worst case linear discriminant analysis as scalable semidefinite feasibility problems in this paper we propose an efficient semidefinite programming sdp approach to worst case linear discriminant analysis wlda compared with the traditional lda wlda considers the dimensionality reduction problem from the worst case viewpoint which is in general more robust for classification however the original problem of wlda is non convex and difficult to optimize in this paper we reformulate the optimization problem of wlda into a sequence of semidefinite feasibility problems to efficiently solve the semidefinite feasibility problems we design a new scalable optimization method with a quasi newton method and eigen decomposition being the core components the proposed method is orders of magnitude faster than standard interior point sdp solvers experiments on a variety of classification problems demonstrate that our approach achieves better performance than standard lda our method is also much faster and more scalable than standard interior point sdp solvers based wlda the computational complexity for an sdp with m constraints and matrices of size d by d is roughly reduced from mathcal o m 3 md 3 m 2 d 2 to mathcal o d 3 m d in our case

eigenfaces vs fisherfaces recognition using class specific linear projection we develop a face recognition algorithm which is insensitive to large variation in lighting direction and facial expression taking a pattern classification approach we consider each pixel in an image as a coordinate in a high dimensional space we take advantage of the observation that the images of a particular face under varying illumination but fixed pose lie in a 3d linear subspace of the high dimensional image space if the face is a lambertian surface without shadowing however since faces are not truly lambertian surfaces and do indeed produce self shadowing images will deviate from this linear subspace rather than explicitly modeling this deviation we linearly project the image into a subspace in a manner which discounts those regions of the face with large deviation our projection method is based on fisher s linear discriminant and produces well separated classes in a low dimensional subspace even under severe variation in lighting and facial expressions the eigenface technique another method based on linearly projecting the image space to a low dimensional subspace has similar computational requirements yet extensive experimental results demonstrate that the proposed fisherface method has error rates that are lower than those of the eigenface technique for tests on the harvard and yale face databases

exploring estimator bias variance tradeoffs using the uniform cr bound we introduce a plane which we call the delta sigma plane that is indexed by the norm of the estimator bias gradient and the variance of the estimator the norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space using a uniform cramer rao cr bound on estimator variance a delta sigma tradeoff curve is specified that defines an unachievable region of the delta sigma plane for a specified statistical model in order to place an estimator on this plane for comparison with the delta sigma tradeoff curve the estimator variance bias gradient and bias gradient norm must be evaluated we present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log likelihood we demonstrate the methods developed in this paper for linear gaussian and nonlinear poisson inverse problems

discriminant subspace analysis a fukunaga koontz approach the fisher linear discriminant fld is commonly used in pattern recognition it finds a linear subspace that maximally separates class patterns according to the fisher criterion several methods of computing the fld have been proposed in the literature most of which require the calculation of the so called scatter matrices in this paper we bring a fresh perspective to fld via the fukunaga koontz transform fkt we do this by decomposing the whole data space into four subspaces with different discriminabilities as measured by eigenvalue ratios by connecting the eigenvalue ratio with the generalized eigenvalue we show where the fisher criterion is maximally satisfied we prove the relationship between fld and fkt analytically and propose a unified framework to understanding some existing work furthermore we extend our theory to the multiple discriminant analysis mda this is done by transforming the data into intraclass and extraclass spaces followed by maximizing the bhattacharyya distance based on our fkt analysis we identify the discriminant subspaces of mda fkt and propose an efficient algorithm which works even when the scatter matrices are singular or too large to be formed our method is general and may be applied to different pattern recognition problems we validate our method by experimenting on synthetic and real data

mse bounds with affine bias dominating the cramer rao bound in continuation to an earlier work we further develop bounds on the mean squared error mse when estimating a deterministic parameter vector thetas0 in a given estimation problem as well as estimators that achieve the optimal performance the traditional cramer rao cr type bounds provide benchmarks on the variance of any estimator of thetas0 under suitable regularity conditions while requiring a priori specification of a desired bias gradient to circumvent the need to choose the bias which is impractical in many applications it was suggested in our earlier work to directly treat the mse which is the sum of the variance and the squared norm of the bias while previously we developed mse bounds assuming a linear bias vector here we study in the same spirit affine bias vectors we demonstrate through several examples that allowing for an affine transformation can often improve the performance significantly over a linear approach using convex optimization tools we show that in many cases we can choose an affine bias that results in an mse bound that is smaller than the unbiased cr bound for all values of thetas0 furthermore we explicitly construct estimators that achieve these bounds in cases where an efficient estimator exists by performing an affine transformation of the standard maximum likelihood ml estimator this leads to estimators that result in a smaller mse than ml for all possible values of thetas0

development of a glottal area index that integrates glottal gap size and open quotient because voice signals result from vocal fold vibration perceptually meaningful vibratory measures should quantify those aspects of vibration that correspond to differences in voice quality in this study glottal area waveforms were extracted from high speed videoendoscopy of the vocal folds principal component analysis was applied to these waveforms to investigate the factors that vary with voice quality results showed that the first principal component derived from tokens without glottal gaps was significantly p 0 01 associated with the open quotient oq the alternating current ac measure had a significant effect p 0 01 on the first principal component among tokens exhibiting glottal gaps a measure ac oq defined as the ratio of ac to oq was proposed to combine both amplitude and temporal characteristics of the glottal area waveform for both complete and incomplete glottal closures analyses of glide phonations in which quality varied continuously from breathy to pressed showed that the ac oq measure was able to characterize the corresponding continuum of glottal area waveform variation regardless of the presence or absence of glottal gaps

mean and variance of implicitly defined biased estimators such as penalized maximum likelihood applications to tomography many estimators in signal processing problems are defined implicitly as the maximum of some objective function examples of implicitly defined estimators include maximum likelihood penalized likelihood maximum a posteriori and nonlinear least squares estimation for such estimators exact analytical expressions for the mean and variance are usually unavailable therefore investigators usually resort to numerical simulations to examine the properties of the mean and variance of such estimators this paper describes approximate expressions for the mean and variance of implicitly defined estimators of unconstrained continuous parameters we derive the approximations using the implicit function theorem the taylor expansion and the chain rule the expressions are defined solely in terms of the partial derivatives of whatever objective function one uses for estimation as illustrations we demonstrate that the approximations work well in two tomographic imaging applications with poisson statistics we also describe a plug in approximation that provides a remarkably accurate estimate of variability even from a single noisy poisson sinogram measurement the approximations should be useful in a wide range of estimation problems

