differential area profiles decomposition properties and efficient computation differential area profiles daps are point based multiscale descriptors used in pattern analysis and image segmentation they are defined through sets of size based connected morphological filters that constitute a joint area opening top hat and area closing bottom hat scale space of the input image the work presented in this paper explores the properties of this image decomposition through sets of area zones an area zone defines a single plane of the dap vector field and contains all the peak components of the input image whose size is between the zone s attribute extrema area zones can be computed efficiently from hierarchical image representation structures in a way similar to regular attribute filters operations on the dap vector field can then be computed without the need for exporting it first and an example with the leveling like convex concave segmentation scheme is given this is referred to as the one pass method and it is demonstrated on the max tree structure its computational performance is tested and compared against conventional means for computing differential profiles relying on iterative application of area openings and closings applications making use of the area zone decomposition are demonstrated in problems related to remote sensing and medical image analysis

asymptotic expansions for multivariate polynomial approximation in this paper the approximation of multivariate functions by multivariate bernstein polynomials is considered building on recent work of lai we can prove that the sequence of these bernstein polynomials possesses an asymptotic expansion with respect to the index n this generalizes a corresponding result due to costabile gualtieri and serra on univariate bernstein polynomials providing at the same time a new proof for it after having shown the existence of an asymptotic expansion we can apply an extrapolation algorithm which accelerates the convergence of the bernstein polynomials considerably this leads to a new and very efficient method for polynomial approximation of multivariate functions numerical examples illustrate our approach

improving performance of fxlms algorithm for active noise control of impulsive noise this paper concerns active noise control anc of impulsive noise modeled using non gaussian stable processes the most famous filtered x least mean square fxlms algorithm for anc systems is based on minimization of variance of error signal for the impulse noise the fxlms algorithm becomes unstable as second order moments do not exist for non gaussian processes among the existing algorithms for anc of impulsive noise one is based on minimizing least mean p power lmp of the error signal resulting in fxlmp algorithm the other is based on modifying on the basis of statistical properties the reference signal in update of fxlms algorithm in this paper the proposed algorithm is an extension of the later approach extensive simulations are carried out which demonstrate the effectiveness of the proposed algorithm it achieves the best performance among the existing algorithms and at the same computational complexity as that of fxlms algorithm

learning group based sparse and low rank representation for hyperspectral image classification previous studies have demonstrated that the structured sparse representation can yield significant improvements in spectral spatial hyperspectral classification however a dictionary that contains all of the training samples in the sparsity aware methods is ineffective in capturing the class discriminative information this paper makes the first attempt to learn group based sparse and low rank representation for improving the dictionary first super pixel segmentation is applied to obtain homogeneous regions that act as spatial groups dictionary is then learned with group based sparse and low rank regularizations to achieve common representation matrix for the same spatial group those group based sparse and low rank regularizations facilitate identifying both local and global structure of the hyperspectral image hsi finally representation matrices of test samples are employed to determine the class labels by a linear support vector machine svm experimental results on two benchmark hsis show that the proposed method achieves better performance than the state of the art methods even with small sample sizes highlightspropose a gslr method to learn structured dictionary for hsi apply fast super pixel segmentation method to gain spatial groups add group based sparse and low rank regularizations for dictionary learning update representation matrix by ialm and dictionary by bcd classify representation matrices of test samples by linear svm

classification of hyperspectral images by tensor modeling and additive morphological decomposition pixel wise classification in high dimensional multivariate images is investigated the proposed method deals with the joint use of spectral and spatial information provided in hyperspectral images additive morphological decomposition amd based on morphological operators is proposed amd defines a scale space decomposition for multivariate images without any loss of information amd is modeled as a tensor structure and tensor principal components analysis is compared as dimensional reduction algorithm versus classic approach experimental comparison shows that the proposed algorithm can provide better performance for the pixel classification of hyperspectral image than many other well known techniques highlights additive morphological decomposition without any loss of information is proposed decomposition is modeled as a tensor structure tensor pca is compared versus pca proposed workflow performs better than other techniques in hsi classification

concentration inequalities for the missing mass and for histogram rule error this paper gives distribution free concentration inequalities for the missing mass and the error rate of histogram rules negative association methods can be used to reduce these concentration problems to concentration questions about independent sums although the sums are independent they are highly heterogeneous such highly heterogeneous independent sums cannot be analyzed using standard concentration inequalities such as hoeffding s inequality the angluin valiant bound bernstein s inequality bennett s inequality or mcdiarmid s theorem the concentration inequality for histogram rule error is motivated by the desire to construct a new class of bounds on the generalization error of decision trees

