lle score a new filter based unsupervised feature selection method based on nonlinear manifold embedding and its application to image recognition the task of feature selection is to find the most representative features from the original high dimensional data because of the absence of the information of class labels selecting the appropriate features in unsupervised learning scenarios is much harder than that in supervised scenarios in this paper we investigate the potential of locally linear embedding lle which is a popular manifold learning method in feature selection task it is straightforward to apply the idea of lle to the graph preserving feature selection framework however we find that this straightforward application suffers from some problems for example it fails when the elements in the feature are all equal it does not enjoy the property of scaling invariance and cannot capture the change of the graph efficiently to solve these problems we propose a new filter based feature selection method based on lle in this paper which is named as lle score the proposed criterion measures the difference between the local structure of each feature and that of the original data our experiments of classification task on two face image data sets an object image data set and a handwriting digits data set show that lle score outperforms state of the art methods including data variance laplacian score and sparsity score

analytic smoothing for equipercentile equating under the common item nonequivalent populations design a cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described statistical techniques based on bootstrap estimation are presented that are designed to aid in choosing an equating method degree of smoothing these include a asymptotic significance tests that compare no equating and linear equating to equipercentile equating b a scheme for estimating total equating error and for dividing total estimated error into systematic and random components the smoothing technique and statistical procedures are explored and illustrated using data from forms of a professional certification test

orthogonal polynomials in transport theories the asymptotical k co behaviour of zeros of the polynomials g v encoun tered in the treatment of direct and inverse problems of scattering in neutron transport as well as radiative transfer theories is investigated in terms of the amplitude kjk of the kth legendre polynomial needed in the expansion of the scattering function the parameters gi describe the anisotropy of scattering of the medium considered in particular it is shown that the asymptotical density of zeros of the polynomials gp v is an inverted semicircle for the anisotropic non multiplying scattering medium

kernelized multiview projection for robust action recognition conventional action recognition algorithms adopt a single type of feature or a simple concatenation of multiple features in this paper we propose to better fuse and embed different feature representations for action recognition using a novel spectral coding algorithm called kernelized multiview projection kmp computing the kernel matrices from different features views via time sequential distance learning kmp can encode different features with different weights to achieve a low dimensional and semantically meaningful subspace where the distribution of each view is sufficiently smooth and discriminative more crucially kmp is linear for the reproducing kernel hilbert space which allows it to be competent for various practical applications we demonstrate kmp s performance for action recognition on five popular action datasets and the results are consistently superior to state of the art techniques

multilinear spatial discriminant analysis for dimensionality reduction in the last few years great efforts have been made to extend the linear projection technique lpt for multidimensional data i e tensor generally referred to as the multilinear projection technique mpt the vectorized nature of lpt requires high dimensional data to be converted into vector and hence may lose spatial neighborhood information of raw data mpt well addresses this problem by encoding multidimensional data as general tensors of a second or even higher order in this paper we propose a novel multilinear projection technique called multilinear spatial discriminant analysis msda to identify the underlying manifold of high order tensor data msda considers both the nonlocal structure and the local structure of data in the transform domain seeking to learn the projection matrices from all directions of tensor data that simultaneously maximize the nonlocal structure and minimize the local structure different from multilinear principal component analysis mpca that aims to preserve the global structure and tensor locality preserving projection tlpp that is in favor of preserving the local structure msda seeks a tradeoff between the nonlocal global and local structures so as to drive its discriminant information from the range of the non local structure and the range of the local structure this spatial discriminant characteristic makes msda have more powerful manifold preserving ability than tlpp and mpca theoretical analysis shows that traditional mpts such as multilinear linear discriminant analysis tlpp mpca and tensor maximum margin criterion could be derived from the msda model by setting different graphs and constraints extensive experiments on face databases orl cmu pie and the extended yale b and the weizmann action database demonstrate the effectiveness of the proposed msda method