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

generalizing discriminant analysis using the generalized singular value decomposition discriminant analysis has been used for decades to extract features that preserve class separability it is commonly defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters the requirement that one of these matrices be nonsingular limits its application to data sets with certain relative dimensions we examine a number of optimization criteria and extend their applicability by using the generalized singular value decomposition to circumvent the nonsingularity requirement the result is a generalization of discriminant analysis that can be applied even when the sample size is smaller than the dimension of the sample data we use classification results from the reduced representation to compare the effectiveness of this approach with some alternatives and conclude with a discussion of their relative merits

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

two dimensional supervised local similarity and diversity projection this paper presents a novel manifold learning method namely two dimensional supervised local similarity and diversity projection 2dslsdp for feature extraction the proposed method defines two weighted adjacency graphs namely similarity graph and diversity graph the affinity matrix of similarity graph is determined by the spatial relationship between vertices of this graph while affinity matrix of diversity graph is determined by the diversity information of vertices of its graph using these two graphs the proposed method constructs local similarity scatter and diversity scatter respectively a concise feature extraction criterion is then raised via minimizing the ratio of the local similarity scatter to local diversity scatter thus 2dslsdp can well preserve not only the adjacency similarity structure but also the diversity of data points which is important for the classification experiments on the ar and umist databases show the effectiveness of the proposed 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

formant frequency estimation of high pitched vowels using weighted linear prediction all pole modeling is a widely used formant estimation method but its performance is known to deteriorate for high pitched voices in order to address this problem several all pole modeling methods robust to fundamental frequency have been proposed this study compares five such previously known methods and introduces a technique weighted linear prediction with attenuated main excitation wlp ame wlp ame utilizes temporally weighted linear prediction lp in which the square of the prediction error is multiplied by a given parametric weighting function the weighting downgrades the contribution of the main excitation of the vocal tract in optimizing the filter coefficients consequently the resulting all pole model is affected more by the characteristics of the vocal tract leading to less biased formant estimates by using synthetic vowels created with a physical modeling approach the results showed that wlp ame yields improved formant frequencies for high pitched sounds in comparison to the previously known methods e g relative error in the first formant of the vowel a decreased from 11 to 3 when conventional lp was replaced with wlp ame experiments conducted on natural vowels indicate that the formants detected by wlp ame changed in a more regular manner between repetitions of different pitch than those computed by conventional lp

controllability of fractional integro differential evolution equations with nonlocal conditions this paper concerns the controllability for a class of fractional integro differential evolution equations with nonlocal initial conditions by using the fractional calculus measure of noncompactness and the monch fixed point theorem we obtain a controllability result for the nonlocal cauchy problem of the fractional integro differential evolution equations involving noncompact semigroups and the nonlocal functions without lipschitz continuity an example is given to illustrate the effectiveness of the abstract results

approximate controllability of semi linear neutral integro differential systems with finite delay abstract this paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in hilbert space since the considered equation admits nonlinear terms involving spatial derivatives the fraction power theory and norm are used to discuss the problem so that the established results can be applied to them the results are obtained by using the sadovskii fixed point theorem and the theory of analytic resolvent operator an example is presented to illustrate the applications of the obtained results

discrete all pole modeling a method for parametric modeling and spectral envelopes when only a discrete set of spectral points is given is introduced this method called discrete all pole dap modeling uses a discrete version of the itakura saito distortion measure as its error criterion one result is an autocorrelation matching condition that overcomes the limitations of linear prediction and produces better fitting spectral envelopes for spectra that are representable by a relatively small discrete set of values such as in voiced speech an iterative algorithm for dap modeling that is shown to converge to a unique global minimum is presented results of applying dap modeling to real and synthetic speech are also presented dap modeling is extended to allow frequency dependent weighting of the error measure so that spectral accuracy can be enhanced in certain frequency regions

penalized maximum likelihood image reconstruction using space alternating generalized em algorithms most expectation maximization em type algorithms for penalized maximum likelihood image reconstruction converge slowly particularly when one incorporates additive background effects such as scatter random coincidences dark current or cosmic radiation in addition regularizing smoothness penalties or priors introduce parameter coupling rendering intractable the m steps of most em type algorithms this paper presents space alternating generalized em sage algorithms for image reconstruction which update the parameters sequentially using a sequence of small hidden data spaces rather than simultaneously using one large complete data space the sequential update decouples the m step so the maximization can typically be performed analytically we introduce new hidden data spaces that are less informative than the conventional complete data space for poisson data and that yield significant improvements in convergence rate this acceleration is due to statistical considerations not numerical overrelaxation methods so monotonic increases in the objective function are guaranteed we provide a general global convergence proof for sage methods with nonnegativity constraints

stable orthogonal local discriminant embedding for linear dimensionality reduction manifold learning is widely used in machine learning and pattern recognition however manifold learning only considers the similarity of samples belonging to the same class and ignores the within class variation of data which will impair the generalization and stableness of the algorithms for this purpose we construct an adjacency graph to model the intraclass variation that characterizes the most important properties such as diversity of patterns and then incorporate the diversity into the discriminant objective function for linear dimensionality reduction finally we introduce the orthogonal constraint for the basis vectors and propose an orthogonal algorithm called stable orthogonal local discriminate embedding experimental results on several standard image databases demonstrate the effectiveness of the proposed dimensionality reduction approach

a lattice algorithm for factoring the spectrum of a moving average process triangular decomposition of the semi infinite covariance matrix of a moving average process can be used as a spectral factorization technique an efficient lattice algorithm is derived for performing the necessary computations this technique is a special case of the fast cholesky decomposition of stationary covariance matrices the algorithm can be used to factor multichannel spectra to a desired degree of accuracy

asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions abstract of concern is a class of abstract semilinear integrodifferential equations with nonlocal initial conditions under some suitable hypotheses we establish some new theorems about the existence of asymptotically almost automorphic solutions to the integrodifferential equations moreover an example is given to illustrate our results

regularized discriminant analysis abstract linear and quadratic discriminant analysis are considered in the small sample high dimensional setting alternatives to the usual maximum likelihood plug in estimates for the covariance matrices are proposed these alternatives are characterized by two parameters the values of which are customized to individual situations by jointly minimizing a sample based estimate of future misclassification risk computationally fast implementations are presented and the efficacy of the approach is examined through simulation studies and application to data these studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved

two dimensional maximum local variation based on image euclidean distance for face recognition manifold learning concerns the local manifold structure of high dimensional data and many related algorithms are developed to improve image classification performance none of them however consider both the relationships among pixels in images and the geometrical properties of various images during learning the reduced space in this paper we propose a linear approach called two dimensional maximum local variation 2dmlv for face recognition in 2dmlv we encode the relationships among pixels in images using the image euclidean distance instead of conventional euclidean distance in estimating the variation of values of images and then incorporate the local variation which characterizes the diversity of images and discriminating information into the objective function of dimensionality reduction extensive experiments demonstrate the effectiveness of our approach

averaging maximum penalized likelihood and bayesian estimation for improving gaussian mixture probability density estimates we apply the idea of averaging ensembles of estimators to probability density estimation in particular we use gaussian mixture models which are important components in many neural network applications we investigate the performance of averaging using three data sets for comparison we employ two traditional regularization approaches i e a maximum penalized likelihood approach and a bayesian approach in the maximum penalized likelihood approach we use penalty functions derived from conjugate bayesian priors such that an expectation maximization em algorithm can be used for training in all experiments the maximum penalized likelihood approach and averaging improved performance considerably if compared to a maximum likelihood approach in two of the experiments the maximum penalized likelihood approach outperformed averaging in one experiment averaging was clearly superior our conclusion is that maximum penalized likelihood gives good results if the penalty term in the cost function is appropriate for the particular problem if this is not the case averaging is superior since it shows greater robustness by not relying on any particular prior assumption the bayesian approach worked very well on a low dimensional toy problem but failed to give good performance in higher dimensional problems

stable local dimensionality reduction approaches dimensionality reduction is a big challenge in many areas a large number of local approaches stemming from statistics or geometry have been developed however in practice these local approaches are often in lack of robustness since in contrast to maximum variance unfolding mvu which explicitly unfolds the manifold they merely characterize local geometry structure moreover the eigenproblems that they encounter are hard to solve we propose a unified framework that explicitly unfolds the manifold and reformulate local approaches as the semi definite programs instead of the above mentioned eigenproblems three well known algorithms locally linear embedding lle laplacian eigenmaps le and local tangent space alignment ltsa are reinterpreted and improved within this framework several experiments are presented to demonstrate the potential of our framework and the improvements of these local algorithms

controllability for a class of integro differential evolution equations involving non local initial conditions abstractthis paper deals with the exact controllability for a class of first order integro differential evolution equations involving non local initial conditions by using sadovskii fixed point theorem exact controllability results are obtained without assuming the compactness and lipschitz conditions for non local functions an example is given to illustrate the effectiveness of the abstract results

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

adaptive maximum margin analysis for image recognition abstract most existing discriminant manifold learning methods aim to maximize the margin among nearby data which is determined in the high dimensional original space as such they do not necessarily best maximize the margin between different classes in the low dimensional space which is a critically important property for image classification to handle this problem we propose an adaptive maximum margin analysis amma for feature extraction amma aims to seek a projection matrix that best maximize the margin which is calculated in the low dimensional space it uses sparse representation to adaptively construct the intrinsic and penalty graphs finally an iterative algorithm is developed to solve the projection matrix extensive experimental results on several image databases illustrate the effectiveness of the proposed approach

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

deep adaptive feature embedding with local sample distributions for person re identification person re identification re id aims to match pedestrians observed by disjoint camera views it attracts increasing attention in computer vision due to its importance to surveillance systems to combat the major challenge of cross view visual variations deep embedding approaches are proposed by learning a compact feature space from images such that the euclidean distances correspond to their cross view similarity metric however the global euclidean distance cannot faithfully characterize the ideal similarity in a complex visual feature space because features of pedestrian images exhibit unknown distributions due to large variations in poses illumination and occlusion moreover intra personal training samples within a local range which are robust to guide deep embedding against uncontrolled variations cannot be captured by a global euclidean distance in this paper we study the problem of person re id by proposing a novel sampling to mine suitable positives i e intra class within a local range to improve the deep embedding in the context of large intra class variations our method is capable of learning a deep similarity metric adaptive to local sample structure by minimizing each sample s local distances while propagating through the relationship between samples to attain the whole intra class minimization to this end a novel objective function is proposed to jointly optimize similarity metric learning local positive mining and robust deep feature embedding this attains local discriminations by selecting local ranged positive samples and the learned features are robust to dramatic intra class variations experiments on benchmarks show state of the art results achieved by our method c 2017 elsevier ltd all rights reserved

sim simultaneous inverse filtering and matching of a glottal flow model for acoustic speech signals a new method simultaneous inverse filtering and model matching sim is proposed that allows one to calculate voice source measures without any user interaction it is based on the discrete all pole modeling dap technique for inverse filtering if which is modified to include a model of the glottal flow as integral part lf model fant et al stl qpsr stockholm 4 1985 1 13 1986 as the correct lf parameters are initially unknown they are estimated in an iterative procedure using multi dimensional optimization techniques that are initialized according to the results of an exhaustive search the error criteria applied reflect how well the if is performed after the spectral contribution of the glottal flow has been removed the resulting optimal lf parameter constellation serves as the basis to calculate 11 voice source measures the performance was evaluated using synthesized signals and recordings of natural utterances for the synthesized signals the accuracy to reproduce the original parameters was high correlations exceeding 0 88 for measures where the starting point of the glottal cycle did not enter explicitly errors were smaller compared to conventional estimation methods where the measures were estimated from the if signal the analysis of natural utterances indicates that problems still exist with regard to robustness but that under advantageous conditions the open quotient the speed quotient the closing quotient the parabolic spectral parameter and the negative peak amplitude of the glottal flow derivative can indeed be determined automatically by the sim method

feature extraction using constrained maximum variance mapping in this paper an efficient feature extraction method named as constrained maximum variance mapping cmvm is developed the proposed algorithm can be viewed as a linear approximation of multi manifolds learning based approach which takes the local geometry and manifold labels into account the cmvm and the original manifold learning based approaches have a point in common that the locality is preserved moreover the cmvm is globally maximizing the distances between different manifolds after the local scatters have been characterized the proposed method focuses on developing a linear transformation that can maximize the dissimilarities between all the manifolds under the constraint of locality preserving compared to most of the up to date manifold learning based methods this trick makes contribution to pattern classification from two aspects on the one hand the local structure in each manifold is still kept on the other hand the discriminant information between manifolds can be explored finally feret face database cmu pie face database and usps handwriting data are all taken to examine the effectiveness and efficiency of the proposed method experimental results validate that the proposed approach is superior to other feature extraction methods such as linear discriminant analysis lda locality preserving projection lpp unsupervised discriminant projection udp and maximum variance projection mvp

semisupervised generalized discriminant analysis generalized discriminant analysis gda is a commonly used method for dimensionality reduction in its general form it seeks a nonlinear projection that simultaneously maximizes the between class dissimilarity and minimizes the within class dissimilarity to increase class separability in real world applications where labeled data are scarce gda may not work very well however unlabeled data are often available in large quantities at very low cost in this paper we propose a novel gda algorithm which is abbreviated as semisupervised generalized discriminant analysis ssgda we utilize unlabeled data to maximize an optimality criterion of gda and formulate the problem as an optimization problem that is solved using the constrained concave convex procedure the optimization procedure leads to estimation of the class labels for the unlabeled data we propose a novel confidence measure and a method for selecting those unlabeled data points whose labels are estimated with high confidence the selected unlabeled data can then be used to augment the original labeled dataset for performing gda we also propose a variant of ssgda called m ssgda which adopts the manifold assumption to utilize the unlabeled data extensive experiments on many benchmark datasets demonstrate the effectiveness of our proposed methods

heterogeneous feature structure fusion for classification the key to feature fusion for classification is to take advantage of the discriminative and complementary information from different feature sets which can be represented as internal within each feature set or external structures across different feature sets traditional approaches tend to preserve either internal or external structures via certain feature projection some early attempts consider both structures implicitly or indirectly without revealing their relative importance and relevance in feature fusion we propose a new unsupervised heterogeneous structure fusion hsf algorithm that is able to jointly optimize two kinds of structures explicitly and directly via unified feature projection specifically the internal structure is represented based on locality preserving projection lpp and the external structure is captured by canonical correlation analysis cca the objective function of hsf combines two feature structures in a closed form which can be optimized alternately via linear programming and eigenvector methods the hsf solution provides not only the optimal feature projection but also the weights that encode the relative importance between two kinds of feature structures the experimental results on image classification face recognition shape analysis and infrared target recognition demonstrate the effectiveness and efficiency of hsf compared with state of the art methods graphical abstractdisplay omitted highlightsthe external and internal feature structures are jointly optimized for fusion two kinds of feature structures are preserved via a unified feature projection the nonlinear relationship between two kinds of feature structures is revealed the new feature fusion algorithm shows great promise in four classification problems

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

discriminative histograms of local dominant orientation d hldo for biometric image feature extraction this paper presents a simple and robust method namely discriminative histograms of local dominant orientation d hldo for biometric image feature extraction in d hldo the local dominant orientation map and the corresponding relative energy map are obtained by applying the singular value decomposition svd to the collected gradient vectors over a local patch the dominant orientation map and the relative energy map are then used to construct the concatenated histogram features local mean based nearest neighbor discriminant analysis lm nnda is finally employed to reduce the redundancy information and get the low dimensional and discriminative features the proposed method is applied to face finger knuckle print and palm biometrics and is examined using the ar cmu pie and frgcv2 0 face image databases the polyu palmprint database and the polyu finger knuckle print database experimental results demonstrate the effectiveness of the proposed d hldo method

fisher discrimination based low rank matrix recovery for face recognition in this paper we consider the issue of computing low rank lr recovery of matrices with sparse errors based on the success of low rank matrix recovery in statistical learning computer vision and signal processing a novel low rank matrix recovery algorithm with fisher discrimination regularization fdlr is proposed standard low rank matrix recovery algorithm decomposes the original matrix into a set of representative basis with a corresponding sparse error for modeling the raw data motivated by the fisher criterion the proposed fdlr executes low rank matrix recovery in a supervised manner i e taking the with class scatter and between class scatter into account when the whole label information are available the paper shows that the formulated model can be solved by the augmented lagrange multipliers and provides additional discriminating power over the standard low rank recovery models the representative bases learned by the proposed method are encouraged to be closer within the same class and as far as possible between different classes meanwhile the sparse error recovered by fdlr is not discarded as usual but treated as a feedback in the following classification tasks numerical simulations demonstrate that the proposed algorithm achieves the state of the art results

statistical properties of linear prediction analysis underlying the challenge of formant bandwidth estimation formant bandwidth estimation is often observed to be more challenging than the estimation of formant center frequencies due to the presence of multiple glottal pulses within a period and short closed phase durations this study explores inherently different statistical properties between linear prediction lp based estimates of formant frequencies and their corresponding bandwidths that may be explained in part by the statistical bounds on the variances of estimated lp coefficients a theoretical analysis of the cramer rao bounds on lp estimator variance indicates that the accuracy of bandwidth estimation is approximately twice as low as that of center frequency estimation monte carlo simulations of all pole vowels with stochastic and mixed source excitation demonstrate that the distributions of estimated lp coefficients exhibit expectedly different variances for each coefficient transforming the lp coefficients to formant parameters results in variances of bandwidth estimates being typically larger than the variances of respective center frequency estimates depending on vowel type and fundamental frequency these results provide additional evidence underlying the challenge of formant bandwidth estimation due to inherent statistical properties of lp based speech analysis

closed phase covariance analysis based on constrained linear prediction for glottal inverse filtering closed phase cp covariance analysis is a widely used glottal inverse filtering method based on the estimation of the vocal tract during the glottal cp since the length of the cp is typically short the vocal tract computation with linear prediction lp is vulnerable to the covariance frame position the present study proposes modification of the cp algorithm based on two issues first and most importantly the computation of the vocal tract model is changed from the one used in the conventional lp into a form where a constraint is imposed on the dc gain of the inverse filter in the filter optimization with this constraint lp analysis is more prone to give vocal tract models that are justified by the source filter theory that is they show complex conjugate roots in the formant regions rather than unrealistic resonances at low frequencies second the new cp method utilizes a minimum phase inverse filter the method was evaluated using synthetic vowels produced by physical modeling and natural speech the results show that the algorithm improves the performance of the cp type inverse filtering and its robustness with respect to the covariance frame position

exploiting the relationships among several binary classifiers via data transformation the structural resemblance among several existing classifiers has motivated us to investigate their underlying relationships by exploring into the mapping solutions of these classifiers we found that they can be linked by simple feature data scaling in other words the key to these relationships lies upon how the replica of feature data are being scaled this finding leads us directly to an exploration of novel classifiers beyond existing settings based on an extensive empirical evaluation we show that the proposed formulation facilitates a tuning capability beyond existing settings for classifier generalization highlightsestablishment of relationship among several binary classifiers exploration of a random projection network for such classifier learning proposal of novel classifier which exploits the established relationship observe the performance of novel classifier on several performance measures

synergistic modes of vocal tract articulation for american english vowels the purpose of this study was to investigate the spatial similarity of vocal tract shaping patterns across speakers and the similarity of their acoustic effects vocal tract area functions for 11 american english vowels were obtained from six speakers three female and three male using magnetic resonance imaging mri each speaker s set of area functions was then decomposed into mean area vectors and representative modes eigenvectors using principal components analysis pca three modes accounted for more than 90 of the variance in the original data sets for each speaker the general shapes of the first two modes were found to be highly correlated across all six speakers to demonstrate the acoustic effects of each mode both in isolation and combined a mapping between the mode scaling coefficients and f1 f2 pairs was generated for each speaker the mappings were unique for all six speakers in terms of the exact shape of the f1 f2 vowel space but the general effect of the modes was the same

minimum variance in biased estimation with singular fisher information matrix this paper extends the work of y c eldar ldquominimum variance in biased estimation bounds and asymptotically optimal estimators rdquo in ieee trans signal process vol 52 pp 1915 1929 jul 2004 which deals with only nonsingular fisher information matrix in order to guarantee the uniform cramer rao bound to be a finite lower bound and also to have a feasible solution to the optimization problem in the work of y c eldar it is proved that the norms of bias gradient matrices of all biased estimators must have a nonzero exact lower bound which mainly depends on the rank of the singular fisher information matrix the smaller the rank of the singular fisher information matrix is the larger the lower bound of norms of bias gradient matrices of all biased estimators is for a specific frobenius norm the exact lower bound is simply the difference between the parameter dimension and the rank of the singular fisher information matrix

face recognition based on the uncorrelated discriminant transformation abstract the extraction of discriminant features is the most fundamental and important problem in face recognition this paper presents a method to extract optimal discriminant features for face images by using the uncorrelated discriminant transformation and kl expansion experiments on the orl database and the nust603 database have been performed experimental results show that the uncorrelated discriminant transformation is superior to the foley sammon discriminant transformation and the new method to extract uncorrelated discriminant features for face images is very effective an error rate of 2 5 is obtained with the experiments on the orl database an average error rate of 1 2 is obtained with the experiments on the nust603 database experiments show that by extracting uncorrelated discriminant features face recognition could be performed with higher accuracy on lower than 16 16 resolution mosaic images it is suggested that for the uncorrelated discriminant transformation the optimal face image resolution can be regarded as the resolution m n which makes the dimensionality n mn of the original image vector space be larger and closer to the number of known face classes

extracting the optimal dimensionality for local tensor discriminant analysis supervised dimensionality reduction with tensor representation has attracted great interest in recent years it has been successfully applied to problems with tensor data such as image and video recognition tasks however in the tensor based methods how to select the suitable dimensions is a very important problem since the number of possible dimension combinations exponentially increases with respect to the order of tensor manually selecting the suitable dimensions becomes an impossible task in the case of high order tensor in this paper we aim at solving this important problem and propose an algorithm to extract the optimal dimensionality for local tensor discriminant analysis experimental results on a toy example and real world data validate the effectiveness of the proposed method

a lower bound on the bayesian mse based on the optimal bias function a lower bound on the minimum mean squared error mse in a bayesian estimation problem is proposed in this paper this bound utilizes a well known connection to the deterministic estimation setting using the prior distribution the bias function which minimizes the cramer rao bound can be determined resulting in a lower bound on the bayesian mse the bound is developed for the general case of a vector parameter with an arbitrary probability distribution and is shown to be asymptotically tight in both the high and low signal to noise ratio snr regimes a numerical study demonstrates several cases in which the proposed technique is both simpler to compute and tighter than alternative methods

on the computation of the cramer rao bound for arma parameter estimation the cramer rao lower bound crlb provides a useful tool for evaluating the performance of parameter estimation techniques several techniques for the computation of the asymptotic form of the crlb for arma models are presented it is shown that the asymptotic crlb can be expressed as an explicit function of the model parameters

efficient computation of the covariance sequence of an autoregressive process an efficient algorithm is presented for computing the covariance sequence of a multichannel autoregressive process represented by a set of reflection coefficients the covariance sequence is shown to be the impulse response of a certain lattice filter related to the optimal predictor

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

integral solution of a class of nonlinear integral equations this paper is concerned with the existence of integral solutions to a general nonlinear integral equationx t f 1 t x f 1 t f 2t 0 f 2 t k t s f 3 s x f 3 s ds t r with the help of krasnoselskii s fixed point theorem and the theory of measure of weak noncompactness we establish a new and general existence theorem for the nonlinear functional integral equation moreover an example which can not be treated by the related theorems in 5 20 22 is given to illustrate the new existence theorem

pareto models for discriminative multiclass linear dimensionality reduction we address the class masking problem in multiclass linear discriminant analysis lda in the multiclass setting lda does not maximize each pairwise distance between classes but rather maximizes the sum of all pairwise distances this results in serious overlaps between classes that are close to each other in the input space and degrades classification performance our research proposes pareto discriminant analysis parda an approach for multiclass discriminative analysis that builds over multiobjective optimizing models parda decomposes the multiclass problem to a set of objective functions each representing the distance between every pair of classes unlike existing lda extensions that maximize the sum of all distances parda maximizes each pairwise distance to maximally separate all class means while minimizing the class overlap in the lower dimensional space experimental results on various data sets show consistent and promising performance of parda when compared with well known multiclass lda extensions highlightswe address the class masking problem cmp in multiclass lda mlda we model mlda as a set of objective functions for pairwise distances between classes we optimize the compound objective function using multiobjective optimization our models overcome the cmp and are extended to multimodal non gaussian data empirical analysis shows consistent and promising performance in favor of our models

a two stage linear discriminant analysis via qr decomposition linear discriminant analysis lda is a well known method for feature extraction and dimension reduction it has been used widely in many applications involving high dimensional data such as image and text classification an intrinsic limitation of classical lda is the so called singularity problems that is it fails when all scatter matrices are singular many lda extensions were proposed in the past to overcome the singularity problems among these extensions pca lda a two stage method received relatively more attention in pca lda the lda stage is preceded by an intermediate dimension reduction stage using principal component analysis pca most previous lda extensions are computationally expensive and not scalable due to the use of singular value decomposition or generalized singular value decomposition in this paper we propose a two stage lda method namely lda qr which aims to overcome the singularity problems of classical lda while achieving efficiency and scalability simultaneously the key difference between lda qr and pca lda lies in the first stage where lda qr applies qr decomposition to a small matrix involving the class centroids while pca lda applies pca to the total scatter matrix involving all training data points we further justify the proposed algorithm by showing the relationship among lda qr and previous lda methods extensive experiments on face images and text documents are presented to show the effectiveness of the proposed algorithm

penalized maximum likelihood estimation of covariance matrices with linear structure in this paper a space alternating generalized expectation maximization sage algorithm is presented for the numerical computation of maximum likelihood ml and penalized ml pml estimates of the parameters of covariance matrices with linear structure for complex gaussian processes by using a less informative hidden data space and a sequential parameter update scheme a sage based algorithm is derived for which convergence of the likelihood is demonstrated to be significantly faster than that of an em based algorithm that has been previously proposed in addition the sage procedure is shown to easily accommodate penalty functions and a sage based algorithm is derived and demonstrated for forming pml estimates with a quadratic smoothness penalty

image reconstruction and restoration overview of common estimation structures and problems developments in the theory of image reconstruction and restoration over the past 20 or 30 years are outlined particular attention is paid to common estimation structures and to practical problems not properly solved yet the problem of image reconstruction and restoration is first formulated some of the current regularization approaches used to solve the problem are then described the concepts of a priori information and compound criterion are introduced a bayesian interpretation of the regularization techniques is given which clarifies the role of the tuning parameters and indicates how they could be estimated the practical aspects of computing the solution first when the hyperparameters are known and second when they must be estimated are then considered conclusions are drawn and points that still need to be investigated are outlined

existence and uniqueness of solutions to semilinear nonlocal parabolic equations abstract the banach contraction mapping theorem and the theory of analytic semigroups are used to prove the existence and uniqueness of solutions to nonlocal semilinear parabolic partial differential equations the equations consist of a parabolic boundary value problem and a relation connecting the initial value to values or weighted averages of values of the solution at other times

semilinear integrodifferential equations with nonlocal initial conditions abstract of concern is the cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions under general and natural hypotheses we establish some new theorems about the existence and uniqueness of solutions for the cauchy problem as a consequence we unify and extend the corresponding theorems given previously for the cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions moreover we present two examples one of which comes from heat conduction in materials with memory to show that the existing results are not applicable to them in contrast with ours

an optimal orthonormal system for discriminant analysis abstract this paper proposes a new discriminant analysis with orthonormal coordinate axes of the feature space in general the number of coordinate axes of the feature space in the traditional discriminant analysis depends on the number of pattern classes therefore the discriminatory capability of the feature space is limited considerably the new discriminant analysis solves this problem completely in addition it is more powerful than the traditional one in so far as the discriminatory power and the mean error probability for coordinate axes are concerned this is also shown by a numerical example

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

dimensionality reduction of multimodal labeled data by local fisher discriminant analysis reducing the dimensionality of data without losing intrinsic information is an important preprocessing step in high dimensional data analysis fisher discriminant analysis fda is a traditional technique for supervised dimensionality reduction but it tends to give undesired results if samples in a class are multimodal an unsupervised dimensionality reduction method called locality preserving projection lpp can work well with multimodal data due to its locality preserving property however since lpp does not take the label information into account it is not necessarily useful in supervised learning scenarios in this paper we propose a new linear supervised dimensionality reduction method called local fisher discriminant analysis lfda which effectively combines the ideas of fda and lpp lfda has an analytic form of the embedding transformation and the solution can be easily computed just by solving a generalized eigenvalue problem we demonstrate the practical usefulness and high scalability of the lfda method in data visualization and classification tasks through extensive simulation studies we also show that lfda can be extended to non linear dimensionality reduction scenarios by applying the kernel trick

maximum likelihood least squares and penalized least squares for pet the em algorithm is the basic approach used to maximize the log likelihood objective function for the reconstruction problem in positron emission tomography pet the em algorithm is a scaled steepest ascent algorithm that elegantly handles the nonnegativity constraints of the problem it is shown that the same scaled steepest descent algorithm can be applied to the least squares merit function and that it can be accelerated using the conjugate gradient approach the experiments suggest that one can cut the computation by about a factor of 3 by using this technique the results are applied to various penalized least squares functions which might be used to produce a smoother image

on a class of retarded integro differential equations with nonlocal initial conditions of concern is the following cauchy problem for fractional integro differential equations with time delay and nonlocal initial condition u t email protected 0 t t s m email protected m 1 au s ds f t u t u k t t 0 u t h t u email protected t email protected email protected 0 where 1 0 a d a x x is a generator of a solution operator on a complex banach space x the convolution integral in the equation is known as the riemann liouville fractional integral k t 0 email protected representing the delay property is a function and h t is an operator defined from email protected 0 xc email protected 0 x into x for some t 0 which constitutes a nonlocal condition the local existence and uniqueness of mild solutions for the cauchy problem under various criteria are proved moreover we present an existence result of the global solution also an example is given to illustrate the applications of the abstract results