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

algebraic feature extraction for image recognition based on an optimal discriminant criterion abstract a novel algebraic feature extraction method for image recognition is presented the main difference between the present method and any other existing algebraic feature extraction method is that the present method uses an optimal discriminant criterion to extract algebraic features for the given training image samples a set of optimal discriminant projection vectors is calculated according to a generalized fisher criterion function on the basis of the optimal discriminant projection vector the projective feature vectors of an image i e algebraic features are extracted by projecting the image onto all optimal discriminant projection vectors the method of calculating the set of optimal discriminant projection vectors is discussed a minimum distance classifier is also proposed for classifying projective feature vectors experimental results showed that the present method has good recognition performance an important conclusion about the present method is that the foley sammon optimal set of discriminant vectors is a special case of the set of optimal discriminant projection vectors

learning over sets using kernel principal angles we consider the problem of learning with instances defined over a space of sets of vectors we derive a new positive definite kernel f a b defined over pairs of matrices a b based on the concept of principal angles between two linear subspaces we show that the principal angles can be recovered using only inner products between pairs of column vectors of the input matrices thereby allowing the original column vectors of a b to be mapped onto arbitrarily high dimensional feature spaces we demonstrate the usage of the matrix based kernel function f a b with experiments on two visual tasks the first task is the discrimination of irregular motion trajectory of an individual or a group of individuals in a video sequence we use the svm approach using f a b where an input matrix represents the motion trajectory of a group of individuals over a certain fixed time frame we show that the classification irregular versus regular greatly outperforms the conventional representation where all the trajectories form a single vector the second application is the visual recognition of faces from input video sequences representing head motion and facial expressions where f a b is used to compare two image sequences

fast cartoon texture image filters can images be decomposed into the sum of a geometric part and a textural part in a theoretical breakthrough y meyer oscillating patterns in image processing and nonlinear evolution equations providence ri american mathematical society 2001 proposed variational models that force the geometric part into the space of functions with bounded variation and the textural part into a space of oscillatory distributions meyer s models are simple minimization problems extending the famous total variation model however their numerical solution has proved challenging it is the object of a literature rich in variants and numerical attempts this paper starts with the linear model which reduces to a low pass high pass filter pair a simple conversion of the linear filter pair into a nonlinear filter pair involving the total variation is introduced this new proposed nonlinear filter pair retains both the essential features of meyer s models and the simplicity and rapidity of the linear model it depends upon only one transparent parameter the texture scale measured in pixel mesh comparative experiments show a better and faster separation of cartoon from texture one application is illustrated edge detection

compound rank k projections for bilinear analysis in many real world applications data are represented by matrices or high order tensors despite the promising performance the existing 2 d discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection making the model less flexible in this paper we propose a novel compound rank k projection crp algorithm for bilinear analysis the crp deals with matrices directly without transforming them into vectors and it therefore preserves the correlations within the matrix and decreases the computation complexity different from the existing 2 d discriminant analysis algorithms objective function values of crp increase monotonically in addition the crp utilizes multiple rank k projection models to enable a larger search space in which the optimal solution can be found in this way the discriminant ability is enhanced we have tested our approach on five data sets including uuim cvl pointing 04 usps and coil20 experimental results show that the performance of our proposed crp performs better than other algorithms in terms of classification accuracy

rapid and brief communication face recognition based on 2d fisherface approach two dimensional 2d discrimination analysis using methods such as 2d pca and image lda is of interest in face recognition because it extracts discriminative features faster than one dimensional 1d discrimination analysis however existing 2d methods generally use more discriminative features and take longer to test than 1d methods 2d pca in particular cannot make full use of the fisher discriminant criterion image lda also has drawbacks in that it cannot perform 2d principal component analysis and discards components with poor discriminative capabilities in addition existing 2d methods cannot provide an automatic strategy to choose 2d principal components or discriminant vectors in this paper we propose 2d fisherface a novel discrimination approach that combines the two stage pca lda strategy and 2d discrimination techniques it can extract face discriminative features by automatically selecting two dimensional principal components and discriminant vectors using the ar database as the test data it is shown that the proposed approach is faster and more effective than several representative 1d and 2d discrimination methods

fuzzy mathematical morphology for color images defined by fuzzy preference relations nowadays the representation and the treatment of color images are still open problems mathematical morphology is the natural area for a rigorous formulation of many problems in image analysis moreover it comprises powerful non linear techniques for filtering texture analysis shape analysis edge detection or segmentation a large number of morphological operators have been widely defined and tested to process binary and gray scale images however the extension of mathematical morphology operators to multi valued functions and in particular to color images is neither direct nor general due to the vectorial nature of the data in this paper basic morphological operators erosion and dilation are extended to color images from a new vector ordering scheme based on a fuzzy order in the rgb color space experimental results show that the proposed color operators can be efficiently used for color image processing highlightsfuzzy mathematical morphology for color images erosion and dilation operators avoid false colors proposed order considers all the components with the same weight