general tensor discriminant analysis and gabor features for gait recognition traditional image representations are not suited to conventional classification methods such as the linear discriminant analysis lda because of the undersample problem usp the dimensionality of the feature space is much higher than the number of training samples motivated by the successes of the two dimensional lda 2dlda for face recognition we develop a general tensor discriminant analysis gtda as a preprocessing step for lda the benefits of gtda compared with existing preprocessing methods such as the principal components analysis pca and 2dlda include the following 1 the usp is reduced in subsequent classification by for example lda 2 the discriminative information in the training tensors is preserved and 3 gtda provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of gtda converges whereas that of 2dlda does not we use human gait recognition to validate the proposed gtda the averaged gait images are utilized for gait representation given the popularity of gabor function based image decompositions for image understanding and object recognition we develop three different gabor function based image representations 1 gabord is the sum of gabor filter responses over directions 2 gabors is the sum of gabor filter responses over scales and 3 gaborsd is the sum of gabor filter responses over scales and directions the gabord gabors and gaborsd representations are applied to the problem of recognizing people from their averaged gait images a large number of experiments were carried out to evaluate the effectiveness recognition rate of gait recognition based on first obtaining a gabor gabord gabors or gaborsd image representation then using gdta to extract features and finally using lda for classification the proposed methods achieved good performance for gait recognition based on image sequences from the university of south florida usf humanid database experimental comparisons are made with nine state of the art classification methods in gait recognition

learning a multiple kernel similarity metric for kinship verification abstract kinship verification kv has recently caught much attention in the computer vision community due to its potential applications ranging from missing children search to social media analysis most of the related work focuses either on developing hand crafted feature representations to describe the faces or on learning the mahalanobis distance metric to measure the similarity between facial images instead in this paper we propose a novel multiple kernel similarity metric mksm in which different from the mahalanobis metric the similarity computation is essentially based on an implicit nonlinear feature transformation the overall mksm is a weighted combination of basic similarities and therefore possesses the capacity for feature fusion the basic similarities are derived from base kernels and local features and the weights are obtained by solving a constrained linear programming lp problem that originates from a large margin lm criterion particularly the lm criterion not only guarantees the generalization on unseen samples when the training set is small but also leads to sparsity in the weight vector which in turn boosts the efficiency at the prediction stage extensive experiments on four publicly available datasets demonstrate the effectiveness of the proposed method

the jackknife estimate of variance tukey s jackknife estimate of variance for a statistic s x 1 x 2 cdots x n which is a symmetric function of i i d random variables x i is investigated using an anova like decomposition of s it is shown that the jackknife variance estimate tends always to be biased upwards a theorem to this effect being proved for the natural jackknife estimate of operatorname var s x 1 x 2 cdots x n 1 based on x 1 x 2 cdots x n

a comparison of several procedures to estimate the confidence interval for attributable risk in case control studies the estimation of a confidence interval for attributable risk from the logistic model based on data from case control studies is a problem for which an accepted solution is lacking two methods one based on the delta method and one bootstrap on the population base have been described but their accuracy has not been compared we present two other methods one based on a jack knife approach and the other using a bootstrap on two samples cases and controls the four methods are compared in a simulation study the four methods are also applied to a case control study on risk factors for preterm delivery the confidence intervals are obtained assuming normality and by logarithmic transformation when attributable risk is not smooth for example when exposure prevalence is low both the jack knife and the delta method tend to fail if attributable risk is close to zero or one normality cannot be assumed and log transformed confidence intervals must be used finally the extension to matched studies is analysed using a case control study on risk factors of cutaneous malignant melanoma in this situation the population based bootstrap is not available

multicriteria parameter estimation for models of stream chemical composition 1 the inability to develop an accurate and precise parameter estimation method for catchment hydrochemical models has been a persistent problem we investigate the use of multicriteria calibration techniques and the selection of the criteria as a first step in solving this problem we applied a multicriteria search algorithm to the alpine hydrochemical model ahm of the emerald lake watershed sequoia national park california a total of 21 chemical and hydrologic criteria were available for determining model performance four subsets of these criteria were selected for the multicriteria analysis using three different methods the first set used the four least correlated observations of stream chemical composition a second set of criteria was determined by using the four species with the least correlated root mean square error criteria values 0 05 for each pair finally two sets were chosen using the results of a multicriteria sensitivity analysis the most accurate and precise results were observed using criteria selected using results from a sensitivity analysis with the correlation analyses being a poor method for selecting criteria this set of criteria emphasizes attributes of the model structure the observations and our understanding of the processes influencing watershed hydrology and water quality also our results gave improved estimates of several hydrologic and biogeochemical processes in addition to identifying a flaw in the current representation of mineral weathering within the ahm as applied to the emerald lake watershed

approximate case influence for the proportional hazards regression model with censored data a method is presented for approximating the influence of individual cases upon regression coefficient estimates obtained from the cox proportional hazards model observations can thus be identified which may greatly influence statistical inferences regarding the effects of prognostic factors upon survival time an example from a cancer clinical trial is given

ensemble manifold regularization we propose an automatic approximation of the intrinsic manifold for general semi supervised learning ssl problems unfortunately it is not trivial to define an optimization function to obtain optimal hyperparameters usually cross validation is applied but it does not necessarily scale up other problems derive from the suboptimality incurred by discrete grid search and the overfitting therefore we develop an ensemble manifold regularization emr framework to approximate the intrinsic manifold by combining several initial guesses algorithmically we designed emr carefully so it 1 learns both the composite manifold and the semi supervised learner jointly 2 is fully automatic for learning the intrinsic manifold hyperparameters implicitly 3 is conditionally optimal for intrinsic manifold approximation under a mild and reasonable assumption and 4 is scalable for a large number of candidate manifold hyperparameters from both time and space perspectives furthermore we prove the convergence property of emr to the deterministic matrix at rate root n extensive experiments over both synthetic and real data sets demonstrate the effectiveness of the proposed framework

learning linear discriminant projections for dimensionality reduction of image descriptors in this paper we present linear discriminant projections ldp for reducing dimensionality and improving discriminability of local image descriptors we place ldp into the context of state of the art discriminant projections and analyze its properties ldp requires a large set of training data with point to point correspondence ground truth we demonstrate that training data produced by a simulation of image transformations leads to nearly the same results as the real data with correspondence ground truth this makes it possible to apply ldp as well as other discriminant projection approaches to the problems where the correspondence ground truth is not available such as image categorization we perform an extensive experimental evaluation on standard data sets in the context of image matching and categorization we demonstrate that ldp enables significant dimensionality reduction of local descriptors and performance increases in different applications the results improve upon the state of the art recognition performance with simultaneous dimensionality reduction from 128 to 30

estimation of allocation rates in a cluster analysis context abstract a sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations the mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the maximum of these posterior probabilities the estimates of the correct allocation rates provide a means of assessing the performance of the mixture approach to clustering the bootstrap technique is investigated for its effectiveness in reducing the bias of the estimates so obtained results are reported for three real data sets and a simulation study it is demonstrated that the proposed estimates generally provide useful information on the unobservable allocation rates of the mixture approach encouraging results are obtained for

discriminative elastic net regularized linear regression in this paper we aim at learning compact and discriminative linear regression models linear regression has been widely used in different problems however most of the existing linear regression methods exploit the conventional zero one matrix as the regression targets which greatly narrows the flexibility of the regression model another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability to this end we present an elastic net regularized linear regression enlr framework and develop two robust linear regression models which possess the following special characteristics first our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix second a robust elastic net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix third the resulting optimization problem of enlr has a closed form solution in each iteration which can be solved efficiently finally rather than directly exploiting the projection matrix for recognition our methods employ the transformed features as the new discriminate representations to make final image classification compared with the traditional linear regression model and some of its variants our method is much more accurate in image classification extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state of the art methods the matlab codes of our methods can be available at http www yongxu org lunwen html

nonparametric estimates of standard error the jackknife the bootstrap and other methods summary we discuss several nonparametric methods for attaching a standard error to a point estimate the jackknife the bootstrap half sampling subsampling balanced repeated replications the infinitesimal jackknife influence function techniques and the delta method the last three methods are shown to be identical all the methods derive from the same basic idea which is also the idea underlying the common parametric methods extended numerical comparisons are made for the special case of the correlation coefficient

an optimal transformation for discriminant and principal component analysis a general method is proposed to describe multivariate data sets using discriminant analysis and principal component analysis first the problem of finding k discriminant vectors in an l class data set is solved and compared to the solution proposed in the literature for two class problems and the classical solution for l class data sets it is shown that the method proposed is better than the classical method for l classes and is a generalization of the optimal set of discriminant vectors proposed for two class problems then the method is combined with a generalized principal component analysis to permit the user to define the properties of each successive computed vector all the methods were tested using measurements made on various kinds of flowers iris data

descriptor learning via supervised manifold regularization for multioutput regression multioutput regression has recently shown great ability to solve challenging problems in both computer vision and medical image analysis however due to the huge image variability and ambiguity it is fundamentally challenging to handle the highly complex input target relationship of multioutput regression especially with indiscriminate high dimensional representations in this paper we propose a novel supervised descriptor learning sdl algorithm for multioutput regression which can establish discriminative and compact feature representations to improve the multivariate estimation performance the sdl is formulated as generalized low rank approximations of matrices with a supervised manifold regularization the sdl is able to simultaneously extract discriminative features closely related to multivariate targets and remove irrelevant and redundant information by transforming raw features into a new low dimensional space aligned to targets the achieved discriminative while compact descriptor largely reduces the variability and ambiguity for multioutput regression which enables more accurate and efficient multivariate estimation we conduct extensive evaluation of the proposed sdl on both synthetic data and real world multioutput regression tasks for both computer vision and medical image analysis experimental results have shown that the proposed sdl can achieve high multivariate estimation accuracy on all tasks and largely outperforms the algorithms in the state of the arts our method establishes a novel sdl framework for multioutput regression which can be widely used to boost the performance in different applications

