pairwise sparsity preserving embedding for unsupervised subspace learning and classification two novel unsupervised dimensionality reduction techniques termed sparse distance preserving embedding sdpe and sparse proximity preserving embedding sppe are proposed for feature extraction and classification sdpe and sppe perform in the clean data space recovered by sparse representation and enhanced euclidean distances over noise removed data are employed to measure pairwise similarities of points in extracting informative features sdpe and sppe aim at preserving pairwise similarities between data points in addition to preserving the sparse characteristics this paper calculates the sparsest representation of all vectors jointly by a convex optimization the sparsest codes enable certain local information of data to be preserved and can endow sdpe and sppe a natural discriminating power adaptive neighborhood and robust characteristic against noise and errors in delivering low dimensional embeddings we also mathematically show sdpe and sppe can be effectively extended for discriminant learning in a supervised manner the validity of sdpe and sppe is examined by extensive simulations comparison with other related state of the art unsupervised algorithms show that promising results are delivered by our techniques

modified principal component analysis an integration of multiple similarity subspace models we modify the conventional principal component analysis pca and propose a novel subspace learning framework modified pca mpca using multiple similarity measurements mpca computes three similarity matrices exploiting the similarity measurements 1 mutual information 2 angle information and 3 gaussian kernel similarity we employ the eigenvectors of similarity matrices to produce new subspaces referred to as similarity subspaces a new integrated similarity subspace is then generated using a novel feature selection approach this approach needs to construct a kind of vector set termed weak machine cell wmc which contains an appropriate number of the eigenvectors spanning the similarity subspaces combining the wrapper method and the forward selection scheme mpca selects a wmc at a time that has a powerful discriminative capability to classify samples mpca is very suitable for the application scenarios in which the number of the training samples is less than the data dimensionality mpca outperforms the other state of the art pca based methods in terms of both classification accuracy and clustering result in addition mpca can be applied to face image reconstruction mpca can use other types of similarity measurements extensive experiments on many popular real world data sets such as face databases show that mpca achieves desirable classification results as well as has a powerful capability to represent data

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

training free generic object detection using locally adaptive regression kernels we present a generic detection localization algorithm capable of searching for a visual object of interest without training the proposed method operates using a single example of an object of interest to find similar matches does not require prior knowledge learning about objects being sought and does not require any preprocessing step or segmentation of a target image our method is based on the computation of local regression kernels as descriptors from a query which measure the likeness of a pixel to its surroundings salient features are extracted from said descriptors and compared against analogous features from the target image this comparison is done using a matrix generalization of the cosine similarity measure we illustrate optimality properties of the algorithm using a naive bayes framework the algorithm yields a scalar resemblance map indicating the likelihood of similarity between the query and all patches in the target image by employing nonparametric significance tests and nonmaxima suppression we detect the presence and location of objects similar to the given query the approach is extended to account for large variations in scale and rotation high performance is demonstrated on several challenging data sets indicating successful detection of objects in diverse contexts and under different imaging conditions

semi supervised lpp algorithms for learning to rank based visual search reranking two feature dimensionality reduction methods for search reranking are proposed the sslpp algorithm improves lpp by incorporating the relevance degree information the proposed pcc sslpp algorithm models the correlation information into sslpp the proposed methods achieve better ndcg performance recent years have witnessed the success of learning to rank technique in visual search reranking generally dimensionality reduction is one of the important stages in this kind of method to deal with the high dimensional visual features however these methods are typically designed for classification and retrieval applications rather than ranking direct utilization of them cannot guarantee the best performance in ranking applications as ranking information e g relevance degree label is absent to solve this problem a semi supervised lpp algorithm called sslpp is proposed the method incorporates the relevance degree information into a manifold dimensionality reduction method i e locality preserving projections lpp to accurately preserve the correlation information between two images in the low intrinsic dimensional space a pearson correlation coefficient pcc based sslpp algorithm called pcc sslpp is further developed the pcc sslpp method models the correlation information between two images in the graph construction step of sslpp besides a novel visual search reranking scheme is also presented based on the proposed sslpp pcc sslpp and learning to rank experiments on two popular real world image reranking datasets demonstrate the effectiveness of the proposed scheme and algorithms in visual search reranking

image outlier detection and feature extraction via l1 norm based 2d probabilistic pca this paper introduces an l1 norm based probabilistic principal component analysis model on 2d data l1 2dppca based on the assumption of the laplacian noise model the laplacian or l1 density function can be expressed as a superposition of an infinite number of gaussian distributions under this expression a bayesian inference can be established based on the variational expectation maximization approach all the key parameters in the probabilistic model can be learned by the proposed variational algorithm it has experimentally been demonstrated that the newly introduced hidden variables in the superposition can serve as an effective indicator for data outliers experiments on some publicly available databases show that the performance of l1 2dppca has largely been improved after identifying and removing sample outliers resulting in more accurate image reconstruction than the existing pca based methods the performance of feature extraction of the proposed method generally outperforms other existing algorithms in terms of reconstruction errors and classification accuracy

constrained large margin local projection algorithms and extensions for multimodal dimensionality reduction a constrained large margin local projection cmlp technique for multimodal dimensionality reduction is proposed we elaborate the criterion of cmlp from a pairwise constrained marginal perspective four effective cmlp solution schemes are presented and the corresponding comparative analyses are given an equivalent weighted least squares formulation for cmlp is also detailed cmlp is originated from the criterion of locality preserving projections lpp but cmlp offers a number of attractive advantages over lpp to keep the intrinsic proximity relations of inter class and intra class similarity pairs the localized pairwise cannot link and must link constraints are applied to specify the types of those neighboring pairs by utilizing the cmlp criterion margins between inter and intra class clusters are significantly enlarged as a result multimodal distributions are effectively preserved to further optimize the cmlp criterion one feasible improvement strategy is described with kernel methods we present the kernelized extensions of our approaches mathematical comparisons and analyses between this work and the related works are also detailed extensive simulations including multivariate manifold visualization and classification on the benchmark ucl orl yale umist mit cbcl and usps datasets are conducted to verify the efficiency of our techniques the presented results reveal that our methods are highly competitive with and even outperform some widely used state of the art algorithms

probabilistic visual learning for object representation we present an unsupervised technique for visual learning which is based on density estimation in high dimensional spaces using an eigenspace decomposition two types of density estimates are derived for modeling the training data a multivariate gaussian for unimodal distributions and a mixture of gaussians model for multimodal distributions those probability densities are then used to formulate a maximum likelihood estimation framework for visual search and target detection for automatic object recognition and coding our learning technique is applied to the probabilistic visual modeling detection recognition and coding of human faces and nonrigid objects such as hands

subspace learning from image gradient orientations we introduce the notion of subspace learning from image gradient orientations for appearance based object recognition as image data are typically noisy and noise is substantially different from gaussian traditional subspace learning from pixel intensities very often fails to estimate reliably the low dimensional subspace of a given data population we show that replacing pixel intensities with gradient orientations and the l2 norm with a cosine based distance measure offers to some extend a remedy to this problem within this framework which we coin image gradient orientations igo subspace learning we first formulate and study the properties of principal component analysis of image gradient orientations igo pca we then show its connection to previously proposed robust pca techniques both theoretically and experimentally finally we derive a number of other popular subspace learning techniques namely linear discriminant analysis lda locally linear embedding lle and laplacian eigenmaps le experimental results show that our algorithms significantly outperform popular methods such as gabor features and local binary patterns and achieve state of the art performance for difficult problems such as illumination and occlusion robust face recognition in addition to this the proposed igo methods require the eigendecomposition of simple covariance matrices and are as computationally efficient as their corresponding l2 norm intensity based counterparts matlab code for the methods presented in this paper can be found at http ibug doc ic ac uk resources

approximate information discriminant analysis a computationally simple heteroscedastic feature extraction technique in this article we develop a novel linear dimensionality reduction technique for classification the technique utilizes the first two statistical moments of data and retains the computational simplicity characteristic of second order techniques such as linear discriminant analysis formally the technique maximizes a criterion that belongs to the class of probability dependence measures and is naturally defined for multiple classes the criterion is based on an approximation of an information theoretic measure and is capable of handling heteroscedastic data the performance of our method along with similar feature extraction approaches is demonstrated based on experimental results with real world datasets our method compares favorably to similar second order linear dimensionality techniques

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

comments on globally maximizing locally minimizing unsupervised discriminant projection with application to face and palm biometrics this paper develops an unsupervised discriminant projection udp technique for dimensionality reduction of high dimensional data in small sample size cases udp can be seen as a linear approximation of a multimanifolds based learning framework which takes into account both the local and nonlocal quantities udp characterizes the local scatter as well as the nonlocal scatter seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter this characteristic makes udp more intuitive and more powerful than the most up to date method locality preserving projection lpp which considers only the local scatter for clustering or classification tasks the proposed method is applied to face and palm biometrics and is examined using the yale feret and ar face image databases and the polyu palmprint database the experimental results show that udp consistently outperforms lpp and pca and outperforms lda when the training sample size per class is small this demonstrates that udp is a good choice for real world biometrics applications

robust regression for face recognition in this paper we address the problem of robust face recognition by formulating the pattern recognition task as a problem of robust estimation using a fundamental concept that in general patterns from a single object class lie on a linear subspace barsi and jacobs 2003 1 we develop a linear model representing a probe image as a linear combination of class specific galleries in the presence of noise the well conditioned inverse problem is solved using the robust huber estimation and the decision is ruled in favor of the class with the minimum reconstruction error the proposed robust linear regression classification rlrc algorithm is extensively evaluated for two important cases of robustness i e illumination variations and random pixel corruption illumination invariant face recognition is demonstrated on three standard databases under exemplary evaluation protocols reported in the literature comprehensive comparative analysis with the state of art illumination tolerant approaches indicates a comparable performance index for the proposed rlrc algorithm the efficiency of the proposed approach in the presence of severe random noise is validated under several exemplary noise models such as dead pixel problem salt and pepper noise speckle noise and additive white gaussian noise awgn the rlrc algorithm is found to be favorable compared with the benchmark generative approaches

repeated filtering in consecutive fractional fourier domains and its application to signal restoration filtering in a single time domain or in a single frequency domain has been generalized to filtering in a single fractional fourier domain we generalize this to repeated filtering in consecutive fractional fourier domains and discuss its applications to signal restoration through an illustrative example

wigner ville spectral analysis of nonstationary processes the wigner ville spectrum has been recently introduced as the unique generalized spectrum for time varying spectral analysis its properties are revised with emphasis on its central role in the analysis of second order properties of nonstationary random signals we propose here a general class of spectral estimators of the wigner ville spectrum this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time frequency representations of deterministic signals with finite energy classical estimators like short time periodograms and the recently introduced pseudo wigner estimators are shown to be special cases of the general class the generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo wigner estimators the effective numerical implementation by an n point fft of pseudo wigner estimators of 2n points is indicated and various examples are given

error analysis of reconstruction from linear canonical transform based sampling in this paper we consider the performance of sampling associated with the linear canonical transform lct which generalizes a large number of classical integral transforms and fundamental operations linked to signal processing and optics first we revisit sampling approximation in the lct domain to introduce a generalized approximation operator then we derive an exact closed form expression for the integrated squared error that occurs when a signal is approximated by a basis of shifted scaled and chirp modulated versions of a generating function in the lct domain several basic properties of the approximation error are presented the derived results can be applied to a wide variety of sampling approximation schemes in the lct domain finally experimental examples are given to illustrate the theoretical derivations

a multi manifold discriminant analysis method for image feature extraction in this paper we propose a multi manifold discriminant analysis mmda method for an image feature extraction and pattern recognition based on graph embedded learning and under the fisher discriminant analysis framework in an mmda the within class graph and between class graph are respectively designed to characterize the within class compactness and the between class separability seeking for the discriminant matrix to simultaneously maximize the between class scatter and minimize the within class scatter in addition in an mmda the within class graph can represent the sub manifold information while the between class graph can represent the multi manifold information the proposed mmda is extensively examined by using the feret ar and orl face databases and the polyu finger knuckle print databases the experimental results demonstrate that an mmda is effective in feature extraction leading to promising image recognition performance

a regularized approach for geodesic based semisupervised multimanifold learning geodesic distance as an essential measurement for data dissimilarity has been successfully used in manifold learning however most geodesic distance based manifold learning algorithms have two limitations when applied to classification 1 class information is rarely used in computing the geodesic distances between data points on manifolds and 2 little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances in this paper we regard geodesic distance as a kind of kernel which maps data from linearly inseparable space to linear separable distance space in doing this a new semisupervised manifold learning algorithm namely regularized geodesic feature learning algorithm is proposed the method consists of three techniques a semisupervised graph construction method replacement of original data points with feature vectors which are built by geodesic distances and a new semisupervised dimension reduction method for feature vectors experiments on the mnist usps handwritten digit data sets mit cbcl face versus nonface data set and an intelligent traffic data set show the effectiveness of the proposed algorithm

normalized cuts and image segmentation we propose a novel approach for solving the perceptual grouping problem in vision rather than focusing on local features and their consistencies in the image data our approach aims at extracting the global impression of an image we treat image segmentation as a graph partitioning problem and propose a novel global criterion the normalized cut for segmenting the graph the normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups we show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion we applied this approach to segmenting static images as well as motion sequences and found the results to be very encouraging

proximity based frameworks for generating embeddings from multi output data this paper is about supervised and semi supervised dimensionality reduction dr by generating spectral embeddings from multi output data based on the pairwise proximity information two flexible and generic frameworks are proposed to achieve supervised dr sdr for multilabel classification one is able to extend any existing single label sdr to multilabel via sample duplication referred to as mesd the other is a multilabel design framework that tackles the sdr problem by computing weight proximity matrices based on simultaneous feature and label information referred to as mope as a generalization of many current techniques a diverse set of different schemes for label based proximity calculation as well as a mechanism for combining label based and feature based weight information by considering information importance and prioritization are proposed for mope additionally we summarize many current spectral methods for unsupervised dr udr single multilabel sdr and semi supervised dr ssdr and express them under a common template representation as a general guide to researchers in the field we also propose a general framework for achieving ssdr by combining existing sdr and udr models and also a procedure of reducing the computational cost via learning with a target set of relation features the effectiveness of our proposed methodologies is demonstrated with experiments with document collections for multilabel text categorization from the natural language processing domain

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

a time frequency formulation of optimum detection a time frequency formulation is proposed for the optimum detection of gaussian signals in white gaussian noise by choosing the wigner ville distribution as the basic time frequency tool it is shown that the corresponding receivers generally take the form of a correlation between time frequency structures matching mathematical optimality with a physically meaningful interpretation the case of low snr is examined and various examples are considered deterministic signal rayleigh fading signal random jitter and random time varying channel a general class of time frequency receivers is proposed which admits as limiting cases different known structures and its suboptimum performance is evaluated possible extensions to more elaborate situations including parameter estimation are mentioned

unsupervised 2d dimensionality reduction with adaptive structure learning in recent years unsupervised two dimensional 2d dimensionality reduction methods for unlabeled large scale data have made progress however performance of these degrades when the learning of similarity matrix is at the beginning of the dimensionality reduction process a similarity matrix is used to reveal the underlying geometry structure of data in unsupervised dimensionality reduction methods because of noise data it is difficult to learn the optimal similarity matrix in this letter we propose a new dimensionality reduction model for 2d image matrices unsupervised 2d dimensionality reduction with adaptive structure learning drasl instead of using a predetermined similarity matrix to characterize the underlying geometry structure of the original 2d image space our proposed approach involves the learning of a similarity matrix in the procedure of dimensionality reduction to realize a desirable neighbors assignment after dimensionality reduction we add a constraint to our model such that there are exact formula see text connected components in the final subspace to accomplish these goals we propose a unified objective function to integrate dimensionality reduction the learning of the similarity matrix and the adaptive learning of neighbors assignment into it an iterative optimization algorithm is proposed to solve the objective function we compare the proposed method with several 2d unsupervised dimensionality methods k means is used to evaluate the clustering performance we conduct extensive experiments on coil20 at t feret usps and yale data sets to verify the effectiveness of our proposed method

time frequency analysis of the impulse response the impulse response is a key function for the analysis and design of systems therefore understanding its properties is a fundamental problem to investigate the nonstationary structure of the impulse response we derive its time frequency representation both in the wigner and smoothed wigner distribution domains first we consider the class of single input single output siso systems which models a wide variety of physical phenomena the obtained wigner distribution for the class of siso systems is made by frequency translated versions of the wigner distribution of the impulse response for a first order system a t shaped function of time and frequency plus the interference terms which are effectively filtered out in the smoothed wigner domain then we consider the case of multiple input multiple output mimo systems whose impulse response is the collection of the individual responses obtained by applying an impulse to every input separately also in this case the wigner distribution of the impulse response depends on the t function we apply our results to a two dimensional mimo harmonic oscillator and to a siso system with three resonances finally we propose the key idea of a system identification method that operates directly in the time frequency domain by fitting the smoothed t function we show that the method works for a nonlinear oscillator with a large cubic term as well as for a time varying harmonic oscillator and that it can tolerate the presence of both stationary and nonstationary noise

on the selection of 2d krawtchouk moments for face recognition sparse representation of images using orthogonal two dimensional krawtchouk moments 2d kcms for face recognition is motivated by their ability to capture region based higher order hidden nonlinear structures from discrete coordinates of finitely supported images and the invariance of affine transformations of these moments to common geometric distortions this paper presents the effectiveness of selecting the discriminatory set of kcms as the global and local face features as opposed to traditional features obtained from heuristic choice of fixed order moments or projection of the moments for recognizing an identity the selection of significantly sparse 2d kcm based features according to the proposed approach results in highly efficient face recognition method as compared to the other methods that use orthogonal moments such as the 2d zernike 2d tchebichef or 2d gaussian hermite experiments on challenging databases viz frgc and ck auc and comparisons with the well established projection texture and moment based methods indicate superior recognition performance in terms of mean accuracy and robustness of the proposed holistic or hybrid type discriminative kcm based method especially when sample sizes are small and the intraclass faces have significant variations due to expressions highlightshybrid type face recognition using discriminative selection of krawtchouk moments a comparative study of different moment based discriminative face features experiments on two challenging databases show superiority of the proposed selection fisher scoring is preferable to lda projection for moment based face recognition effective facial parts are identified for recognition of expression variant faces

fractional power spectrum in this paper by investigating the definitions of the fractional power spectrum and the fractional correlation for the deterministic process we consider the case associated with the random process in an explicit manner the fractional power spectral relations for the fractional fourier domain filter are derived and the expression for the fractional power spectrum in terms of the fractional correlation is obtained in addition the definitions and the properties of the fractional white noise and the chirp stationary process are presented simulation results verify the theoretical derivations and demonstrate the potential applications such as detection and parameter estimation of chirp signals fractional power spectral estimation and system identification in the fractional fourier domain

a novel framework for learning geometry aware kernels the data from real world usually have nonlinear geometric structure which are often assumed to lie on or close to a low dimensional manifold in a high dimensional space how to detect this nonlinear geometric structure of the data is important for the learning algorithms recently there has been a surge of interest in utilizing kernels 1 to exploit the manifold structure of the data such kernels are called geometry aware kernels and are widely used in the machine learning algorithms the performance of these algorithms critically relies on the choice of the geometry aware kernels intuitively a good geometry aware kernel should utilize additional information other than the geometric information in many applications it is required to compute the out of sample data directly however most of the geometry aware kernel methods are restricted to the available data given beforehand with no straightforward extension for out of sample data in this paper we propose a framework for more general geometry aware kernel learning the proposed framework integrates multiple sources of information and enables us to develop flexible and effective kernel matrices then we theoretically show how the learned kernel matrices are extended to the corresponding kernel functions in which the out of sample data can be computed directly under our framework a novel family of geometry aware kernels is developed especially some existing geometry aware kernels can be viewed as instances of our framework the performance of the kernels is evaluated on dimensionality reduction classification and clustering tasks the empirical results show that our kernels significantly improve the performance 1 kernel refers to kernel function or kernel matrix which should be understood from the context

gabor based kernel pca with doubly nonlinear mapping for face recognition with a single face image in this paper a novel gabor based kernel principal component analysis pca with doubly nonlinear mapping is proposed for human face recognition in our approach the gabor wavelets are used to extract facial features then a doubly nonlinear mapping kernel pca dkpca is proposed to perform feature transformation and face recognition the conventional kernel pca nonlinearly maps an input image into a high dimensional feature space in order to make the mapped features linearly separable however this method does not consider the structural characteristics of the face images and it is difficult to determine which nonlinear mapping is more effective for face recognition in this paper a new method of nonlinear mapping which is performed in the original feature space is defined the proposed nonlinear mapping not only considers the statistical property of the input features but also adopts an eigenmask to emphasize those important facial feature points therefore after this mapping the transformed features have a higher discriminating power and the relative importance of the features adapts to the spatial importance of the face images this new nonlinear mapping is combined with the conventional kernel pca to be called doubly nonlinear mapping kernel pca the proposed algorithm is evaluated based on the yale database the ar database the orl database and the yaleb database by using different face recognition methods such as pca gabor wavelets plus pca and gabor wavelets plus kernel pca with fractional power polynomial models experiments show that consistent and promising results are obtained

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

learning discriminative singular value decomposition representation for face recognition abstract face representation is a critical step in face recognition recently singular value decomposition svd based representation methods have attracted researchers attentions for their power of alleviating the facial variations the svd representation reveals that the svd basis set is important for the recognition purpose and the corresponding singular values svs are regulated to form a more effective representation image however there exists a common problem in the existing svd based representation methods they all empirically make a rule to regulate the svs which is obviously not optimal in theory to address this problem in this paper we propose a novel method named learning discriminative singular value decomposition representation ldsvdr for face recognition we build an individual svd basis set for each image and then learn a common set of svs by taking account of the information in the basis sets according to a discriminant criterion across the training images the proposed model is solved by sequential quadratic programming sqp method extensive experiments are conducted on three popular face databases and the results demonstrate the effectiveness of our method when dealing with variations of illumination occlusion disguise and face sketch recognition task

fractional fourier analysis of random signals and the notion of spl alpha stationarity of the wigner ville distribution in this paper a generalized notion of wide sense stationarity for random signals is presented the notion of stationarity is fundamental in the fourier analysis of random signals for this purpose a definition of the fractional correlation between two random variables is introduced it is shown that for wide sense stationary random signals the fractional correlation and the fractional power spectral density functions form a fractional fourier transform pair thus the concept of stationarity plays an important role in the analysis of random signals through the fractional fourier transform for signals nonstationary in the standard formulation but stationary furthermore we define the wigner ville distribution in terms of the fractional correlation function in which the standard fourier analysis is the particular case for 2 and it leads to the wiener khinchin theorem