learning theory for distribution regression we focus on the distribution regression problem regressing to vector valued outputs from probability measures many important machine learning and statistical tasks fit into this framework including multi instance learning and point estimation problems without analytical solution such as hyperparameter or entropy estimation despite the large number of available heuristics in the literature the inherent two stage sampled nature of the problem makes the theoretical analysis quite challenging since in practice only samples from sampled distributions are observable and the estimates have to rely on similarities computed between sets of points to the best of our knowledge the only existing technique with consistency guarantees for distribution regression requires kernel density estimation as an intermediate step which often performs poorly in practice and the domain of the distributions to be compact euclidean in this paper we study a simple analytically computable ridge regression based alternative to distribution regression where we embed the distributions to a reproducing kernel hilbert space and learn the regressor from the embeddings to the outputs our main contribution is to prove that this scheme is consistent in the two stage sampled setup under mild conditions on separable topological domains enriched with kernels we present an exact computational statistical efficiency trade off analysis showing that our estimator is able to match the one stage sampled minimax optimal rate caponnetto and de vito 2007 steinwart et al 2009 this result answers a 17 year old open question establishing the consistency of the classical set kernel haussler 1999 gartner et al 2002 in regression we also cover consistency for more recent kernels on distributions including those due to christmann and steinwart 2010

optimal discriminant plane for a small number of samples and design method of classifier on the plane abstract in a previous work zi quan hong and jing yu yang minimum distance classifier on the optimal discriminant plane we suggested and derived a method for constructing classifier on the optimal discriminant plane using minimum distance criteria in this paper the problem of solving optimal discriminant plane for a small number of samples is discussed which is based on the above paper by the same authors in the case of a small number of samples generalized eigenequation ax bx established for a large number of samples usually has no solution because within class scatter matrix is singular to obtain the solution of the generalized eigenequation a new method is suggested in which the singular value perturbation is added to the within class scatter matrix such that the matrix becomes a nonsingular matrix therefore the generalized eigenequation can be solved using existing algorithms we proved that the generalized eigenequations on the optimal discriminant plane are stable in respect of eigenvalues and the generalized eigenvectors are indeed the optimal discriminant directions if the perturbation is subject to some certain conditions the experimental results have shown that our method works well and the minimum distance classifier on the optimal discriminant plane can be constructed with high performance even in the case of a small number of samples

segmented minimum noise fraction transformation for efficient feature extraction of hyperspectral images in this paper a segmented minimum noise fraction mnf transformation is proposed for efficient feature extraction of hyperspectral images hsis the original bands can be partitioned into several highly correlated subgroups based on the correlation matrix image of the hyperspectral data the mnf is implemented separately on each subgroup of the data and then the bhattacharyya distance is used as the band separability measure for feature extraction consequently the extracted features can then be significantly classified using state of art classifiers i e k nn or svm experiments on two benchmark hsis collected by aviris and rosis demonstrate that the proposed method significantly reduces the transformation time in comparison with the conventional mnf the fisher scalars criterion shows that the class separability with the segmented mnf is the best and the extracted features even exhibit higher classification accuracy compared with the pca or mnf highlightsa segmented minimum noise fraction mnf transformation is proposed for efficient feature extraction of hyperspectral images hsis the proposed method significantly reduces the transformation time in comparison with the conventional mnf the class separability of the extracted features is improved the extracted features by smnf even exhibit higher classification accuracy compared with the pca or mnf

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

from sample similarity to ensemble similarity probabilistic distance measures in reproducing kernel hilbert space this paper addresses the problem of characterizing ensemble similarity from sample similarity in a principled manner using a reproducing kernel as a characterization of sample similarity we suggest a probabilistic distance measure in the reproducing kernel hilbert space rkhs as the ensemble similarity assuming normality in the rkhs we derive analytic expressions for probabilistic distance measures that are commonly used in many applications such as chernoff distance or the bhattacharyya distance as its special case kullback leibler divergence etc since the reproducing kernel implicitly embeds a nonlinear mapping our approach presents a new way to study these distances whose feasibility and efficiency is demonstrated using experiments with synthetic and real examples further we extend the ensemble similarity to the reproducing kernel for ensemble and study the ensemble similarity for more general data representations

tensor decompositions and applications this survey provides an overview of higher order tensor decompositions their applications and available software a tensor is a multidimensional or n way array decompositions of higher order tensors i e n way arrays with n geq 3 have applications in psycho metrics chemometrics signal processing numerical linear algebra computer vision numerical analysis data mining neuroscience graph analysis and elsewhere two particular tensor decompositions can be considered to be higher order extensions of the matrix singular value decomposition candecomp parafac cp decomposes a tensor as a sum of rank one tensors and the tucker decomposition is a higher order form of principal component analysis there are many other tensor decompositions including indscal parafac2 candelinc dedicom and paratuck2 as well as nonnegative variants of all of the above the n way toolbox tensor toolbox and multilinear engine are examples of software packages for working with tensors

optimal fisher discriminant analysis using the rank decomposition abstract the fisher optimal discriminant vector is a very efficient means in high dimensional pattern analysis in the case of a small number of samples the within class scatter matrix s w is singular therefore the calculation of the fisher optimal discriminant vector becomes very important in this paper the conception of the rank decomposition of matrices is first introduced and a new method for calculating the fisher optimal discriminant vector is presented which is particularly well suited to the case of a small number of samples in the sense that the scatter matrices are rank deficient the new method is compared with the pseudoinverse and perturbation methods in tian j opt soc am a 5 1670 1672 1988 and hong and yang pattern recognition 24 317 324 1991 an important conclusion is proved in the three methods our method is the best one for calculating the fisher optimal discriminant vectors in the cases of both a large and a small number of samples the experimental results have also shown that our method can give the highest recognition rate in the case of a small number of samples among the three methods

general subspace learning with corrupted training data via graph embedding we address the following subspace learning problem supposing we are given a set of labeled corrupted training data points how to learn the underlying subspace which contains three components an intrinsic subspace that captures certain desired properties of a data set a penalty subspace that fits the undesired properties of the data and an error container that models the gross corruptions possibly existing in the data given a set of data points these three components can be learned by solving a nuclear norm regularized optimization problem which is convex and can be efficiently solved in polynomial time using the method as a tool we propose a new discriminant analysis i e supervised subspace learning algorithm called corruptions tolerant discriminant analysis ctda in which the intrinsic subspace is used to capture the features with high within class similarity the penalty subspace takes the role of modeling the undesired features with high between class similarity and the error container takes charge of fitting the possible corruptions in the data we show that ctda can well handle the gross corruptions possibly existing in the training data whereas previous linear discriminant analysis algorithms arguably fail in such a setting extensive experiments conducted on two benchmark human face data sets and one object recognition data set show that ctda outperforms the related algorithms

a novel feature extraction method for image recognition based on similar discriminant function sdf abstract the extraction of image features is the most fundamental and important problem in image recognition in this paper a similarity measure of matrices is first presented and a similar discriminant function sdf of images is established based on the discriminant function we further propose a novel feature extraction method for image recognition for each class of training image samples an optimal projection axis maximizing the similarity among these training image samples for the class is calculated unlike the common methods of feature extraction we extract a projective feature vector for a training image sample by projecting the image on the optimal projection axis of the class itself and a set of projective feature vectors for a testing image sample by projecting the image on all the optimal projection axes finally a hierarchical classifier in the optimal discriminant space is designed to recognize images in order to test the efficiency of our method it is used to recognize human faces and english characters experimental results have shown that our method has good recognition performance and the extracted projective feature vectors contain more recognition information than commonly used image features

adaptive volterra filter with continuous lp norm using a logarithmic cost for nonlinear active noise control abstract the filtered x least mean lp norm fxlmp algorithm is proven to be useful for nonlinear active noise control nanc systems however its performance deteriorates when the impulsive noises are presented in nanc systems to surmount this shortcoming a new nonlinear adaptive algorithm based on volterra expansion model vfxloglmp is developed in this paper which is derived by minimizing the lp norm of logarithmic cost it is found that the fxlmp and vfxloglmp require to select an appropriate value of p according to the prior information on noise characteristics which prohibit their practical applications based on vfxloglmp algorithm we proposed a continuous lp norm algorithm with logarithmic cost vfxlogclmp which does not need the parameter selection and thresholds estimation benefiting from the various error norms for 1 p 2 it remains the robustness of vfxloglmp moreover the convergence behavior of vfxlogclmp for moving average secondary paths and stochastic input signals is performed compared to the existing algorithms two versions of the proposed algorithms have much better convergence and stability in impulsive noise environments

algebraic feature extraction of image for recognition abstract the extraction of image features is one of the fundamental tasks in image recognition up until now there have been several kinds of features to be used for the purpose of image recognition as follows 1 visual features 2 statistical features of pixel 3 transform coefficient features in addition there is another kind of feature which the author believes is very useful i e 4 algebraic features which represent intrinsic attributions of an image singular values sv of image are this kind of feature in this paper we prove that sv feature vector has some important properties of algebraic and geometric invariance and insensitiveness to noise these properties are very useful for the description and recognition of images as an example sv feature vector is used for the problem of recognizing human facial images in this paper using sv feature vector samples of facial images a normal pattern bayes classification model based on sammon s optimal descriminant plane is constructed the experimental result shows that sv feature vector has good performance of class separation

description and discrimination of planar shapes using shape matrices a shape descriptor has been developed which can describe a shape independent of its translation rotation and scaling the description is in the form of a matrix and it is obtained by a polar quantization of a shape the quantization process takes into consideration not only a shape s outer geometry but its inner geometry as well the descriptor is information preserving and if the quantization parameters are selected properly it is possible to reconstruct an original shape from its description in this technique shape discrimination is possible by a simple exclusive or operation on shape descriptions

multilinear discriminant analysis for higher order tensor data classification in the past decade great efforts have been made to extend linear discriminant analysis for higher order data classification generally referred to as multilinear discriminant analysis mda existing examples include general tensor discriminant analysis gtda and discriminant analysis with tensor representation dater both the two methods attempt to resolve the problem of tensor mode dependency by iterative approximation gtda is known to be the first mda method that converges over iterations however its performance relies highly on the tuning of the parameter in the scatter difference criterion although dater usually results in better classification performance it does not converge yet the number of iterations executed has a direct impact on dater s performance in this paper we propose a closed form solution to the scatter difference objective in gtda namely direct gtda dgtda which also gets rid of parameter tuning we demonstrate that dgtda outperforms gtda in terms of both efficiency and accuracy in addition we propose constrained multilinear discriminant analysis cmda that learns the optimal tensor subspace by iteratively maximizing the scatter ratio criterion we prove both theoretically and experimentally that the value of the scatter ratio criterion in cmda approaches its extreme value if it exists with bounded error leading to superior and more stable performance in comparison to dater

active noise control with on line estimation of non gaussian noise characteristics abstract active noise control anc is a methodology for attenuating noise based on adaptive signal processing algorithms anc is well assessed for the attenuation of gaussian noise but the rejection of non gaussian impulsive noise signals represents a much more critical task that may even impair algorithm convergence to overcome this problem the adaptive filter weight update process must be modified by discarding or discounting samples associated with impulsive noise this can be done either by modeling the impulsive noise with a non gaussian distribution such as the symmetric stable s s distribution or by applying an outlier detection method with both approaches the accuracy in the noise description appears to be crucial for effective noise reduction this paper proposes two novel approaches for the attenuation of impulsive noise both for invariant and time varying noise distributions the first one is based on the on line estimation of an s s model of the noise probabilistic description the second relies on a simple on line recursive procedure that reliably estimates amplitude thresholds for outlier detection both methods compare favorably with competitor approaches while maintaining a sufficiently low algorithm complexity several examples are shown to demonstrate the algorithms effectiveness

1d lda vs 2d lda when is vector based linear discriminant analysis better than matrix based recent advances have shown that algorithms with 2d matrix based representation perform better than the traditional 1d vector based ones in particular 2d lda has been widely reported to outperform 1d lda however would the matrix based linear discriminant analysis be always superior and when would 1d lda be better in this paper we investigate into these questions and have a comprehensive comparison between 1d lda and 2d lda in theory and in experiments we analyze the heteroscedastic problem in 2d lda and formulate mathematical equalities to explore the relationship between 1d lda and 2d lda then we point out potential problems in 2d lda it is shown that 2d lda has eliminated the information contained in the covariance information between different local geometric structures such as the rows or the columns which is useful for discriminant feature extraction whereas 1d lda could preserve such information interestingly this new finding indicates that 1d lda is able to gain higher fisher score than 2d lda in some extreme case furthermore sufficient conditions on which 2d lda would be bayes optimal for two class classification problem are derived and comparison with 1d lda in this aspect is also analyzed this could help understand how 2d lda is expected to achieve at its best further discover its relationship with 1d lda and well support other findings after the theoretical analysis comprehensive experimental results are reported by fairly and extensively comparing 1d lda with 2d lda in contrast to the existing view that some 2d lda based algorithms would perform better than 1d lda when the number of training samples for each class is small or when the number of discriminant features used is small we show that it is not always true and show that some standard 1d lda based algorithms could perform better in those cases on some challenging data sets

regularized discriminant analysis and its application to face recognition the linear fisher discriminant analysis lda is a well known and popular statistical method in pattern recognition and classi5cation the basic idea is to optimize the discriminant criteria in which the ratio between the interand the intra class distance is maximized this approach is theoretically sound and a number of papers have shown its superior performance when applying in pattern recognition applications 1 5 however this approach su ers from the small size problem this problem occurs when the sample size is small compared with the size of feature vector which always appears in the face recognition applications this is because the typical image dimension for face image is greater than 32 32 and usually only 2 6 images are used for training thus the within class covariance estimation cw will be singular in this case the eigenvalue problem is ill posed the fisher index in t will be reached at the null space of cw and will always result in in5nity index in t a number of methods have been proposed in the last decade to overcome the limitation of lda on small sample size these methods in applying to face recognition can be roughly grouped into three categories the 5rst approach applied a dimension reduction method such as principal component analysis pca to extract important components for lda this approach is straightforward but the dimension reduction method may remove some useful information for recognition the second approach modi5es the fisher s optimization criteria theoretically this approach can solve the problem but the constraints 1 3 will limit the

kernel independent component analysis we present a class of algorithms for independent component analysis ica which use contrast functions based on canonical correlations in a reproducing kernel hilbert space on the one hand we show that our contrast functions are related to mutual information and have desirable mathematical properties as measures of statistical dependence on the other hand building on recent developments in kernel methods we show that these criteria and their derivatives can be computed efficiently minimizing these criteria leads to flexible and robust algorithms for ica we illustrate with simulations involving a wide variety of source distributions showing that our algorithms outperform many of the presently known algorithms

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

adaptive nonlinear neuro controller with an integrated evaluation algorithm for nonlinear active noise systems an adaptive nonlinear neuro controller with an integrated evaluation algorithm for nonlinear active noise control systems is proposed to attenuate the nonlinear and non gaussian noises inspired by the structure of the hammerstein or wiener model the proposed controller is realized by the static nonlinear memory function mapping on the basis of a single neuron a generalized filtered x gradient descent algorithm based on an integrated evaluation criterion is developed to adaptively adjust the weights of the controller where the weighted sum of renyi s quadratic error entropy and the mean square error is applied as the integrated performance index which improves the performance of the adaptive algorithm by introducing the information entropy in addition the convergence of the proposed approach is analyzed and the computational complexity among different methods is investigated the proposed scheme can effectively attenuate the nonlinear and non gaussian noises and has a relative simple structure and less learning parameters the simulation results demonstrate the validity of the proposed method for attenuating the nonlinear and non gaussian noises

classification of partial 2 d shapes using fourier descriptors we present a method for the classification of 2 d partial shapes using fourier descriptors we formulate the problem as one of estimating the fourier descriptors of the unknown complete shape from the observations derived from an arbitrarily rotated and scaled shape with missing segments the method used for obtaining the estimates of the fourier descriptors minimizes a sum of two terms the first term of which is a least square fit to the given data subject to the condition that the number of missing boundary points is not known and the second term is the perimeter2 area of the unknown shape experiments with synthetic and real boundaries show that estimates closer to the true values of fourier descriptors of complete boundaries are obtained also classification experiments performed using real boundaries indicate that reasonable classification accuracies are obtained even when 20 30 percent of the data is missing

a converse of asymptotic formulae in simultaneous approximation in the general setting of simultaneous approximation by sequences of linear shape preserving operators this paper contains a sort of converse result of voronovskaya type asymptotic formulae as a by product a saturation result is derived applications to some very well known approximation processes are also presented

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

novel fisher discriminant classifiers at the present several applications need to classify high dimensional points belonging to highly unbalanced classes unfortunately when the training set cardinality is small compared to the data dimensionality small sample size problem the classification performance of several well known classifiers strongly decreases similarly the classification accuracy of several discriminative methods decreases when non linearly separable and unbalanced classes are treated in this paper we firstly survey state of the art methods that employ improved versions of linear discriminant analysis lda to deal with the above mentioned problems secondly we propose a family of classifiers based on the fisher subspace estimation which efficiently deal with the small sample size problem non linearly separable classes and unbalanced classes the promising results obtained by the proposed techniques on benchmark datasets and the comparison with state of the art predictors show the efficacy of the proposed techniques

the complete asymptotic expansion for the meyer konig and zeller operators abstract we present the complete asymptotic expansion for the meyer konig and zeller operators m n f t x as n tends to infinity all coefficients of n k k 1 2 are calculated explicitly in terms of stirling numbers of the first and second kind