numerical cubature from archimedes hat box theorem archimedes hat box theorem states that uniform measure on a sphere projects to uniform measure on an interval this fact can be used to derive simpson s rule we present various constructions of and lower bounds for numerical cubature formulas using moment maps as a generalization of archimedes theorem we realize some well known cubature formulas on simplices as projections of spherical designs we combine cubature formulas on simplices and tori to make new formulas on spheres in particular sn admits a 7 cubature formula and sometimes a 7 design with o n4 points we establish a local lower bound on the density of a positive interior cubature formula on a simplex using the moment map along the way we establish other quadrature and cubature results of independent interest for each t we construct a lattice trigonometric 2t 1 cubature formula in n dimensions with o nt points we derive a variant of the moller lower bound using vector bundles and we show that gaussian quadrature is very sharply locally optimal among positive quadrature formulas

multiview alignment hashing for efficient image search hashing is a popular and efficient method for nearest neighbor search in large scale data spaces by embedding high dimensional feature descriptors into a similarity preserving hamming space with a low dimension for most hashing methods the performance of retrieval heavily depends on the choice of the high dimensional feature descriptor furthermore a single type of feature cannot be descriptive enough for different images when it is used for hashing thus how to combine multiple representations for learning effective hashing functions is an imminent task in this paper we present a novel unsupervised multiview alignment hashing approach based on regularized kernel nonnegative matrix factorization which can find a compact representation uncovering the hidden semantics and simultaneously respecting the joint probability distribution of data in particular we aim to seek a matrix factorization to effectively fuse the multiple information sources meanwhile discarding the feature redundancy since the raised problem is regarded as nonconvex and discrete our objective function is then optimized via an alternate way with relaxation and converges to a locally optimal solution after finding the low dimensional representation the hashing functions are finally obtained through multivariable logistic regression the proposed method is systematically evaluated on three data sets 1 caltech 256 2 cifar 10 and 3 cifar 20 and the results show that our method significantly outperforms the state of the art multiview hashing techniques

local feature discriminant projection in this paper we propose a novel subspace learning algorithm called local feature discriminant projection lfdp for supervised dimensionality reduction of local features lfdp is able to efficiently seek a subspace to improve the discriminability of local features for classification we make three novel contributions first the proposed lfdp is a general supervised subspace learning algorithm which provides an efficient way for dimensionality reduction of large scale local feature descriptors second we introduce the differential scatter discriminant criterion dsdc to the subspace learning of local feature descriptors which avoids the matrix singularity problem third we propose a generalized orthogonalization method to impose on projections leading to a more compact and less redundant subspace extensive experimental validation on three benchmark datasets including uiuc sports scene 15 and mit indoor demonstrates that the proposed lfdp outperforms other dimensionality reduction methods and achieves state of the art performance for image classification

on bootstrap resampling and iteration summary we propose a single unifying approach to bootstrap resampling applicable to a very wide range of statistical problems it enables attention to be focused sharply on one or more characteristics which are of major importance in any particular problem such as coverage error or length for confidence intervals or bias for point estimation our approach leads easily and directly to a very general form of bootstrap iteration unifying and generalizing present disparate accounts of this subject it also provides simple solutions to relatively complex problems such as a suggestion by lehmann 1986 for conditionally short confidence intervals we set out a single unifying principle guiding the operation of bootstrap resampling applicable to a very wide range of statistical problems including bias reduction shrinkage hypothesis testing and confidence interval construction our principle differs from other approaches in that it focuses attention directly on a measure of quality or accuracy expressed in the form of an equation whose solution is sought a very general form of bootstrap iteration is an immediate consequence of iterating the empirical solution to this equation so as to improve accuracy when employed for bias reduction iteration of the resampling principle yields a competitor to the generalized jackknife enabling bias to be reduced to arbitrarily low levels when applied to confidence intervals it produces the techniques of hall 1986 and beran 1987 the resampling principle leads easily to solutions of new complex problems such as empirical versions of confidence intervals proposed by lehmann 1986 lehmann argued that an ideal confidence interval is one which is short when it covers the true parameter value but not necessarily otherwise the resampling principle suggests a simple empirical means of constructing such intervals section 2 describes the general principle and 3 shows how it leads naturally to bootstrap iteration there we show that in many problems of practical interest such as bias reduction and coverage error reduction in two sided confidence intervals each iteration reduces error by the factor n 1 where n is sample size in the case of confidence intervals our result sharpens one of beran 1987 who showed that coverage error is reduced by the factor n 2 in two sided intervals the main exception to our n 1 rule is coverage error of one sided intervals where error is reduced by the factor n a at each iteration our approach to bootstrap iteration serves to unify not just the philosophy of iteration for different statistical problems but also different techniques of iteration for the same