one shot detection with laplacian object and fast matrix cosine similarity one shot generic object detection involves searching for a single query object in a larger target image relevant approaches have benefited from features that typically model the local similarity patterns in this paper we combine local similarity encoded by local descriptors with a global context i e a graph structure of pairwise affinities among the local descriptors embedding the query descriptors into a low dimensional but discriminatory subspace unlike principal components that preserve global structure of feature space we actually seek a linear approximation to the laplacian eigenmap that permits us a locality preserving embedding of high dimensional region descriptors our second contribution is an accelerated but exact computation of matrix cosine similarity as the decision rule for detection obviating the computationally expensive sliding window search we leverage the power of fourier transform combined with integral image to achieve superior runtime efficiency that allows us to test multiple hypotheses for pose estimation within a reasonably short time our approach to one shot detection is training free and experiments on the standard data sets confirm the efficacy of our model besides low computation cost of the proposed codebook free object detector facilitates rather straightforward query detection in large data sets including movie videos

riemannian manifold learning recently manifold learning has been widely exploited in pattern recognition data analysis and machine learning this paper presents a novel framework called riemannian manifold learning rml based on the assumption that the input high dimensional data lie on an intrinsically low dimensional riemannian manifold the main idea is to formulate the dimensionality reduction problem as a classical problem in riemannian geometry that is how to construct coordinate charts for a given riemannian manifold we implement the riemannian normal coordinate chart which has been the most widely used in riemannian geometry for a set of unorganized data points first two input parameters the neighborhood size k and the intrinsic dimension d are estimated based on an efficient simplicial reconstruction of the underlying manifold then the normal coordinates are computed to map the input high dimensional data into a low dimensional space experiments on synthetic data as well as real world images demonstrate that our algorithm can learn intrinsic geometric structures of the data preserve radial geodesic distances and yield regular embeddings

flexible manifold embedding a framework for semi supervised and unsupervised dimension reduction we propose a unified manifold learning framework for semi supervised and unsupervised dimension reduction by employing a simple but effective linear regression function to map the new data points for semi supervised dimension reduction we aim to find the optimal prediction labels f for all the training samples x the linear regression function h x and the regression residue f0 f h x simultaneously our new objective function integrates two terms related to label fitness and manifold smoothness as well as a flexible penalty term defined on the residue f0 our semi supervised learning framework referred to as flexible manifold embedding fme can effectively utilize label information from labeled data as well as a manifold structure from both labeled and unlabeled data by modeling the mismatch between h x and f we show that fme relaxes the hard linear constraint f h x in manifold regularization mr making it better cope with the data sampled from a nonlinear manifold in addition we propose a simplified version referred to as fme u for unsupervised dimension reduction we also show that our proposed framework provides a unified view to explain and understand many semi supervised supervised and unsupervised dimension reduction techniques comprehensive experiments on several benchmark databases demonstrate the significant improvement over existing dimension reduction algorithms

optimal filtering in fractional fourier domains for time invariant degradation models and stationary signals and noise the classical fourier domain wiener filter which can be implemented in o n log n time gives the minimum mean square error estimate of the original undistorted signal for time varying degradations and nonstationary processes however the optimal linear estimate requires o n sup 2 time for implementation we consider filtering in fractional fourier domains which enables significant reduction of the error compared with ordinary fourier domain filtering for certain types of degradation and noise especially of chirped nature while requiring only o n log n implementation time thus improved performance is achieved at no additional cost expressions for the optimal filter functions in fractional domains are derived and several illustrative examples are given in which significant reduction of the error by a factor of 50 is obtained

complete neighborhood preserving embedding for face recognition neighborhood preserving embedding npe is a linear approximation to the locally linear embedding algorithm which can preserve the local neighborhood structure on the data manifold however in typical face recognition where the number of data samples is smaller than the dimension of data space it is difficult to directly apply npe to high dimensional matrices because of computational complexity moreover in such case npe often suffers from the singularity problem of eigenmatrix which makes the direct implementation of the npe algorithm almost impossible in practice principal component analysis or singular value decomposition is applied as a preprocessing step to attack these problems nevertheless this strategy may discard dimensions that contain important discriminative information and the eigensystem computation of npe could be unstable towards a practical dimensionality reduction method for face data we develop a new scheme in this paper namely the complete neighborhood preserving embedding cnpe cnpe transforms the singular generalized eigensystem computation of npe into two eigenvalue decomposition problems moreover a feasible and effective procedure is proposed to alleviate the computational burden of high dimensional matrix for typical face image data experimental results on the orl face database and the yale face database show that the proposed cnpe algorithm achieves better performance than other feature extraction methods such as eigenfaces fisherfaces and npe etc

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

stationary signal processing on graphs graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets in this context it is of high importance to develop flexible models of signals defined over graphs or networks in this paper we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs we show that stationarity is expressed through the graph localization operator reminiscent of translation we prove that stationary graph signals are characterized by a well defined power spectral density that can be efficiently estimated even for large graphs we leverage this new concept to derive wiener type estimation procedures of noisy and partially observed signals and illustrate the performance of this new model for denoising and regression

an efficient discriminant based solution for small sample size problem classification of high dimensional statistical data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size problem to address the problem of high dimensional data classification in the face of a limited number of samples a novel principal component analysis pca based feature extraction classification scheme is proposed the proposed method yields a piecewise linear feature subspace and is particularly well suited to difficult recognition problems where achievable classification rates are intrinsically low such problems are often encountered in cases where classes are highly overlapped or in cases where a prominent curvature in data renders a projection onto a single linear subspace inadequate the proposed feature extraction classification method uses class dependent pca in conjunction with linear discriminant feature extraction and performs well on a variety of real world datasets ranging from digit recognition to classification of high dimensional bioinformatics and brain imaging data

feature extraction using two dimensional local graph embedding based on maximum margin criterion in this paper we propose a novel method for image feature extraction namely the two dimensional local graph embedding which is based on maximum margin criterion and thus not necessary to convert the image matrix into high dimensional image vector and directly avoid computing the inverse matrix in the discriminant criterion this method directly learns the optimal projective vectors from 2d image matrices by simultaneously considering local graph embedding and maximum margin criterion the proposed method avoids huge feature matrix problem in eigenfaces fisherfaces laplacianfaces maximum margin criterion mmc and inverse matrix in 2d fisherfaces 2d laplacianfaces and 2d local graph embedding discriminant analysis 2dlgeda so that computational time would be saved for feature extraction experimental results on the yale and the usps databases show the effectiveness of the proposed method under various experimental conditions

orthogonal tensor neighborhood preserving embedding for facial expression recognition in this paper a generalized tensor subspace model is concluded from the existing tensor dimensionality reduction algorithms with this model we investigate the orthogonality of the bases of the high order tensor subspace and propose the orthogonal tensor neighborhood preserving embedding otnpe algorithm we evaluate the algorithm by applying it to facial expression recognition where both the 2nd order gray level raw pixels and the encoded 3rd order tensor formed gabor features of facial expression images are utilized the experiments show the excellent performance of our algorithm for the dimensionality reduction of the tensor formed data especially when they lie on some smooth and compact manifold embedded in the high dimensional tensor space

a comparative study of feature extraction methods and their application to p rbf nns in face recognition problem this study is concerned with a design of a face recognition algorithm realized based on feature extraction with the aid of the 2 directional 2 dimensional linear discriminant analysis referred to as 2d 2lda the 2dlda algorithm yields high accuracy but comes with an unresolved problem of handling large feature matrices present in face recognition problems the proposed 2d 2lda algorithm is computationally more efficient and produces more powerful discrimination decision the proposed p rbf nns is used as a recognition module the architecture of this module consists of three functional components the coefficients of the p rbf nns model are obtained by fuzzy inference method forming the inference part of fuzzy rules the essential design parameters including learning rate momentum fuzzification coefficient and the feature selection mechanism of the networks are optimized by means of differential evolution de the experimental results reported for benchmark face datasets the yale orl database and ic ci dataset demonstrate the effectiveness and efficiency of 2d 2lda algorithm compared with other pre processing approaches such as lpp 2d pca 2d lpp sr pca 2d 2pca and fusion of pca lda the experimental results show that 2d 2lda based p rbf nns achieves higher performance than being reported by other methods