bernstein type operators which preserve polynomials abstract in this paper we present the sequence of linear bernstein type operators defined for f c 0 1 by b n f 1 b n being the classical bernstein operators and being any function that is continuously differentiable times on 0 1 such that 0 0 1 1 and x 0 for x 0 1 we investigate its shape preserving and convergence properties as well as its asymptotic behavior and saturation moreover these operators and others of king type are compared with each other and with b n we present as an interesting byproduct sequences of positive linear operators of polynomial type with nice geometric shape preserving properties which converge to the identity which in a certain sense improve b n in approximating a number of increasing functions and which apart from the constant functions fix suitable polynomials of a prescribed degree the notion of convexity with respect to plays an important role

asymptotic expansion of multivariate conservative linear operators in this paper we study the asymptotic expansion of the partial derivatives of a sequence of linear conservative operators we find sufficient conditions on the sequence that guarantee that such an expansion can be derived from the asymptotic formula for the nondifferentiated sequence our results are valid even if the operators of the sequence present difficult conservative properties different form the classical preservation of the usual convexities we use our theorems to obtain the complete asymptotic expansions and voronovskaja formulae for the partial derivatives of multivariate versions of the meyer konig and zeller operators and the bleimann butzer and hahn operators

a linear constrained distance based discriminant analysis for hyperspectral image classification abstract fisher s linear discriminant analysis lda is a widely used technique for pattern classification problems it employs fisher s ratio ratio of between class scatter matrix to within class scatter matrix to derive a set of feature vectors by which high dimensional data can be projected onto a low dimensional feature space in the sense of maximizing class separability this paper presents a linear constrained distance based discriminant analysis lcda that uses a criterion for optimality derived from fisher s ratio criterion it not only maximizes the ratio of inter distance between classes to intra distance within classes but also imposes a constraint that all class centers must be aligned along predetermined directions when these desired directions are orthogonal the resulting classifier turns out to have the same operation form as the classifier derived by the orthogonal subspace projection osp approach recently developed for hyperspectral image classification because of that lcda can be viewed as a constrained version of osp in order to demonstrate its performance in hyperspectral image classification airborne visible infrared imaging spectrometer aviris and hyperspectral digital imagery collection experiment hydice data are used for experiments

dimensionality reduction of image features using the canonical contextual correlation projection a linear discriminative supervised technique for reducing feature vectors extracted from image data to a lower dimensional representation is proposed it is derived from classical linear discriminant analysis lda extending this technique to cases where there is dependency between the output variables i e the class labels and not only between the input variables the latter can readily be dealt with in standard lda the novel method is useful for example in supervised segmentation tasks in which high dimensional feature vectors describe the local structure of the image the principal idea is that where standard lda merely takes into account a single class label for every feature vector the new technique incorporates class labels of its neighborhood in the analysis as well in this way the spatial class label configuration in the vicinity of every feature vector is accounted for resulting in a technique suitable for e g image data this extended lda that takes spatial label context into account is derived from a formulation of standard lda in terms of canonical correlation analysis the novel technique is called the canonical contextual correlation projection cccp an additional drawback of lda is that it cannot extract more features than the number of classes minus one in the two class case this means that only a reduction to one dimension is possible our contextual lda approach can avoid such extreme deterioration of the classification space and retain more than one dimension the technique is exemplified on a pixel based medical image segmentation problem in which it is shown that it may give significant improvement in segmentation accuracy

a kernel optimization method based on the localized kernel fisher criterion it is widely recognized that whether the selected kernel matches the data determines the performance of kernel based methods ideally it is expected that the data is linearly separable in the kernel induced feature space therefore fisher linear discriminant criterion can be used as a cost function to optimize the kernel function however the data may not be linearly separable even after kernel transformation in many applications e g the data may exist as multimodally distributed structure in this case a nonlinear classifier is preferred and obviously fisher criterion is not a suitable choice as kernel optimization rule motivated by this issue we propose a localized kernel fisher criterion instead of traditional fisher criterion as the kernel optimization rule to increase the local margins between embedded classes in kernel induced feature space experimental results based on some benchmark data and measured radar high resolution range profile hrrp data show that the classification performance can be improved by using the proposed method

