a model whose associated piecewise polynomial estimator performs approximately as well as the best one in the sense that its quadratic risk is close to the infimum of the risks the risk bound we provide is nonasymptotic in a second part we apply this result to tree structured collections of partitions which look like the one constructed in the first step of the cart algorithm and we propose an extension of the cart algorithm to build a piecewise polynomial estimator of a regression function

the transfer ideal of quadratic forms and a hasse norm theorem mod squares any finite degree field extension k f determines an ideal jk f of the witt ring wf of f called the transfer ideal which is the image of any nonzero transfer map wk wf the ideal 59k f is computed for certain field extensions concentrating on the case where k has the form f va a ai e f when f and k are global fields we investigate whether there is a local global principle for membership in tkifthis is shown to be equivalent to the existence of a hasse norm theorem mod squares i e a local global principle for the image of the norm map nk f k k 2 f f 2 it is shown that such a hasse norm theorem holds whenever k f aj va although it does not always hold for more general extensions of global fields even some galois extensions with group z 2z x z 4z

why bandwidth selectors tend to choose smaller bandwidths and a remedy summary this note is concerned with the problem of automatic data driven bandwidth selectors for nonparametric regression though some selectors were shown to be consistent and asymptotically unbiased by rice 1984 and hardle hall marron 1988 it is often observed in simulation studies that most selectors are biased toward undersmoothing an explanation for this is given the source of the large sample variation in the bandwidth estimates is also pointed out this leads to the consideration of a new procedure which is a simple modification of a classical selector a simulation study suggests that the proposed selector is much more consistent than the classical one

point set registration coherent point drift point set registration is a key component in many computer vision tasks the goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other multiple factors including an unknown nonrigid spatial transformation large dimensionality of point set noise and outliers make the point set registration a challenging problem we introduce a probabilistic method called the coherent point drift cpd algorithm for both rigid and nonrigid point set registration we consider the alignment of two point sets as a probability density estimation problem we fit the gaussian mixture model gmm centroids representing the first point set to the data the second point set by maximizing the likelihood we force the gmm centroids to move coherently as a group to preserve the topological structure of the point sets in the rigid case we impose the coherence constraint by reparameterization of gmm centroid locations with rigid parameters and derive a closed form solution of the maximization step of the em algorithm in arbitrary dimensions in the nonrigid case we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation we also introduce a fast algorithm that reduces the method computation complexity to linear we test the cpd algorithm for both rigid and nonrigid transformations in the presence of noise outliers and missing points where cpd shows accurate results and outperforms current state of the art methods

robust point matching for nonrigid shapes by preserving local neighborhood structures in previous work on point matching a set of points is often treated as an instance of a joint distribution to exploit global relationships in the point set for nonrigid shapes however the local relationship among neighboring points is stronger and more stable than the global one in this paper we introduce the notion of a neighborhood structure for the general point matching problem we formulate point matching as an optimization problem to preserve local neighborhood structures during matching our approach has a simple graph matching interpretation where each point is a node in the graph and two nodes are connected by an edge if they are neighbors the optimal match between two graphs is the one that maximizes the number of matched edges existing techniques are leveraged to search for an optimal solution with the shape context distance used to initialize the graph matching followed by relaxation labeling updates for refinement extensive experiments show the robustness of our approach under deformation noise in point locations outliers occlusion and rotation it outperforms the shape context and tps rpm algorithms on most scenarios

legendre polynomials based feature extraction for online signature verification consistency analysis of feature combinations in this paper feature combinations associated with the most commonly used time functions related to the signing process are analyzed in order to provide some insight on their actual discriminative power for online signature verification a consistency factor is defined to quantify the discriminative power of these different feature combinations a fixed length representation of the time functions associated with the signatures based on legendre polynomials series expansions is proposed the expansion coefficients in these series are used as features to model the signatures two different signature styles namely western and chinese from a publicly available signature database are considered to evaluate the performance of the verification system two state of the art classifiers namely support vector machines and random forests are used in the verification experiments error rates comparable to the ones reported over the same signature datasets in a recent signature verification competition show the potential of the proposed approach the experimental results also show that there is a good correlation between the consistency factor and the verification errors suggesting that consistency values could be used to select the optimal feature combination highlightsa feature extraction approach based on legendre series representation of the time functions associated with the signatures is proposed a consistency factor is proposed to quantify the discriminative power of different combinations of the time functions the correlation between the proposed consistency factor and the verification performance of a feature combination is analyzed a recent signature database containing western and chinese signatures is used the verification performance is quantified based on log likelihood ratios

robust point set registration using gaussian mixture models in this paper we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers the key idea of this registration framework is to represent the input point sets using gaussian mixture models then the problem of point set registration is reformulated as the problem of aligning two gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized we show that the popular iterative closest point icp method and several existing point set registration methods in the field are closely related and can be reinterpreted meaningfully in our general framework our instantiation of this general framework is based on the the l2 distance between two gaussian mixtures which has the closed form expression and in turn leads to a computationally efficient registration algorithm the resulting registration algorithm exhibits inherent statistical robustness has an intuitive interpretation and is simple to implement we also provide theoretical and experimental comparisons with other robust methods for point set registration

bandwidth selection for indirect density estimation based on corrupted histogram data abstract motivated by a number of practical applications we consider a class of indirect nonparametric density estimation problems in which the observed data consist of a histogram of binned empirically corrected counts due to variability in the process of correction the histogram cannot be modeled in terms of simple scaled poisson statistics this departure necessitates the development of a new methodology for bandwidth selection a variant of the method of unbiased risk estimation is proposed the methodology is studied using numerical simulations and asymptotic analysis tools in the context of a class of idealized density deconvolution problems the methodology is adapted for application to the practical reconstruction problem of positron emission tomography pet realistic numerical simulations and physical phantom data are presented to validate the approach in this setting some illustrations with cerebral glucose utilization and myocardial blood flow studies from some actual patient data sets

nonparametric variable selection the earth algorithm we consider regression experiments involving a response variable y and a large number of predictor variables x1 xd many of which may be irrelevant for the prediction of y and thus must be removed before y can be predicted from the x s we consider two procedures that select variables by using importance scores that measure the strength of the relationship between predictor variables and a response and keep those variables whose importance scores exceed a threshold in the first of these procedures scores are obtained by randomly drawing subregions tubes of the predictor space that constrain all but one predictor and in each subregion computing a signal to noise ratio efficacy based on a nonparametric univariate regression of y on the unconstrained variable the subregions are adapted to boost weak variables iteratively by searching hunting for the subregions in which the efficacy is maximized the efficacy can be viewed as an approximation to a one to one function of the probability of identif

variable selection via gibbs sampling abstract a crucial problem in building a multiple regression model is the selection of predictors to include the main thrust of this article is to propose and develop a procedure that uses probabilistic considerations for selecting promising subsets this procedure entails embedding the regression setup in a hierarchical normal mixture model where latent variables are used to identify subset choices in this framework the promising subsets of predictors can be identified as those with higher posterior probability the computational burden is then alleviated by using the gibbs sampler to indirectly sample from this multinomial posterior distribution on the set of possible subset choices those subsets with higher probability the promising ones can then be identified by their more frequent appearance in the gibbs sample

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation