on the hencl s notion of absolute continuity abstract we prove that a slight modification of the notion of absolute continuity introduced in d bongiorno absolutely continuous functions in r n j math anal appl 303 2005 119 134 is equivalent to the notion of n absolute continuity given by s hencl in s hencl on the notions of absolute continuity for functions of several variables fund math 173 2002 175 189

finite element formulations for transient dynamic analysis in structural systems with viscoelastic treatments containing fractional derivative models this paper presents finite element formulations for transient dynamic analysis in structural systems with damping treatments in which viscoelastic materials are characterized by means of fractional derivative models in contrast to other formulations such as that of padovan employing the principle of virtual work the proposed formulations begin from the local equation of linear momentum and make use of the weighted residual method providing a matrix equation of motion involving fractional operators the numerical approximations of these are developed through the grunwald letnikov definition which allows to formulate explicit and implicit numerical schemes the principal advantage of the proposed formulations is that the history of the displacements and external forces must be stored but not that of the stress which reduces computational time and storage needs numerical applications are presented for a cantilever beam where a viscoelastic treatment has been applied using damping material modelled by a five parameter fractional derivative model the results of the proposed formulation are compared among them and with those of padovan for different damping values and for different load cases the influence of the truncation of grunwald coefficients and of the integration time step is also investigated copyright 2006 john wiley sons ltd

a modified algorithm for generalized discriminant analysis generalized discriminant analysis gda is an extension of the classical linear discriminant analysis lda from linear domain to a nonlinear domain via the kernel trick however in the previous algorithm of gda the solutions may suffer from the degenerate eigenvalue problem i e several eigenvectors with the same eigenvalue which makes them not optimal in terms of the discriminant ability in this letter we propose a modified algorithm for gda mgda to solve this problem the mgda method aims to remove the degeneracy of gda and find the optimal discriminant solutions which maximize the between class scatter in the subspace spanned by the degenerate eigenvectors of gda theoretical analysis and experimental results on the orl face database show that the mgda method achieves better performance than the gda method

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

scalable and flexible multiview max var canonical correlation analysis generalized canonical correlation analysis gcca aims at finding latent low dimensional common structure from multiple views feature vectors in different domains of the same entities unlike principal component analysis that handles a single view g cca is able to integrate information from different feature spaces here we focus on max var gcca a popular formulation that has recently gained renewed interest in multilingual processing and speech modeling the classic max var gcca problem can be solved optimally via eigen decomposition of a matrix that compounds the whitened correlation matrices of the views but this solution has serious scalability issues and is not directly amenable to incorporating pertinent structural constraints such as nonnegativity and sparsity on the canonical components we posit regularized max var gcca as a nonconvex optimization problem and propose an alternating optimization based algorithm to handle it our algorithm alternates between inexact solutions of a regularized least squares subproblem and a manifold constrained nonconvex subproblem thereby achieving substantial memory and computational savings an important benefit of our design is that it can easily handle structure promoting regularization we show that the algorithm globally converges to a critical point at a sublinear rate and approaches a global optimal solution at a linear rate when no regularization is considered judiciously designed simulations and large scale word embedding tasks are employed to showcase the effectiveness of the proposed algorithm

fractional visco elastic euler bernoulli beam abstract aim of this paper is the response evaluation of fractional visco elastic euler bernoulli beam under quasi static and dynamic loads starting from the local fractional visco elastic relationship between axial stress and axial strain it is shown that bending moment curvature shear and the gradient of curvature involve fractional operators solution of particular example problems are studied in detail providing a correct position of mechanical boundary conditions moreover it is shown that for homogeneous beam both correspondence principles also hold in the case of euler bernoulli beam with fractional constitutive law virtual work principle is also derived and applied to some case studies

a novel multiset integrated canonical correlation analysis framework and its application in feature fusion multiset canonical correlation analysis mcca is difficult to effectively express the integrated correlation among multiple feature vectors in feature fusion thus this paper firstly presents a novel multiset integrated canonical correlation analysis micca framework the micca establishes a discriminant correlation criterion function of multi group variables based on generalized correlation coefficient the criterion function can clearly depict the integrated correlation among multiple feature vectors then the paper presents a multiple feature fusion theory and algorithm using the micca method the detailed process of the algorithm is as follows firstly extract multiple feature vectors from the same patterns by using different feature extraction methods then extract multiset integrated canonical correlation features using micca finally form effective discriminant feature vectors through two given feature fusion strategies for pattern classification the multi group feature fusion method based on micca not only achieves the aim of feature fusion but also removes the redundancy between features the experiment results on cenparmi handwritten arabic numerals and uci multiple features database show that the micca method has better recognition rates and robustness than the fusion methods based on canonical correlation analysis cca and mcca

absolutely continuous functions with values in a banach space abstract let be an open subset of r n n 1 and let x be a banach space we prove that absolutely continuous functions f x are continuous and differentiable in some sense almost everywhere in

discontinuous galerkin method for an integro differential equation modeling dynamic fractional order viscoelasticity an integro differential equation modeling dynamic fractional order viscoelasticity with a mittag leffler type convolution kernel is considered a discontinuous galerkin method based on piecewise constant polynomials is formulated for temporal semidiscretization of the problem stability estimates of the discrete problem are proved that are used to prove optimal order a priori error estimates the theory is illustrated by a numerical example

multiview vector valued manifold regularization for multilabel image classification in computer vision image datasets used for classification are naturally associated with multiple labels and comprised of multiple views because each image may contain several objects e g pedestrian bicycle and tree and is properly characterized by multiple visual features e g color texture and shape currently available tools ignore either the label relationship or the view complementarily motivated by the success of the vector valued function that constructs matrix valued kernels to explore the multilabel structure in the output space we introduce multiview vector valued manifold regularization rm mv 3 rm mr to integrate multiple features rm mv 3 rm mr exploits the complementary property of different features and discovers the intrinsic local geometry of the compact support shared by different features under the theme of manifold regularization we conduct extensive experiments on two challenging but popular datasets pascal voc 07 and mir flickr and validate the effectiveness of the proposed rm mv 3 rm mr for image classification