minimum variance in biased estimation bounds and asymptotically optimal estimators we develop a uniform cramer rao lower bound ucrlb on the total variance of any estimator of an unknown vector of parameters with bias gradient matrix whose norm is bounded by a constant we consider both the frobenius norm and the spectral norm of the bias gradient matrix leading to two corresponding lower bounds we then develop optimal estimators that achieve these lower bounds in the case in which the measurements are related to the unknown parameters through a linear gaussian model tikhonov regularization is shown to achieve the ucrlb when the frobenius norm is considered and the shrunken estimator is shown to achieve the ucrlb when the spectral norm is considered for more general models the penalized maximum likelihood pml estimator with a suitable penalizing function is shown to asymptotically achieve the ucrlb to establish the asymptotic optimality of the pml estimator we first develop the asymptotic mean and variance of the pml estimator for any choice of penalizing function satisfying certain regularity constraints and then derive a general condition on the penalizing function under which the resulting pml estimator asymptotically achieves the ucrlb this then implies that from all linear and nonlinear estimators with bias gradient whose norm is bounded by a constant the proposed pml estimator asymptotically results in the smallest possible variance

global plus local linear discriminant analysis lda is one of the most popular supervised feature extraction techniques used in machine learning and pattern classification however lda only captures global geometrical structure information of the data and ignores the geometrical structure information of local data points though many articles have been published to address this issue most of them are incomplete in the sense that only part of the local information is used we show here that there are total three kinds of local information namely local similarity information local intra class pattern variation and local inter class pattern variation we first propose a new method called enhanced within class lda ewlda algorithm to incorporate the local similarity information and then propose a complete framework called complete global local lda cglda algorithm to incorporate all these three kinds of local information experimental results on two image databases demonstrate the effectiveness of our algorithms there are three kinds of local information that exist for linear discriminant analysis for incorporating the local similarity information we propose the ewlda algorithm for incorporating the three kinds of local information we propose the cglda algorithm

a new lda based face recognition system which can solve the small sample size problem a new lda based face recognition system is presented in this paper linear discriminant analysis lda is one of the most popular linear projection techniques for feature extraction the major drawback of applying lda is that it may encounter the small sample size problem in this paper we propose a new lda based technique which can solve the small sample size problem we also prove that the most expressive vectors derived in the null space of the within class scatter matrix using principal component analysis pca are equal to the optimal discriminant vectors derived in the original space using lda the experimental results show that the new lda process improves the performance of a face recognition system signi cantly 2000 pattern recognition society published by elsevier science ltd all rights reserved

efficient and robust feature extraction by maximum margin criterion in pattern recognition feature extraction techniques are widely employed to reduce the dimensionality of data and to enhance the discriminatory information principal component analysis pca and linear discriminant analysis lda are the two most popular linear dimensionality reduction methods however pca is not very effective for the extraction of the most discriminant features and lda is not stable due to the small sample size problem in this paper we propose some new linear and nonlinear feature extractors based on maximum margin criterion mmc geometrically feature extractors based on mmc maximize the average margin between classes after dimensionality reduction it is shown that mmc can represent class separability better than pca as a connection to lda we may also derive lda from mmc by incorporating some constraints by using some other constraints we establish a new linear feature extractor that does not suffer from the small sample size problem which is known to cause serious stability problems for lda the kernelized nonlinear counterpart of this linear feature extractor is also established in the paper our extensive experiments demonstrate that the new feature extractors are effective stable and efficient

optimality analysis of sensor target localization geometries the problem of target localization involves estimating the position of a target from multiple noisy sensor measurements it is well known that the relative sensor target geometry can significantly affect the performance of any particular localization algorithm the localization performance can be explicitly characterized by certain measures for example by the cramer rao lower bound which is equal to the inverse fisher information matrix on the estimator variance in addition the cramer rao lower bound is commonly used to generate a so called uncertainty ellipse which characterizes the spatial variance distribution of an efficient estimate i e an estimate which achieves the lower bound the aim of this work is to identify those relative sensor target geometries which result in a measure of the uncertainty ellipse being minimized deeming such sensor target geometries to be optimal with respect to the chosen measure the optimal sensor target geometries for range only time of arrival based and bearing only localization are identified and studied in this work the optimal geometries for an arbitrary number of sensors are identified and it is shown that an optimal sensor target configuration is not in general unique the importance of understanding the influence of the sensor target geometry on the potential localization performance is highlighted via formal analytical results and a number of illustrative examples

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

existence of solutions for neutral integro differential equations with state dependent delay in this paper we study the existence and regularity of solutions for a neutral functional integro differential equation with state dependent delay in banach space the mild solutions are investigated by sadovskii fixed point theorem under compactness condition for the resolvent operator and the theory of fractional power and a norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives the strict solutions are obtained under holder continuity condition hence this work extends and develops the existed results on this topic in the end an example is provided to illustrate the application of the obtained results

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

modeling the glottal volume velocity waveform for three voice types the purpose of this study was to model features of the glottal volume velocity waveform for three voice types modal voice vocal fry and breathy voice the study analyzed data measured from two sustained vowels and one sentence uttered by nine adult male subjects who represented examples of the three voice types the primary analysis procedure was glottal inverse filtering which estimated the glottal volume velocity waveform the estimated glottal volume velocity waveform was then fit to an lf model waveform four parameters of the lf model were adjusted to minimize the mean squared error between the estimated glottal waveform and the lf model waveform statistical averages and standard deviations of the four parameters of the lf glottal waveform model were calculated using the data for each voice type the four lf model parameters characterize important low frequency features of the glottal waveform namely the glottal pulse width pulse skewness abruptness of closure of the glottal pulse and the

a novel location penalized maximum likelihood estimator for bearing only target localization in this paper we present a location penalized maximum likelihood lpml estimator for bearing only target localization we develop a new penalized maximum likelihood cost function by transforming the variables of target position and bearings the new penalized likelihood function can also be recognized as a posterior distribution under a bayesian framework by penalizing a prior we give analysis of the asymptotic properties and show that both traditional bearing maximum likelihood tbml and lpml estimators are asymptotically efficient estimators to compare the performances of the tbml and lpml estimators we analyze the cramer rao lower bound crlb of the two estimators and show that the bound of the lpml estimator is lower than that of the tbml estimator extensive simulations are performed it is observed that the new lpml algorithm consistently outperforms other well known algorithms field experiments are also conducted by applying this method to localize a vehicle using real world data acquired by an acoustic array sensor network the new lpml algorithm demonstrates superior performance in all the field experiments