robust bilateral lp norm two dimensional linear discriminant analysis abstract traditional linear discriminant analysis lda may suffer from a sensitivity to outliers and the small sample size sss problem while the lp norm measure for 0

geometric mean for subspace selection subspace selection approaches are powerful tools in pattern classification and data visualization one of the most important subspace approaches is the linear dimensionality reduction step in the fisher s linear discriminant analysis flda which has been successfully employed in many fields such as biometrics bioinformatics and multimedia information management however the linear dimensionality reduction step in flda has a critical drawback for a classification task with c classes if the dimension of the projected subspace is strictly lower than c 1 the projection to a subspace tends to merge those classes which are close together in the original feature space if separate classes are sampled from gaussian distributions all with identical covariance matrices then the linear dimensionality reduction step in flda maximizes the mean value of the kullback leibler kl divergences between different classes based on this viewpoint the geometric mean for subspace selection is studied in this paper three criteria are analyzed 1 maximization of the geometric mean of the kl divergences 2 maximization of the geometric mean of the normalized kl divergences and 3 the combination of 1 and 2 preliminary experimental results based on synthetic data uci machine learning repository and handwriting digits show that the third criterion is a potential discriminative subspace selection method which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in flda and its several representative extensions

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

orthogonal polynomials in neutron transport theory the asymptotic average properties of zeros of the polynomials gkm x which play a fundamental role in neutron transport and radiative transfer theories are investigated analytically in terms of the angular expansion coefficients wk of the scattering kernel for three wide classes of scattering models in particular it is found that the scattering models of eccleston mccormick shultis et al and henyey greenstein belong in one of the above mentioned classes and their associated polynomials gkm x have the same asymptotic density of zeros

evaluating the use of goodness of fit measures in hydrologic and hydroclimatic model validation correlation and correlation based measures e g the coefficient of determination have been widely used to evaluate the goodness of fit of hydrologic and hydroclimatic models these measures are oversensitive to extreme values outliers and are insensitive to additive and proportional differences between model predictions and observations because of these limitations correlation based measures can indicate that a model is a good predictor even when it is not in this paper useful alternative goodness of fit or relative error measures including the coefficient of efficiency and the index of agreement that overcome many of the limitations of correlation based measures are discussed modifications to these statistics to aid in interpretation are presented it is concluded that correlation and correlation based measures should not be used to assess the goodness of fit of a hydrologic or hydroclimatic model and that additional evaluation measures such as summary statistics and absolute error measures should supplement model evaluation tools

supervised matrix factorization hashing for cross modal retrieval the target of cross modal hashing is to embed heterogeneous multimedia data into a common low dimensional hamming space which plays a pivotal part in multimedia retrieval due to the emergence of big multimodal data recently matrix factorization has achieved great success in cross modal hashing however how to effectively use label information and local geometric structure is still a challenging problem for these approaches to address this issue we propose a cross modal hashing method based on collective matrix factorization which considers both the label consistency across different modalities and the local geometric consistency in each modality these two elements are formulated as a graph laplacian term in the objective function leading to a substantial improvement on the discriminative power of latent semantic features obtained by collective matrix factorization moreover the proposed method learns unified hash codes for different modalities of an instance to facilitate cross modal search and the objective function is solved using an iterative strategy the experimental results on two benchmark data sets show the effectiveness of the proposed method and its superiority over state of the art cross modal hashing methods

interval estimation for treatment effects using propensity score matching in causal studies without random assignment of treatment causal effects can be estimated using matched treated and control samples where matches are obtained using estimated propensity scores propensity score matching can reduce bias in treatment effect estimators in cases where the matched samples have overlapping covariate distributions despite its application in many applied problems there is no universally employed approach to interval estimation when using propensity score matching in this article we present and evaluate approaches to interval estimation when using propensity score matching