a new method of feature fusion and its application in image recognition a new method of feature extraction based on feature fusion is proposed in this paper according to the idea of canonical correlation analysis cca at first the theory framework of cca used in pattern recognition and its reasonable description are discussed the process can be explained as follows extract two groups of feature vectors with the same pattern establish the correlation criterion function between the two groups of feature vectors and extract their canonical correlation features to form effective discriminant vector for recognition then the problem of canonical projection vectors is solved when two total scatter matrixes are singular such that it fits for the case of high dimensional space and small sample size in this sense the applicable range of cca is extended at last the inherent essence of this method used in recognition is analyzed further in theory experimental results on concordia university cenparmi database of handwritten arabic numerals and yale face database show that recognition rate is far higher than that of the algorithm adopting single feature or the existing fusion algorithm

salient feature and reliable classifier selection for facial expression classification a novel facial expression classification fec method is presented and evaluated the classification process is decomposed into multiple two class classification problems a choice that is analytically justified and unique sets of features are extracted for each classification problem specifically for each two class problem an iterative feature selection process that utilizes a class separability measure is employed to create salient feature vectors sfvs where each sfv is composed of a selected feature subset subsequently two class discriminant analysis is applied on the sfvs to produce salient discriminant hyper planes sdhs which are used to train the corresponding two class classifiers to properly integrate the two class classification results and produce the fec decision a computationally efficient and fast classification scheme is developed during each step of this scheme the most reliable classifier is identified and utilized thus a more accurate final classification decision is produced the jaffe and the mmi databases are used to evaluate the performance of the proposed salient feature and reliable classifier selection sfrcs methodology classification rates of 96 71 and 93 61 are achieved under the leave one sample out evaluation strategy and 85 92 under the leave one subject out evaluation strategy

sparse and kernel opls feature extraction based on eigenvalue problem solving orthonormalized partial least squares opls is a popular multivariate analysis method to perform supervised feature extraction usually in machine learning papers opls projections are obtained by solving a generalized eigenvalue problem however in statistical papers the method is typically formulated in terms of a reduced rank regression problem leading to a formulation based on a standard eigenvalue decomposition a first contribution of this paper is to derive explicit expressions for matching the opls solutions derived under both approaches and discuss that the standard eigenvalue formulation is also normally more convenient for feature extraction in machine learning more importantly since optimization with respect to the projection vectors is carried out without constraints via a minimization problem inclusion of penalty terms that favor sparsity is straightforward in the paper we exploit this fact to propose modified versions of opls in particular relying on the 1 norm we propose a sparse version of linear opls as well as a non linear kernel opls with pattern selection we also incorporate a group lasso penalty to derive an opls method with true feature selection the discriminative power of the proposed methods is analyzed on a benchmark of classification problems furthermore we compare the degree of sparsity achieved by our methods and compare them with other state of the art methods for sparse feature extraction highlightswe establish the connection between opls and reduced rank regression problem evd formulation a novel sparse opls is proposed which enhances the solution obtained following the procrustres approach we propose a novel sparse kernel opls feature extractor for improved performance interpretability and efficiency

discriminative learning and recognition of image set classes using canonical correlations we address the problem of comparing sets of images for object recognition where the sets may represent variations in an object s appearance due to changing camera pose and lighting conditions canonical correlations also known as principal or canonical angles which can be thought of as the angles between two d dimensional subspaces have recently attracted attention for image set matching canonical correlations offer many benefits in accuracy efficiency and robustness compared to the two main classical methods parametric distribution based and nonparametric sample based matching of sets here this is first demonstrated experimentally for reasonably sized data sets using existing methods exploiting canonical correlations motivated by their proven effectiveness a novel discriminative learning method over sets is proposed for set classification specifically inspired by classical linear discriminant analysis lda we develop a linear discriminant function that maximizes the canonical correlations of within class sets and minimizes the canonical correlations of between class sets image sets transformed by the discriminant function are then compared by the canonical correlations classical orthogonal subspace method osm is also investigated for the similar purpose and compared with the proposed method the proposed method is evaluated on various object recognition problems using face image sets with arbitrary motion captured under different illuminations and image sets of 500 general objects taken at different views the method is also applied to object category recognition using eth 80 database the proposed method is shown to outperform the state of the art methods in terms of accuracy and efficiency

fractional calculus a different approach to the analysis of viscoelastically damped structures fractional calculus is used to construct stress strain relationships for viscoelastic materials these relationships are used in the finite element analysis of viscoelastically damped structures and closed form solutions to the equations of motion are found the attractive feature of this approach is that very few empirical parameters are required to model the viscoelastic material and calculate the response of the structure for general loading conditions

long range cohesive interactions of non local continuum faced by fractional calculus abstract a non local continuum model including long range forces between non adjacent volume elements has been studied in this paper the proposed continuum model has been obtained as limit case of two fully equivalent mechanical models i a volume element model including contact forces between adjacent volumes as well as long range interactions distance decaying between non adjacent elements ii a discrete point spring model with local springs between adjacent points and non local springs with distance decaying stiffness connecting non adjacent points under the assumption of fractional distance decaying interactions between non adjacent elements a fractional differential equation involving marchaud type fractional derivatives has been obtained for unbounded domains it is shown that for unbounded domains the two mechanical models revert to lazopoulos and eringen model with fractional distance decaying functions it has also been shown that for a confined bar the stress strain relation is substantially different from that obtained simply using the truncated marchaud derivatives since a double integral instead of convolution integral appears moreover in the analysis of bounded domains the governing equations turn out to an integro differential equation including only the integral part of marchaud fractional derivatives on finite interval the mechanical boundary condition for the proposed model has been introduced consistently on the basis of mechanical considerations and the constitutive law of the proposed continuum model has been reported by mathematical induction several numerical applications have been reported to show verify and assess the concepts listed in this paper

multiview matrix completion for multilabel image classification there is growing interest in multilabel image classification due to its critical role in web based image analytics based applications such as large scale image retrieval and browsing matrix completion mc has recently been introduced as a method for transductive semisupervised multilabel classification and has several distinct advantages including robustness to missing data and background noise in both feature and label space however it is limited by only considering data represented by a single view feature which cannot precisely characterize images containing several semantic concepts to utilize multiple features taken from different views we have to concatenate the different features as a long vector however this concatenation is prone to over fitting and often leads to very high time complexity in mc based image classification therefore we propose to weightedly combine the mc outputs of different views and present the multiview mc mvmc framework for transductive multilabel image classification to learn the view combination weights effectively we apply a cross validation strategy on the labeled set in particular mvmc splits the labeled set into two parts and predicts the labels of one part using the known labels of the other part the predicted labels are then used to learn the view combination coefficients in the learning process we adopt the average precision ap loss which is particular suitable for multilabel image classification since the ranking based criteria are critical for evaluating a multilabel classification system a least squares loss formulation is also presented for the sake of efficiency and the robustness of the algorithm based on the ap loss compared with the other losses is investigated experimental evaluation on two real world data sets pascal voc 07 and mir flickr demonstrate the effectiveness of mvmc for transductive semisupervised multilabel image classification and show that mvmc can exploit complementary properties of different features and output consistent labels for improved multilabel image classification

fractional order embedding canonical correlation analysis and its applications to multi view dimensionality reduction and recognition due to the noise disturbance and limited number of training samples within set and between set sample covariance matrices in canonical correlation analysis cca usually deviate from the true ones in this paper we re estimate within set and between set covariance matrices to reduce the negative effect of this deviation specifically we use the idea of fractional order to respectively correct the eigenvalues and singular values in the corresponding sample covariance matrices and then construct fractional order within set and between set scatter matrices which can obviously alleviate the problem of the deviation on this basis a new approach is proposed to reduce the dimensionality of multi view data for classification tasks called fractional order embedding canonical correlation analysis fecca the proposed method is evaluated on various handwritten numeral face and object recognition problems extensive experimental results on the cenparmi uci at t ar and coil 20 databases show that fecca is very effective and obviously outperforms the existing joint dimensionality reduction or feature extraction methods in terms of classification accuracy moreover its improvements for recognition rates are statistically significant on most cases below the significance level 0 05 a new method namely fecca is presented for multi view dimensionality reduction fractional order within set and between set scatter matrices are constructed by sample spectrum modeling the extracted features by fecca have strong discriminant power for recognition experimental results show fecca has better recognition rates than the existing joint feature extraction methods

new insights on free energies and saint venant s principle in viscoelasticity explicit expressions for the minimum free energy of a linear viscoelastic material and noll s definition of state are used here to explore spatial energy decay estimates for viscoelastic bodies in the full dynamical case and in the quasi static approximation in the inertial case chirita et al obtained a certain spatial decay inequality for a space time integral over a portion of the body and over a finite time interval of the total mechanical energy this involves the work done on histories which is not a function of state in general here it is shown that for free energies which are functions of state and obey a certain reasonable property the spatial decay of the corresponding space time integral is stronger than the one involving the work done on the past history it turns out that the bound obtained is optimal for the minimal free energy two cases are discussed for the quasi static approximation the first case deals with general states so that general histories belonging to the equivalence class of any given state can be considered the continuity of the stress functional with respect to the norm based on the minimal free energy is proved and the energy measure based on the minimal free energy turns out to obey the decay inequality derived chirita et al for the quasi static case the second case explores a crucial point for viscoelastic materials namely that the response is influenced by the rate of application of loads quite surprisingly the analysis of this phenomenon in the context of saint venant principles has never been carried out explicitly before even in the linear case this effect is explored by considering states the related histories of which are sinusoidal the spatial decay parameter is shown to be frequency dependent i e it depends on the rate of load application and it is proved that of those considered the most conservative estimate of the frequency dependent decay is associated with the minimal free energy a comparison is made of the results for sinusoidal histories at low frequencies and general histories

uncorrelated multi set feature learning for color face recognition most existing color face feature extraction methods need to perform color space transformation and they reduce correlation of color components on the data level that has no direct connection with classification some methods extract features from r g and b components serially with orthogonal constraints on the feature level yet the serial extraction manner might make discriminabilities of features derived from three components distinctly different multi set feature learning can jointly learn features from multiple sets of data effectively in this paper we propose two novel color face recognition approaches namely multi set statistical uncorrelated projection analysis msupa and multi set discriminating uncorrelated projection analysis mdupa which extract discriminant features from three color components together and simultaneously reduce the global statistical and global discriminating feature level correlation between color components in a multi set manner respectively experiments on multiple public color face databases demonstrate that the proposed approaches outperform several related state of the arts we propose a multi set statistical uncorrelated projection analysis approach we define a supervised correlation that is the discriminating correlation we propose a multi set discriminating uncorrelated projection analysis approach performance of our approaches is demonstrated on multiple color face databases

multi target regression via robust low rank learning multi target regression has recently regained great popularity due to its capability of simultaneously learning multiple relevant regression tasks and its wide applications in data mining computer vision and medical image analysis while great challenges arise from jointly handling inter target correlations and input output relationships in this paper we propose multi layer multi target regression mmr which enables simultaneously modeling intrinsic inter target correlations and nonlinear input output relationships in a general framework via robust low rank learning specifically the mmr can explicitly encode inter target correlations in a structure matrix by matrix elastic nets men the mmr can work in conjunction with the kernel trick to effectively disentangle highly complex nonlinear input output relationships the mmr can be efficiently solved by a new alternating optimization algorithm with guaranteed convergence the mmr leverages the strength of kernel methods for nonlinear feature learning and the structural advantage of multi layer learning architectures for inter target correlation modeling more importantly it offers a new multi layer learning paradigm for multi target regression which is endowed with high generality flexibility and expressive ability extensive experimental evaluation on 18 diverse real world datasets demonstrates that our mmr can achieve consistently high performance and outperforms representative state of the art algorithms which shows its great effectiveness and generality for multivariate prediction

variational bayesian approach to canonical correlation analysis as a dimension reduction algorithm canonical correlation analysis cca encounters the issue of selecting the number of canonical correlations in this letter we present a bayesian model selection algorithm for cca based on a probabilistic interpretation a hierarchical bayesian model is applied to probabilistic cca and learned by variational approximation this method not only estimates the model parameters but also automatically determines the number of canonical correlations and avoids overfitting experiments show that it performs better compared with maximum likelihood and some other model selection methods

discriminative feature extraction by a neural implementation of canonical correlation analysis the canonical correlation analysis cca aims at measuring linear relationships between two sets of variables views that can be used for feature extraction in classification problems with multiview data however the correlated features extracted by the cca may not be class discriminative since cca does not utilize the class labels in its traditional formulation although there is a method called discriminative cca dcca that aims to increase the discriminative ability of cca inspired from the linear discriminant analysis lda it has been shown that the extracted features with this method are identical to those by the lda with respect to an orthogonal transformation therefore dcca is simply equivalent to applying single view regular lda to each one of the views separately besides dcca and the other similar dcca approaches have generalization problems due to the sample covariance matrices used in their computation which are sensitive to outliers and noisy samples in this paper we propose a method called discriminative alternating regression d ar to explore correlated and also discriminative features d ar utilizes two alternating multilayer perceptrons each with a linear hidden layer learning to predict both the class labels and the outputs of each other we show that the features found by d ar on training sets significantly accomplish higher classification accuracies on test sets of facial expression recognition object recognition and image retrieval experimental data sets

the finite element method for the mechanically based model of non local continuum summary in this paper the finite element method fem for the mechanically based non local elastic continuum model is proposed in such a model each volume element of the domain is considered mutually interacting with the others beside classical interactions involved by the cauchy stress field by means of central body forces that are monotonically decreasing with their inter distance and proportional to the product of the interacting volume elements the constitutive relations of the long range interactions involve the product of the relative displacement of the centroids of volume elements by a proper distance decaying function which accounts for the decrement of the long range interactions as long as distance increases in this study the elastic problem involving long range central interactions for isotropic elastic continuum will be solved with the aid of the fem the accuracy of the solution obtained with the proposed fem code is compared with other solutions obtained with galerkins approximation as well as with finite difference method moreover a parametric study regarding the effect of the material length scale in the mechanically based model and in the kroner eringen non local elasticity has been investigated for a plane elasticity problem copyright 2011 john wiley sons ltd

multiset canonical correlations using globality preserving projections with applications to feature extraction and recognition multiset features extracted from the same patterns always represent different characteristics of data thus it is very valuable to perform the extraction on multiple feature sets this paper addresses the issue of multiset correlation feature extraction mcfe in multiple feature representations a novel method is proposed to carry out the mcfe for classification called multiset canonical correlations using globality preserving projections mcc gps which can perform joint dimensionality reduction for high dimensional data mcc gp integrates correlational characteristics of feature pairs and global geometric information of data in the transformed low dimensional space this makes mcc gps have better discriminant ability than a previous method proposed by the authors called multiset integrated canonical correlation analysis micca which only considers correlations for recognition tasks furthermore mcc gp can subsume two popular feature extraction methods into its framework under some constraints this also provides a new insight for these two methods the proposed method is applied to pattern recognition and examined using the coil 100 and eth 80 object databases and ar cmu pie and yale face databases extensive experimental results show that mcc gp outperforms micca and multiset canonical correlation analysis in terms of classification accuracy and efficiency

complete canonical correlation analysis with application to multi view gait recognition canonical correlation analysis cca is a well known multivariate analysis method for quantifying the correlations between two sets of multidimensional variables however for multi view gait recognition it is difficult to directly apply cca to deal with two sets of high dimensional vectors because of computational complexity moreover in such situation the eigenmatrix of cca is usually singular which makes the direct implementation of the cca algorithm almost impossible in practice pca or singular value decomposition is employed as a preprocessing step to solve these problems nevertheless this strategy may discard dimensions that contain important discriminative information and correlation information to overcome the shortcomings of cca when dealing with two sets of high dimensional vectors we develop a novel method named complete canonical correlation analysis c3a in our method we first reformulate the traditional cca so that we can avoid the computing of the inverse of a high dimensional matrix with the help of this reformulation c3a further transforms the singular generalized eigensystem computation of cca into two stable eigenvalue decomposition problems moreover a feasible and effective method is proposed to alleviate the computational burden of high dimensional matrix for typical gait image data experimental results on two benchmark gait databases casia gait database and the challenge usf gait database demonstrate the effectiveness of the proposed method highlightswe overcome the shortcomings of cca when dealing with high dimensional matrix the singularity of generalized eigenvalue problem in cca is overcome naturally the important discriminative information is preserved completely in our algorithm our scheme learns stable and complete solutions the multi view gait recognition is achieved based on our method

stability analysis of beck s column over a fractional order hereditary foundation this paper considers the case of beck s column resting on a hereditary bed of independent springpots the springpot possesses an intermediate rheological behaviour among linear spring and linear da

characterizing the response of pet and fmri data using multivariate linear models this paper presents a new method for characterizing brain responses in both pet and fmri data the aim is to capture the correlations between the scans of an experiment and a set of external predictor variables that are thought to affect the scans such as type intensity or shape of stimulus response its main feature is a canonical variates analysis cva of the estimated effects of the predictors from a multivariate linear model mlm the advantage of this over current methods is that temporal correlations can be incorporated into the model making the mlm method suitable for fmri as well as pet data moreover tests for the presence of any correlation and inference about the number of canonical variates needed to capture that correlation can be based on standard multivariate statistics rather than simulations when applied to an fmri data set previously analyzed by another cva method the mlm method reveals a pattern of responses that is closer to that detected in an earlier non cva analysis

multiset canonical correlations analysis and multispectral truly multitemporal remote sensing data this paper describes two and multiset canonical correlations analysis cca for data fusion multisource multiset or multitemporal exploratory data analysis these techniques transform multivariate multiset data into new orthogonal variables called canonical variates cvs which when applied in remote sensing exhibit ever decreasing similarity as expressed by correlation measures over sets consisting of 1 spectral variables at fixed points in time r mode analysis or 2 temporal variables with fixed wavelengths t mode analysis the cvs are invariant to linear and affine transformations of the original variables within sets which means for example that the r mode cvs are insensitive to changes over time in offset and gain in a measuring device in a case study cvs are calculated from landsat thematic mapper tm data with six spectral bands over six consecutive years both rand t mode cvs clearly exhibit the desired characteristic they show maximum similarity for the low order canonical variates and minimum similarity for the high order canonical variates these characteristics are seen both visually and in objective measures the results from the multiset cca r and t mode analyses are very different this difference is ascribed to the noise structure in the data the cca methods are related to partial least squares pls methods this paper very briefly describes multiset cca based multiset pls also the cca methods can be applied as multivariate extensions to empirical orthogonal functions eof techniques multiset cca is well suited for inclusion in geographical information systems gis

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

rapid and brief communication a theorem on the generalized canonical projective vectors this paper proposes a kind of generalized canonical projective vectors gcpv based on the framework of canonical correlation analysis cca applying image recognition apart from canonical projective vectors cpv the process of obtaining gcpv contains the class information of samples such that the combined features extracted according to the basis of gcpv can give a better classification performance the experimental result based on the concordia university cenparmi handwritten arabian numeral database has proved that our method is superior to the method based on cpv

regular subclasses in the sobolev space w_ loc 1 n abstract we study some slight modifications of the class a c n r m introduced in d bongiorno absolutely continuous functions in r n j math anal and appl 303 2005 119 134 in particular we prove that the classes a c n r m 0 1 introduced in c di bari c vetro a remark on absolutely continuous functions in r n rend circ matem palermo 55 2006 296 304 are independent by and contain properly the class a c n r m moreover we prove that a c n r m a c n r m a c n r m where a c n r m is the symmetric class of a c n r m 0 1

local canonical correlation analysis for nonlinear common variables discovery in this paper we address the problem of hidden common variables discovery from multimodal data sets of nonlinear high dimensional observations we present a metric based on local applications of canonical correlation analysis cca and incorporate it in a kernel based manifold learning technique we show that this metric discovers the hidden common variables underlying the multimodal observations by estimating the euclidean distance between them our approach can be viewed both as an extension of cca to a nonlinear setting as well as an extension of manifold learning to multiple data sets experimental results show that our method indeed discovers the common variables underlying high dimensional nonlinear observations without assuming prior rigid model assumptions

space time fractional zener wave equation the space time fractional zener wave equation describing viscoelastic materials obeying the time fractional zener model and the space fractional strain measure is derived and analysed this model includes waves with finite speed as well as non propagating disturbances the existence and the uniqueness of the solution to the generalized cauchy problem are proved special cases are investigated and numerical examples are presented

sparse canonical correlation analysis new formulation and algorithm in this paper we study canonical correlation analysis cca which is a powerful tool in multivariate data analysis for finding the correlation between two sets of multidimensional variables the main contributions of the paper are 1 to reveal the equivalent relationship between a recursive formula and a trace formula for the multiple cca problem 2 to obtain the explicit characterization for all solutions of the multiple cca problem even when the corresponding covariance matrices are singular 3 to develop a new sparse cca algorithm and 4 to establish the equivalent relationship between the uncorrelated linear discriminant analysis and the cca problem we test several simulated and real world datasets in gene classification and cross language document retrieval to demonstrate the effectiveness of the proposed algorithm the performance of the proposed method is competitive with the state of the art sparse cca algorithms

canonical correlation analysis on data with censoring and error information we developed a probabilistic model for canonical correlation analysis in the case when the associated datasets are incomplete this case can arise where data entries either contain measurement errors or are censored i e nonignorable missing due to uncertainties in instrument calibration and physical limitations of devices and experimental conditions the aim of our model is to estimate the true correlation coefficients through eliminating the effects of measurement errors and abstracting helpful information from censored data as exact inference is not possible for the proposed model a modified variational expectation maximization em algorithm was developed in the algorithm developed we approximated the posteriors of the latent variables as normal distributions in the experiment the modified e step approximation accuracy is first empirically demonstrated by being compared to hybrid monte carlo hmc sampling the following experiments were carried out on synthetic datasets with different numbers of censored data and different correlation coefficient settings to compare the proposed algorithm with a maximum a posteriori map solution and a markov chain em solution experimental results showed that the variational em solution compares favorably against the map solution approaching the accuracy of the markov chain em while maintaining computational simplicity we finally applied the proposed algorithm to finding the mostly correlated properties of galaxy group with the x ray luminosity

non linear metric learning using pairwise similarity and dissimilarity constraints and the geometrical structure of data the problem of clustering with side information has received much recent attention and metric learning has been considered as a powerful approach to this problem until now various metric learning methods have been proposed for semi supervised clustering although some of the existing methods can use both positive must link and negative cannot link constraints they are usually limited to learning a linear transformation i e finding a global mahalanobis metric in this paper we propose a framework for learning linear and non linear transformations efficiently we use both positive and negative constraints and also the intrinsic topological structure of data we formulate our metric learning method as an appropriate optimization problem and find the global optimum of this problem the proposed non linear method can be considered as an efficient kernel learning method that yields an explicit non linear transformation and thus shows out of sample generalization ability experimental results on synthetic and real world data sets show the effectiveness of our metric learning method for semi supervised clustering tasks

independent component analysis of gabor features for face recognition we present an independent gabor features igfs method and its application to face recognition the novelty of the igf method comes from 1 the derivation of independent gabor features in the feature extraction stage and 2 the development of an igf features based probabilistic reasoning model prm classification method in the pattern recognition stage in particular the igf method first derives a gabor feature vector from a set of downsampled gabor wavelet representations of face images then reduces the dimensionality of the vector by means of principal component analysis and finally defines the independent gabor features based on the independent component analysis ica the independence property of these gabor features facilitates the application of the prm method for classification the rationale behind integrating the gabor wavelets and the ica is twofold on the one hand the gabor transformed face images exhibit strong characteristics of spatial locality scale and orientation selectivity these images can thus produce salient local features that are most suitable for face recognition on the other hand ica would further reduce redundancy and represent independent features explicitly these independent features are most useful for subsequent pattern discrimination and associative recall experiments on face recognition using the face recognition technology feret and the orl datasets where the images vary in illumination expression pose and scale show the feasibility of the igf method in particular the igf method achieves 98 5 correct face recognition accuracy when using 180 features for the feret dataset and 100 accuracy for the orl dataset using 88 features

generalized viscoelastic models their fractional equations with solutions recently fractional calculus fc has encountered much success in the description of complex dynamics in particular fc has proved to be a valuable tool to handle viscoelastic aspects in this paper we construct fractional rheological constitutive equations on the basis of well known mechanical models especially the maxwell the kelvin voigt the zener and the poynting thomson model to this end we introduce a fractional element in addition to the standard purely elastic and purely viscous elements as we proceed to show many of the fractional differential equations which we obtain by this construction method admit closed form analytical solutions in terms of fox h functions of the minag leffler type

generalized fractional diffusion equations for accelerating subdiffusion and truncated levy flights fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time for processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order such equations were introduced in a v chechkin r gorenflo and i sokolov phys rev e 66 046129 2002 for the description of the processes getting more anomalous in the course of time decelerating subdiffusion and accelerating superdiffusion here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time which we call respectively accelerating subdiffusion and decelerating superdiffusion for the former process by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time for the latter process we demonstrate by a particular example how the power law truncated levy stable distribution evolves in time to the distribution with power law asymptotics and gaussian shape in the central part the special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics

face recognition a convolutional neural network approach we present a hybrid neural network for human face recognition which compares favourably with other methods the system combines local image sampling a self organizing map som neural network and a convolutional neural network the som provides a quantization of the image samples into a topological space where inputs that are nearby in the original space are also nearby in the output space thereby providing dimensionality reduction and invariance to minor changes in the image sample and the convolutional neural network provides partial invariance to translation rotation scale and deformation the convolutional network extracts successively larger features in a hierarchical set of layers we present results using the karhunen loeve transform in place of the som and a multilayer perceptron mlp in place of the convolutional network for comparison we use a database of 400 images of 40 individuals which contains quite a high degree of variability in expression pose and facial details we analyze the computational complexity and discuss how new classes could be added to the trained recognizer

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

the structure of the torelli group i a finite set of generators for j this is the first of three papers concerning the so called torelli group let m mg be a compact orientable surface of genus g having n boundary components and let 9 xg be its mapping class group that is the group of orientation preserving diffeomorphisms of m which are 1 on the boundary am modulo isotopies which fix 3m pointwise this group is also known to the complex analysts as the teichmuller group or modular group if n 0 or 1 let further 4 jg be the subgroup of d1 which acts trivially on h1 m z the topologists have no traditional name for a but the analysts tell me it was known classically and is called the torelli group several interesting problems and conjectures exist concerning f the principal one can be found in kirby s problem list k and asks if gg is finitely generated in this first paper we shall answer the question affirmatively for both gg 0 and fgg when g 3 and shall give a fairly simple set of generators two other conjectures were made by the author the first involves the subgroup j of f which is generated by twists on nulhomologous simple closed curves ji produces a surjective homomorphism t fgg 1 a3h1 m z which kills c and it is conjectured there that in fact 5y ker t the proof of this is the content of the second paper in the third paper we use the results of the second to compute the abelianization f f explicitly thereby verifying another conjecture in ji the first reasonably simple but infinite set of generators for fg0 was produced by powell in p his generators consist of two types a twists on bounding simple closed curves b opposite twists on a bounding pair of disjoint homologous simple closed curves each of which are nonbounding using his result the author showed in j2 that the maps of the second type which we call bp maps for bounding pair are actually sufficient to generate both kg 0 and fg 1 for g 3 and in fact that we need only those whose two curves bound a genus one subsurface of m note that for g 2 all bp maps are trivial and hence the result fails in this case in the finite set of generators produced in this paper only

fractional differential equations and related exact mechanical models the aim of the paper is the description of fractional order differential equations in terms of exact mechanical models this result will be archived in the paper for the case of linear multiphase fractional hereditariness involving linear combinations of power laws in relaxation creep functions the mechanical model corresponding to fractional order differential equations is the extension of a recently introduced exact mechanical representation di paola and zingales 2012 33 and di paola et al 2012 34 of fractional order integrals and derivatives some numerical applications have been reported in the paper to assess the capabilities of the model in terms of a peculiar arrangement of linear springs and dashpots

a shape and texture based enhanced fisher classifier for face recognition this paper introduces a new face coding and recognition method the enhanced fisher classifier efc which employs the enhanced fisher linear discriminant model efm on integrated shape and texture features shape encodes the feature geometry of a face while texture provides a normalized shape free image the dimensionalities of the shape and the texture spaces are first reduced using principal component analysis constrained by the efm for enhanced generalization the corresponding reduced shape and texture features are then combined through a normalization procedure to form the integrated features that are processed by the efm for face recognition experimental results using 600 face images corresponding to 200 subjects of varying illumination and facial expressions show that 1 the integrated shape and texture features carry the most discriminating information followed in order by textures masked images and shape images and 2 the new coding and face recognition method efc performs the best among the eigenfaces method using l sub 1 or l sub 2 distance measure and the mahalanobis distance classifiers using a common covariance matrix for all classes or a pooled within class covariance matrix in particular efc achieves 98 5 recognition accuracy using only 25 features

fractional order theory of thermoelasticity in this work a new theory of thermoelasticity is derived using the methodology of fractional calculus the theories of coupled thermoelasticity and of generalized thermoelasticity with one relaxation time follow as limit cases a uniqueness theorem for this model is proved a variational principle and a reciprocity theorem are derived

face recognition based on a group decision making combination approach abstract this paper proposes a novel and real time classifiers combination approach group decision making combination gdc approach which can dynamically select the classifiers and perform linear combination we also prove that the orthogonal wavelet transform can be regarded as an effective image s preprocessing tool adapted to classifiers combination gdc has been successfully used for face recognition which can improve on the recognition rate for the algebraic features experiment results also show that it is superior to the conventional combination method majority voting method

continuous and discontinuous galerkin methods with finite elements in space and time for parallel computing of viscoelastic deformation abstract new non symmetric variational and discretized formulations with space time finite elements are proposed for viscoelastic problems based on the continuous galerkin method cgm and discontinuous galerkin method dgm viscoelastic behaviour is described by the three parameter malvern model which is represented by means of internal variables it allows to use only differential equations for the constitutive equations instead of integrodifferential ones the variational formulation reduces to two types of equations for total displacements and internal displacements internal variables namely to the equilibrium equation and the evolution equation for the internal displacements which are fulfilled in the weak form using continuous trial functions a continuous space time finite element formulation is obtained with simultaneous discretization in space and time subdividing the total observation time interval into time slabs and introducing discontinuous trial functions being continuous within time slabs and allowing jumps across interfaces a more general discontinuous finite element formulation is obtained the difference between these two formulations for one time slab consists in the satisfaction of initial conditions which are fulfilled exactly for the continuous formulation and in a weak form for the discontinuous case the proposed approach has some very attractive advantages with respect to semidiscretization methods regarding the possibility of adaptive space time refinements and parallel processing on mimd parallel computers the considered numerical examples show the effectiveness of simultaneous space time finite element calculations and a high convergence rate for adaptive refinement numerical efficiency is an advantage of dgm in comparison with cgm for discontinuously changing e g piecewise constant boundary conditions in time