existence of mild solutions for fractional integrodifferential equations of sobolev type with nonlocal conditions abstract this paper is concerned with the fractional integrodifferential equations of sobolev type with nonlocal condition in a separable banach space with the help of the theory of propagation family as well as the theory of the measures of noncompactness and the condensing maps we obtain the existence result of mild solutions for above equations two examples are given to illustrate the existence theorem

enhanced fisher discriminant criterion for image recognition many previous studies have shown that image recognition can be significantly improved by fisher linear discriminant analysis flda technique however flda ignores the variation of data points from the same class which characterizes the most important modes of variability of patterns and helps to improve the generalization capability of flda thus the performance of flda on testing data is not good enough in this paper we propose an enhanced fisher discriminant criterion efdc efdc explicitly considers the intra class variation and incorporates the intra class variation into the fisher discriminant criterion to build a robust and efficient dimensionality reduction function efdc obtains a subspace which best detects the discriminant structure and simultaneously preserves the modes of variability of patterns which will result in stable intraclass representation experimental results on four image database show a clear improvement over the results of flda based methods

tensor linear laplacian discrimination tlld for feature extraction discriminant feature extraction plays a central role in pattern recognition and classification in this paper we propose the tensor linear laplacian discrimination tlld algorithm for extracting discriminant features from tensor data tlld is an extension of linear discriminant analysis lda and linear laplacian discrimination lld in directions of both nonlinear subspace learning and tensor representation based on the contextual distance the weights for the within class scatters and the between class scatter can be determined to capture the principal structure of data clusters this makes tlld free from the metric of the sample space which may not be known moreover unlike lld the parameter tuning of tlld is very easy experimental results on face recognition texture classification and handwritten digit recognition show that tlld is effective in extracting discriminative features

efficient construction of canonical ladder forms for vector autoregressive processes the paper treats the problem of constructing canonical ladder realizations for vector autoregressive ar processes specified by their characteristic matrix polynomials the difficulty of this problem is rooted in the fact that the backward matrix polynomial corresponding to a given vector ar process is a nontrivial function of the forward matrix polynomial the construction calls for solving a discrete lyapunov equation in block controller form two efficient procedures for solving this equation are presented both requiring a number of operations that is proportional to at most the square of the model order applications of the new procedures to stability tests simulation of ar processes and model reduction are described

minimum bias multiple taper spectral estimation two families of orthonormal tapers are proposed for multitaper spectral analysis minimum bias tapers and sinusoidal tapers spl upsisup k where spl upsisub nsup k spl radic 2 n 1 sin spl pi kn n 1 and n is the number of points the resulting sinusoidal multitaper spectral estimate is s spl circ f 1 2k n 1 spl sigmasub j 1sup k y f j 2n 2 y f j 2n 2 sup 2 where y f is the fourier transform of the stationary time series s f is the spectral density and k is the number of tapers for fixed j the sinusoidal tapers converge to the minimum bias tapers like 1 n since the sinusoidal tapers have analytic expressions no numerical eigenvalue decomposition is necessary both the minimum bias and sinusoidal tapers have no additional parameter for the spectral bandwidth the bandwidth of the jth taper is simply 1 n centered about the frequencies spl plusmn j 2n 2 thus the bandwidth of the multitaper spectral estimate can be adjusted locally by simply adding or deleting tapers the band limited spectral concentration spl intsub wsup w v f sup 2 df of both the minimum bias and sinusoidal tapers is very close to the optimal concentration achieved by the slepian 1978 tapers in contrast the slepian tapers can have the local bias spl intsub 1 2 sup 1 2 f sup 2 v f sup 2 df much larger than of the minimum bias tapers and the sinusoidal tapers

uniformly improving the cramer rao bound and maximum likelihood estimation an important aspect of estimation theory is characterizing the best achievable performance in a given estimation problem as well as determining estimators that achieve the optimal performance the traditional cramer rao type bounds provide benchmarks on the variance of any estimator of a deterministic parameter vector under suitable regularity conditions while requiring a priori specification of a desired bias gradient in applications it is often not clear how to choose the required bias a direct measure of the estimation error that takes both the variance and the bias into account is the mean squared error mse which is the sum of the variance and the squared norm of the bias here we develop bounds on the mse in estimating a deterministic parameter vector x0 over all bias vectors that are linear in x0 which includes the traditional unbiased estimation as a special case in some settings it is possible to minimize the mse over all linear bias vectors more generally direct minimization is not possible since the optimal solution depends on the unknown x0 nonetheless we show that in many cases we can find bias vectors that result in an mse bound that is smaller than the cramer rao lower bound crlb for all values of x0 furthermore we explicitly construct estimators that achieve these bounds in cases where an efficient estimator exists by performing a simple linear transformation on the standard maximum likelihood ml estimator this leads to estimators that result in a smaller mse than the ml approach for all possible values of x0

low complexity methods for estimation after parameter selection statistical inference of multiple parameters often involves a preliminary parameter selection stage the selection stage has an impact on subsequent estimation for example by introducing a selection bias the post selection maximum likelihood psml estimator is shown to reduce the selection bias and the post selection mean squared error psmse compared with conventional estimators such as the maximum likelihood ml estimator however the computational complexity of the psml is usually high due to the multi dimensional exhaustive search for a global maximum of the post selection log likelihood psll function moreover the psll involves the probability of selection that in general does not have an analytical form in this paper we develop new low complexity post selection estimation methods for a two stage estimation after parameter selection architecture the methods are based on implementing the iterative maximization by parts mbp approach which is based on the decomposition of the psll function into easily optimized and complicated parts the proposed second best psml method applies the mbp psml algorithm with a pairwise probability of selection between the two highest ranked parameters w r t the selection rule the proposed sa psml method is based on using stochastic approximation sa and monte carlo integrations to obtain a non parametric estimation of the gradient of the probability of selection and then applying the mbp psml algorithm on this approximation for low complexity performance analysis we develop the empirical post selection cram acute text e r rao type lower bound simulations demonstrate that the proposed post selection estimation methods are tractable and reduce both the bias and the psmse compared with the ml estimator while only requiring moderate computational complexity