orthogonal laplacianfaces for face recognition following the intuition that the naturally occurring face data may be generated by sampling a probability distribution that has support on or near a submanifold of ambient space we propose an appearance based face recognition method called orthogonal laplacianface our algorithm is based on the locality preserving projection lpp algorithm which aims at finding a linear approximation to the eigenfunctions of the laplace beltrami operator on the face manifold however lpp is nonorthogonal and this makes it difficult to reconstruct the data the orthogonal locality preserving projection olpp method produces orthogonal basis functions and can have more locality preserving power than lpp since the locality preserving power is potentially related to the discriminating power the olpp is expected to have more discriminating power than lpp experimental results on three face databases demonstrate the effectiveness of our proposed algorithm

learning local feature descriptors using convex optimisation the objective of this work is to learn descriptors suitable for the sparse feature detectors used in viewpoint invariant matching we make a number of novel contributions towards this goal first it is shown that learning the pooling regions for the descriptor can be formulated as a convex optimisation problem selecting the regions using sparsity second it is shown that descriptor dimensionality reduction can also be formulated as a convex optimisation problem using mahalanobis matrix nuclear norm regularisation both formulations are based on discriminative large margin learning constraints as the third contribution we evaluate the performance of the compressed descriptors obtained from the learnt real valued descriptors by binarisation finally we propose an extension of our learning formulations to a weakly supervised case which allows us to learn the descriptors from unannotated image collections it is demonstrated that the new learning methods improve over the state of the art in descriptor learning on the annotated local patches data set of brown et al and unannotated photo collections of philbin et al

orthogonal polynomials and differential equations in neutron transport and radiative transfer theories abstract there is a set of orthogonal polynomials gn x which plays a relevant role in the treatment of the case of anisotropic scattering in neutron transport and radiative transfer theories they appear also in the spherical harmonics treatment of the isotropic scattering these polynomials are orthogonal with respect to a weight function which is continuous in the interval 1 1 and has a finite number of symmetric dirac masses although some other structural properties of these polynomials e g the three term recurrence relation as well as some properties of their zeros have been published much more need to be known in particular neither the second order differential equation nor the density of zeros i e the number of zeros per unit of interval of the polynomial gn x have been found here we obtain the second order differential equation in the case that these polynomials are hypergeometric so leaving open the general case furthermore the exact expressions of the moments around the origin of the density of zeros of gn x are given in the general case the asymptotic density of zeros is also pointed out finally these polynomials are shown to belong to the nevai s class

comparison of variance estimation approaches in a two state markov model for longitudinal data with misclassification we examine the behaviour of the variance covariance parameter estimates in an alternating binary markov model with misclassification transition probabilities specify the state transitions for a process that is not directly observable the state of an observable process which may not correctly classify the state of the unobservable process is obtained at discrete time points misclassification probabilities capture the two types of classification errors variance components of the estimated transition parameters are calculated with three estimation procedures observed information jackknife and bootstrap techniques simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation the three approaches generally provide similar variance estimates for large samples and moderate misclassification in these situations the resampling methods are reasonable alternatives when programming partial derivatives is not appealing with smaller chains or higher misclassification probabilities the bootstrap method appears to be the best choice

the problem of a covariate time qualitative interaction in a survival study we introduce a test for the equality of two survival distributions against the specific alternative of crossing hazards although this kind of alternative is somewhat rare designing a test specifically aimed at detecting such departures from the null hypothesis in this direction leads to powerful procedures upon which we can call in those few cases where such departures are suspected furthermore the proposed test and an approximate version of the test are seen to suffer only moderate losses in power when compared with their optimal counterparts should the alternative be one of proportional hazards our interest in the problem is motivated by clinical studies on the role of acute graft versus host disease as a risk factor in leukemic children and we discuss the analysis of this study in detail the model we use in this work is a special case of the one introduced by anderson and senthilselvan 1982 applied statistics 31 44 51 we propose overcoming an inferential problem stemming from their model by using the methods of davies 1977 biometrika 64 247 254 1987 biometrika 74 33 43 backed up by resampling techniques we also look at an approach relying directly on resampling techniques the distributional aspects of this approach under the null hypothesis are interesting but practically its behaviour is such that its use cannot be generally recommended outlines of the necessary asymptotic theory are presented and for this we use the tools of martingale theory