bayesian canonical correlation analysis canonical correlation analysis cca is a classical method for seeking correlations between two multivariate data sets during the last ten years it has received more and more attention in the machine learning community in the form of novel computational formulations and a plethora of applications we review recent developments in bayesian models and inference methods for cca which are attractive for their potential in hierarchical extensions and for coping with the combination of large dimensionalities and small sample sizes the existing methods have not been particularly successful in fulfilling the promise yet we introduce a novel efficient solution that imposes group wise sparsity to estimate the posterior of an extended model which not only extracts the statistical dependencies correlations between data sets but also decomposes the data into shared and data set specific components in statistics literature the model is known as inter battery factor analysis ibfa for which we now provide a bayesian treatment

absolutely continuous functions in rn abstract for each 0 1 we consider a natural n dimensional extension of the classical notion of absolute continuous function we compare it with the mal s and hencl s definitions it follows that each absolute continuous function is continuous weak differentiable with gradient in l n differentiable almost everywhere and satisfies the formula on change of variables

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

automatic classification of single facial images we propose a method for automatically classifying facial images based on labeled elastic graph matching a 2d gabor wavelet representation and linear discriminant analysis results of tests with three image sets are presented for the classification of sex race and expression a visual interpretation of the discriminant vectors is provided

appearance models based on kernel canonical correlation analysis this paper introduces a new approach to constructing appearance models based on kernel canonical correlation analysis kernel cca kernel cca is a non linear extension of cca where a non linear transformation of the input data is performed implicitly using kernel methods although in this respect it is similar to other generalized linear methods kernel cca is especially well suited for relating two sets of measurements the benefits of our method compared to standard feature extraction methods based on pca will be illustrated experimentally for the task of estimating an object s pose from raw brightness images

an energetic formulation for the linear viscoelastic problem part i theoretical results and first calculations an extremal principle is formulated for the linear viscoelastic problem with general viscous kernel this is an extension of the classical total potential energy principle of the linear elasticity then a discretized formulation in space and time is shown for frame structures using finite element technique several numerical examples for two different kinds of viscoelastic materials testify the accuracy and reliability of the proposed method the matrix conditioning indexes obtained are compared with those achieved by applying the least square method

locality preserved maximum information projection dimensionality reduction is usually involved in the domains of artificial intelligence and machine learning linear projection of features is of particular interest for dimensionality reduction since it is simple to calculate and analytically analyze in this paper we propose an essentially linear projection technique called locality preserved maximum information projection lpmip to identify the underlying manifold structure of a data set lpmip considers both the within locality and the between locality in the processing of manifold learning equivalently the goal of lpmip is to preserve the local structure while maximize the out of locality global information of the samples simultaneously different from principal component analysis pca that aims to preserve the global information and locality preserving projections lpps that is in favor of preserving the local structure of the data set lpmip seeks a tradeoff between the global and local structures which is adjusted by a parameter alpha so as to find a sub space that detects the intrinsic manifold structure for classification tasks computationally by constructing the adjacency matrix lpmip is formulated as an eigenvalue problem lpmip yields orthogonal basis functions and completely avoids the singularity problem as it exists in lpp further we develop an efficient and stable lpmip qr algorithm for implementing lpmip especially on high dimensional data set theoretical analysis shows that conventional linear projection methods such as weighted pca maximum margin criterion mmc linear discriminant analysis lda and lpp could be derived from the lpmip framework by setting different graph models and constraints extensive experiments on face digit and facial expression recognition show the effectiveness of the proposed lpmip method

relaxational metric adaptation and its application to semi supervised clustering and content based image retrieval the performance of many supervised and unsupervised learning algorithms is very sensitive to the choice of an appropriate distance metric previous work in metric learning and adaptation has mostly been focused on classification tasks by making use of class label information in standard clustering tasks however class label information is not available in order to adapt the metric to improve the clustering results some background knowledge or side information is needed one useful type of side information is in the form of pairwise similarity or dissimilarity information recently some novel methods e g the parametric method proposed by xing et al for learning global metrics based on pairwise side information have been shown to demonstrate promising results in this paper we propose a nonparametric method called relaxational metric adaptation rma for the same metric adaptation problem while rma is local in the sense that it allows locally adaptive metrics it is also global because even patterns not in the vicinity can have long range effects on the metric adaptation process experimental results for semi supervised clustering based on both simulated and real world data sets show that rma outperforms xing et al s method under most situations besides applying rma to semi supervised learning we have also used it to improve the performance of content based image retrieval systems through metric adaptation experimental results based on two real world image databases show that rma significantly outperforms other methods in improving the image retrieval performance

graph regularized multiset canonical correlations with applications to joint feature extraction abstract multiset canonical correlation analysis mcca is a powerful technique for analyzing linear correlations among multiple representation data however it usually fails to discover the intrinsic geometrical and discriminating structure of multiple data spaces in real world applications in this paper we thus propose a novel algorithm called graph regularized multiset canonical correlations grmccs which explicitly considers both discriminative and intrinsic geometrical structure in multiple representation data grmcc not only maximizes between set cumulative correlations but also minimizes local intraclass scatter and simultaneously maximizes local interclass separability by using the nearest neighbor graphs on within set data thus it can leverage the power of both mcca and discriminative graph laplacian regularization extensive experimental results on the ar cmu pie yale b at t and eth 80 datasets show that grmcc has more discriminating power and can provide encouraging recognition results in contrast with the state of the art algorithms

penalized discriminant analysis fisher s linear discriminant analysis lda is a popular data analytic tool for studying the relationship between a set of predictors and a categorical response in this paper we describe a penalized version of lda it is designed for situations in which there are many highly correlated predictors such as those obtained by discretizing a function or the grey scale values of the pixels in a series of images in cases such as these it is natural efficient and sometimes essential to impose a spatial smoothness constraint on the coefficients both for improved prediction performance and interpretability we cast the classification problem into a regression framework via optimal scoring using this our proposal facilitates the use of any penalized regression technique in the classification setting the technique is illustrated with examples in speech recognition and handwritten character recognition

absolutely continuous functions of several variables abstract a class of absolutely continuous functions ofnvariables is introduced the absolute continuity implies continuity weak differentiability with gradient inln differentiability almost everywhere area coarea and degree formulae this gives a unified approach to some previously known conditions for the mentioned results based on monotonicity finite dilatation or higher integrability of the gradient