dimensionality reduction for hyperspectral data based on class aware tensor neighborhood graph and patch alignment to take full advantage of hyperspectral information to avoid data redundancy and to address the curse of dimensionality concern dimensionality reduction dr becomes particularly important to analyze hyperspectral data exploring the tensor characteristic of hyperspectral data a dr algorithm based on class aware tensor neighborhood graph and patch alignment is proposed here first hyperspectral data are represented in the tensor form through a window field to keep the spatial information of each pixel second using a tensor distance criterion a class aware tensor neighborhood graph containing discriminating information is obtained in the third step employing the patch alignment framework extended to the tensor space we can obtain global optimal spectral spatial information finally the solution of the tensor subspace is calculated using an iterative method and low dimensional projection matrixes for hyperspectral data are obtained accordingly the proposed method effectively explores the spectral and spatial information in hyperspectral data simultaneously experimental results on 3 real hyperspectral datasets show that compared with some popular vector and tensor based dr algorithms the proposed method can yield better performance with less tensor training samples required

generalized discriminant analysis using a kernel approach we present a new method that we call generalized discriminant analysis gda to deal with nonlinear discriminant analysis using kernel function operator the underlying theory is close to the support vector machines svm insofar as the gda method provides a mapping of the input vectors into high dimensional feature space in the transformed space linear properties make it easy to extend and generalize the classical linear discriminant analysis lda to nonlinear discriminant analysis the formulation is expressed as an eigenvalue problem resolution using a different kernel one can cover a wide class of nonlinearities for both simulated data and alternate kernels we give classification results as well as the shape of the decision function the results are confirmed using real data to perform seed classification

multilinear discriminant analysis for face recognition there is a growing interest in subspace learning techniques for face recognition however the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma in this paper we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order first we propose a discriminant tensor criterion whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction then a novel approach called k mode optimization is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions we call this algorithm multilinear discriminant analysis mda which has the following characteristics 1 multiple interrelated subspaces can collaborate to discriminate different classes 2 for classification problems involving higher order tensors the mda algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem and 3 the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k mode optimization we provide extensive experiments on orl cmu pie and feret databases by encoding face images as second or third order tensors to demonstrate that the proposed mda algorithm based on higher order tensors has the potential to outperform the traditional vector based subspace learning algorithms especially in the cases with small sample sizes

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

blockwise projection matrix versus blockwise data on undersampled problems analysis comparison and applications linear subspace methods are extensively used in many areas such as pattern recognition and machine learning among them block subspace methods are efficient in terms of the computational complexity in this paper we perform a thorough analysis on block subspace methods and give a theoretical framework for understanding block subspace methods it reveals the relationship between block subspace methods and classical subspace methods we theoretically show that blockwise pca has larger reconstruction errors than classical pca and classical lda has stronger discriminant power than blockwise lda in the case of the same number of reduced features in addition based on the fisher criterion we also give a strategy for selecting an approximate block size for classification problems the comprehensive experiments on face images and gene expression data are used to evaluate our results and a comparative analysis for various methods is made experimental results demonstrate that overly combining subspaces of block subspace methods without considering the subspace distance may yield undesirable performance on undersampled problems

a multivariate faa di bruno formula with applications a multivariate faa di bruno formula for computing arbitrary partial derivatives of a function composition is presented it is shown by way of a general identity how such derivatives can also be expressed in the form of an infinite series applications to stochastic processes and multivariate cumulants are then delineated

a recursive least square algorithm for active control of mixed noise most currently available active control algorithms target noise sources with relatively singular characteristics such as tonal or wideband noise however noise in some practical environments is a mixture of different sounds generated by different sources where the existing algorithms designed for single noise sources may not be optimal this kind of noise is generally referred to as mixed noise and this paper develops a specific active control algorithm for mixed noise based on the recursive least square structure by minimizing the weighted summation of the logarithmic transformation of posterior errors and taking the commutation error into consideration the proposed algorithm not only reduces broadband narrowband and impulse noise successfully but also mixtures of them simulation results demonstrate the superiority of the proposed algorithm over existing algorithms such as the filtered x least mean square filtered x logarithmic least mean square filtered x normalized least mean square and filtered weight filtered x normalized least mean square algorithms in terms of convergence rate and noise reduction

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

a generalized optimal set of discriminant vectors abstract a generalized optimal set of discriminant vectors for linear feature extraction is presented first the criteria of selecting the generalized optimal discriminant vectors are introduced and then a unified solving method is derived to solve the vectors of the generalized optimal set in both cases of a large number of samples and a small number of samples the experimental results show that the present method is superior to the foley sammon method foley and sammon ieee trans comput 24 281 289 1975 the positive pseudoinverse method tian et al opt engng 25 7 834 839 1986 the perturbation method hong and yang pattern recognition 24 317 324 1991 and the matrix rank decomposition method cheng et al pattern recognition 25 101 111 1992 in terms of correct classification rate