continuous time random walks for analyzing the transport of a passive tracer in a single fissure 1 the selection of the correct model for describing contaminant transport in fractured media remains a challenging problem in subsurface hydrology in this work the experimental data corresponding to nonsorbing tracer runs in natural fissures of moreno et al 1985 are analyzed the advection dispersion equation ade model yields a poor fit in the late time regions of the experimental breakthrough curves denoting the existence of anomalous or non fickian transport continuous time random walks ctrw are proposed for describing this kind of transport using two of the most studied forms for the transition rate probability the asymptotic and truncated power law models the ctrw approach produces better fits to the experimental data than the ade model in all the simulations a moderately dispersive transport was found which is interpreted as being as a result of the effects of the small and intermediate scale heterogeneities

a note on the jackknife the bootstrap and the delta method estimators of bias and variance three methods for the nonparametric reduction of bias and estimation of variance are in common use the jackknife the delta method i e the method of statistical differentials and the bootstrap in recent work efron 1981 a b 1982 has compared these three methods numerically for the case of the sample correlation coefficient for present purposes we define the procedures as follows consider a statistic tn thought of as an estimator of an unknown parameter 0 we wish to study the possibility of bias reduction by estimating the bias and subtracting off the estimate and variance estimation for g tj considered as an estimator of g 0 throughout we assume that we observe x1 xn independent and identically distributed with common cumulative distribution function f let tn denote the abovementioned statistic computed based on x1 xn we assume tn to be symmetric in its arguments furthermore let t 1 denote the above mentioned statistic computed based upon the sample of size n 1 consisting of x1 xi1 xi 1 xn the jackknife estimator of the bias of g tn is then given as b n n 1 1 g t 1 g tn n and the jackknife variance estimator is just

structure preserving binary representations for rgb d action recognition in this paper we propose a novel binary local representation for rgb d video data fusion with a structure preserving projection our contribution consists of two aspects toacquire a general feature for the video data we convert the problem to describing the gradient fields of rgb and depth information of video sequences with the local fluxes of the gradient fields which include the orientation and the magnitude of the neighborhood of each point a new kind of continuous local descriptor called local flux feature lff is obtained then the lffs from rgb and depth channels are fused into a hamming space via the structure preserving projection spp specifically an orthogonal projection matrix is applied to preserve the pairwise structure with a shape constraint to avoid the collapse of data structure in the projected space furthermore a bipartite graph structure of data is taken into consideration which is regarded as a higher level connection between samples and classes than the pairwise structure of local features theextensive experiments show not only the high efficiency of binary codes and the effectiveness of combining lffs from rgb d channels via spp on various action recognition benchmarks of rgb d data but also the potential power of lff for general action recognition

ensemble predictions of runoff in ungauged catchments a new approach to regionalization of conceptual rainfall runoff models is presented on the basis of ensemble modeling and model averaging it is argued that in principle this approach represents an improvement on the established procedure of regressing parameter values against numeric catchment descriptors using daily data from 127 catchments in the united kingdom alternative schemes for defining prior and posterior likelihoods of candidate models are tested in terms of accuracy of ungauged catchment predictions a probability distributed model structure is used and alternative parameter sets are identified using data from each of a number of gauged catchments using the models of the 10 gauged catchments most similar to the ungauged catchment provides generally the best results and performs significantly better than the regression method especially for predicting low flows the ensemble of candidate models provides an indication of uncertainty in ungauged catchment predictions although this is not a robust estimate of possible flow ranges and frequently fails to encompass flow peaks options for developing the new method to resolve these problems are discussed

duplex metric learning for image set classification image set classification has attracted much attention because of its broad applications despite the success made so far the problems of intra class diversity and inter class similarity still remain two major challenges to explore a possible solution to these challenges this paper proposes a novel approach termed duplex metric learning dml for image set classification the proposed dml consists of two progressive metric learning stages with different objectives used for feature learning and image classification respectively the metric learning regularization is not only used to learn powerful feature representations but also well explored to train an effective classifier at the first stage we first train a discriminative stacked autoencoder dsae by layer wisely imposing a metric learning regularization term on the neurons in the hidden layers and meanwhile minimizing the reconstruction error to obtain new feature mappings in which similar samples are mapped closely to each other and dissimilar samples are mapped farther apart at the second stage we discriminatively train a classifier and simultaneously fine tune the dsae by optimizing a new objective function which consists of a classification error term and a metric learning regularization term finally two simple voting strategies are devised for image set classification based on the learnt classifier in the experiments we extensively evaluate the proposed framework for the tasks of face recognition object recognition and face verification on several commonly used data sets and state of the art results are achieved in comparison with existing methods