geometry of surfaces with caputo fractional derivatives and applications to incompressible two dimensional flows geometric structures of surfaces are formulated based on caputo fractional derivatives the gauss frame of a surface with fractional order is introduced then the non locality of the fractional derivative characterizes the asymmetric second fundamental form the mean and gaussian curvatures of the surface are defined in the case of fractional order based on the fractional curvatures incompressible two dimensional flows are discussed the stream functions are obtained from a fractional continuity equation the asymmetric second fundamental form of stream function surface is related to the path dependence of flux moreover the fractional curvatures are calculated for the stream function surfaces of uniform and corner flows the uniform flow with fractional order is characterized by the non vanishing mean curvature the non locality of corner flow is expressed by the mean and gaussian curvatures with fractional order in particular the fractional order within the stream function of corner flow determines the change of sign of gaussian curvature therefore the non local property of incompressible flows can be investigated by the fractional curvatures

a kernel approach for semisupervised metric learning while distance function learning for supervised learning tasks has a long history extending it to learning tasks with weaker supervisory information has only been studied recently in particular some methods have been proposed for semisupervised metric learning based on pairwise similarity or dissimilarity information in this paper we propose a kernel approach for semisupervised metric learning and present in detail two special cases of this kernel approach the metric learning problem is thus formulated as an optimization problem for kernel learning an attractive property of the optimization problem is that it is convex and hence has no local optima while a closed form solution exists for the first special case the second case is solved using an iterative majorization procedure to estimate the optimal solution asymptotically experimental results based on both synthetic and real world data show that this new kernel approach is promising for nonlinear metric learning

shape appearance correlated active appearance model among the challenges faced by current active shape or appearance models facial feature localization in the wild with occlusion in a novel face image i e in a generic environment is regarded as one of the most difficult computer vision tasks in this paper we propose an active appearance model aam to tackle the problem of generic environment firstly a fast face model initialization scheme is proposed based on the idea that the local appearance of feature points can be accurately approximated with locality constraints nearest neighbors which have similar poses and textures to a test face are retrieved from a training set for constructing the initial face model to further improve the fitting of the initial model to the test face an orthogonal cca occa is employed to increase the correlation between shape features and appearance features represented by principal component analysis pca with these two contributions we propose a novel aam namely the shape appearance correlated aam sac aam and the optimization is solved by using the recently proposed fast simultaneous inverse compositional fast sic algorithm experiment results demonstrate a 5 10 improvement on controlled and semi controlled datasets and with around 10 improvement on wild face datasets in terms of fitting accuracy compared to other state of the art aam models a fast face model initialization scheme is proposed for aams orthogonal cca is employed to increase the correlation between shape and appearance a shape appearance correlated aam is proposed to tackle the generic problem of localizing feature points on unseen faces

canonical correlation analysis for multilabel classification a least squares formulation extensions and analysis canonical correlation analysis cca is a well known technique for finding the correlations between two sets of multidimensional variables it projects both sets of variables onto a lower dimensional space in which they are maximally correlated cca is commonly applied for supervised dimensionality reduction in which the two sets of variables are derived from the data and the class labels respectively it is well known that cca can be formulated as a least squares problem in the binary class case however the extension to the more general setting remains unclear in this paper we show that under a mild condition which tends to hold for high dimensional data cca in the multilabel case can be formulated as a least squares problem based on this equivalence relationship efficient algorithms for solving least squares problems can be applied to scale cca to very large data sets in addition we propose several cca extensions including the sparse cca formulation based on the 1 norm regularization we further extend the least squares formulation to partial least squares in addition we show that the cca projection for one set of variables is independent of the regularization on the other set of multidimensional variables providing new insights on the effect of regularization on cca we have conducted experiments using benchmark data sets experiments on multilabel data sets confirm the established equivalence relationships results also demonstrate the effectiveness and efficiency of the proposed cca extensions

a fractional order model for aging materials an application to concrete abstract in this paper the hereditariness of aging materials is modeled within the framework of fractional calculus of variable order a relevant application is made for the long term behavior of concrete for which the creep function is evaluated with the aid of model b3 the corresponding relaxation function is derived through the volterra iterated kernels and a comparison with the numerically obtained relaxation function of model b3 is also reported the proposed fractional hereditary aging model fham for concretes leads to a relaxation function that fully agrees with the well established model b3 furthermore the fham takes full advantage of the formalism of fractional order calculus to yield semi analytic expressions in terms of material parameters

penalized partial least square discriminant analysis with l 1 norm for multi label data multi label data are prevalent in real world due to its great potential applications multi label learning has now been receiving more and more attention from many fields however how to effectively exploit the correlations of variables and labels and tackle the high dimensional problems of data are two major challenging issues for multi label learning in this paper we make an attempt to cope with these two problems by proposing an effective multi label learning algorithm specifically we make use of the technique of partial least square discriminant analysis to identify a common latent space between the variable space and the label space of multi label data moreover considering the label space of the multi label data is sparse a l1 norm penalty is further performed to constrain the y loadings of the optimization problem of partial least squares making them sparse the merit of our method is that it can capture the correlations and perform dimension reduction at the same time the experimental results conducted on eleven public data sets show that our method is promising and superior to the state of the art multi label classifiers in most cases highlightsa new and effective learning method for the multi label data is proposed the method exploits the sparse property of the label space fully the method captures the correlations of the variables by using partial least squares discriminant analysis dimension reduction has also applied to the high dimensional data the sparse purpose is achieved by performing the l1 norm penalty

facial expression recognition using kernel canonical correlation analysis kcca in this correspondence we address the facial expression recognition problem using kernel canonical correlation analysis kcca following the method proposed by lyons et al and zhang et al we manually locate 34 landmark points from each facial image and then convert these geometric points into a labeled graph lg vector using the gabor wavelet transformation method to represent the facial features on the other hand for each training facial image the semantic ratings describing the basic expressions are combined into a six dimensional semantic expression vector learning the correlation between the lg vector and the semantic expression vector is performed by kcca according to this correlation we estimate the associated semantic expression vector of a given test image and then perform the expression classification according to this estimated semantic expression vector moreover we also propose an improved kcca algorithm to tackle the singularity problem of the gram matrix the experimental results on the japanese female facial expression database and the ekman s pictures of facial affect database illustrate the effectiveness of the proposed method