a diameter sensitive flow entropy method for reliability consideration in water distribution system design flow entropy is a measure of uniformity of pipe flows in water distribution systems by maximizing flow entropy one can identify reliable layouts or connectivity in networks in order to overcome the disadvantage of the common definition of flow entropy that does not consider the impact of pipe diameter on reliability an extended definition of flow entropy termed as diameter sensitive flow entropy is proposed this new methodology is then assessed by using other reliability methods including monte carlo simulation a pipe failure probability model and a surrogate measure resilience index integrated with water demand and pipe failure uncertainty the reliability assessment is based on a sample of wds designs derived from an optimization process for each of the two benchmark networks correlation analysis is used to evaluate quantitatively the relationship between entropy and reliability to ensure reliability a comparative analysis between the flow entropy and the new method is conducted the results demonstrate that the diameter sensitive flow entropy shows consistently much stronger correlation with the three reliability measures than simple flow entropy therefore the new flow entropy method can be taken as a better surrogate measure for reliability and could be potentially integrated into the optimal design problem of wdss sensitivity analysis results show that the velocity parameters used in the new flow entropy has no significant impact on the relationship between diameter sensitive flow entropy and reliability

two books on density estimation here k is a kernel function usually a symmetric probability density function and h is a smoothing parameter or bandwidth the value of which determines how much the data are smoothed to produce the density estimate the first published paper specifically on density estimation was rosenblatt 1956 however density estimates were suggested several years earlier by fix and hodges 1951 in a technical report it is regrettable that this report was never published since it contains a great deal of interesting discussion and insight much of which is still pertinent today in these days of computer graphics and exploratory data analysis it is often supposed that the primary purpose for which density estimation was ordained was as a method for producing pretty perhaps too pretty pictures from data however a glance at fix and hodges 1951 shows that this is not at all the case their interest in density estimation stemmed from the discrimination or classification problem of allocating an observation z to one of two populations a and b if the distributions underlying the populations a and b are not known but have to be estimated from data and if the statistician is unwilling to make parametric assumptions of the kind tacitly present in fisher s linear discriminant method then a natural approach is to construct estimates of the densities fa and f b and then to base a discriminant rule on the ratio of these two density estimates since these early papers there has been a large amount of research into density estimation and related subjects the main emphasis of much of this work has been to investigate the theoretical properties and particularly the asymptotic properties of various methods of density estimation in certain quarters

parameter analysis and estimates for the modis evapotranspiration algorithm and multiscale verification accurate estimation of terrestrial evapotranspiration e is critical to understand the world s energy and water cycles mod16 is the core algorithm of the widely used global e data set the moderate resolution imaging spectroradiometer modis e product however it exhibits considerable uncertainties in some regions based on the data from 175 flux towers we identified the key parameters of the mod16 algorithm using the sobol sensitivity analysis method across biomes the output of the mod16 algorithm was sensitive to eight parameters among them beta which is treated as a constant 0 2 kpa across biomes in the original mod16 algorithm was identified as the parameter to which the algorithm was most sensitive we used the differential evolution markov chain method to obtain the proper posterior distributions for each key parameter across a range of biomes the values of the key parameters for the different biomes were accurately estimated by differential evolution markov chain in comparison with data from the flux towers we then evaluated the performances of the original mod16 and the optimized mod16 and compared them at multiple spatial scales i e site catchment and global we obtained relatively consistent and more reliable e simulations using the optimized mod16 at all three scales in the future more attention should be paid to uncertainties in the algorithm s structure and its parameterizations of soil moisture constraint canopy resistance and energy partitioning

parameter estimation for weibull probability distribution function of initial fatigue quality this paper considers the problem of determining the parameters of a weibull distribution when a limited set of experimental data of such a distribution is available the problem is of particular interest in the probabilistic approach to durability analysis of flight structures in which the distribution of time to crack initiation for a given crack length as well as the equivalent initial flaw size distribution are usually described through a three parameter weibull distribution the aims of this paper are the determination of a high quality estimation procedure and the solution of the problem of the determination of the number of experimental data that are necessary to estimate with a given confidence level the parameters of the distribution and some related statistics the maximum likelihood and the least square methods are compared with regard to the estimation quality it is shown by monte carlo simulations that the maximum likelihood approach gives better results than the least square approach the problem of obtaining confidence intervals for the number of cracks with greater length than the reference one for a fixed service time on a single sample basis is addressed and solved through the bootstrap method