subclass graph embedding and a marginal fisher analysis paradigm subspace learning techniques have been extensively used for dimensionality reduction dr in many pattern classification problem domains recently methods like subclass discriminant analysis sda and clustering based discriminant analysis cda which use subclass information for the discrimination between the data classes have attracted much attention in parallel important work has been accomplished on graph embedding ge which is a general framework unifying several subspace learning techniques in this paper ge has been extended in order to integrate subclass discriminant information resulting to the novel subclass graph embedding sge framework which is the main contribution of our work it is proven that sge encapsulates a diversity of both supervised and unsupervised unimodal methods like locality preserving projections lpp principal component analysis pca and linear discriminant analysis lda the theoretical link of sda and cda methods with sge is also established along these lines it is shown that sge comprises a generalization of the typical ge framework including subclass dr methods moreover it allows for an easy utilization of kernels for confronting non linearly separable data employing sge in this paper a novel dr algorithm which uses subclass discriminant information called subclass marginal fisher analysis smfa has been proposed through a series of experiments on various real world datasets it is shown that smfa outperforms in most of the cases the state of the art demonstrating the efficacy and power of sge as a platform to develop new methods highlightsgraph embedding is extended in order to integrate subclass informationthe novel subclass graph embedding framework is proposed the kernelized version of the new framework is presentedsubclass graph embedding encapsulates various subspace learning methods a novel subclass marginal fisher analysis method is proposed

joint low rank and sparse principal feature coding for enhanced robust representation and visual classification recovering low rank and sparse subspaces jointly for enhanced robust representation and classification is discussed technically we first propose a transductive low rank and sparse principal feature coding lspfc formulation that decomposes given data into a component part that encodes low rank sparse principal features and a noise fitting error part to well handle the outside data we then present an inductive lspfc i lspfc i lspfc incorporates embedded low rank and sparse principal features by a projection into one problem for direct minimization so that the projection can effectively map both inside and outside data into the underlying subspaces to learn more powerful and informative features for representation to ensure that the learned features by i lspfc are optimal for classification we further combine the classification error with the feature coding error to form a unified model discriminative lspfc d lspfc to boost performance the model of d lspfc seamlessly integrates feature coding and discriminative classification so the representation and classification powers can be enhanced the proposed approaches are more general and several recent existing low rank or sparse coding algorithms can be embedded into our problems as special cases visual and numerical results demonstrate the effectiveness of our methods for representation and classification

double nuclear norm based matrix decomposition for occluded image recovery and background modeling robust principal component analysis rpca is a new emerging method for exact recovery of corrupted low rank matrices it assumes that the real data matrix has low rank and the error matrix is sparse this paper presents a method called double nuclear norm based matrix decomposition dnmd for dealing with the image data corrupted by continuous occlusion the method uses a unified low rank assumption to characterize the real image data and continuous occlusion specifically we assume all image vectors form a low rank matrix and each occlusion induced error image is a low rank matrix as well compared with rpca the low rank assumption of dnmd is more intuitive for describing occlusion moreover dnmd is solved by alternating direction method of multipliers our algorithm involves only one operator the singular value shrinkage operator dnmd as a transductive method is further extended into inductive dnmd idnmd both dnmd and idnmd use nuclear norm for measuring the continuous occlusion induced error while many previous methods use l 1 l 2 or other m estimators extensive experiments on removing occlusion from face images and background modeling from surveillance videos demonstrate the effectiveness of the proposed methods

max min distance analysis by using sequential sdp relaxation for dimension reduction we propose a new criterion for discriminative dimension reduction max min distance analysis mmda given a data set with c classes represented by homoscedastic gaussians mmda maximizes the minimum pairwise distance of these c classes in the selected low dimensional subspace thus unlike fisher s linear discriminant analysis flda and other popular discriminative dimension reduction criteria mmda duly considers the separation of all class pairs to deal with general case of data distribution we also extend mmda to kernel mmda kmmda dimension reduction via mmda kmmda leads to a nonsmooth max min optimization problem with orthonormal constraints we develop a sequential convex relaxation algorithm to solve it approximately to evaluate the effectiveness of the proposed criterion and the corresponding algorithm we conduct classification and data visualization experiments on both synthetic data and real data sets experimental results demonstrate the effectiveness of mmda kmmda associated with the proposed optimization algorithm

a survey of multilinear subspace learning for tensor data increasingly large amount of multidimensional data are being generated on a daily basis in many applications this leads to a strong demand for learning algorithms to extract useful information from these massive data this paper surveys the field of multilinear subspace learning msl for dimensionality reduction of multidimensional data directly from their tensorial representations it discusses the central issues of msl including establishing the foundations of the field via multilinear projections formulating a unifying msl framework for systematic treatment of the problem examining the algorithmic aspects of typical msl solutions and categorizing both unsupervised and supervised msl algorithms into taxonomies lastly the paper summarizes a wide range of msl applications and concludes with perspectives on future research directions

feature extraction using two dimensional maximum embedding difference in this paper we propose a novel method combining graph embedding and difference criterion techniques for image feature extraction namely two dimensional maximum embedding difference 2dmed this method directly extracts the optimal projective vectors from 2d image matrices by simultaneously considering characteristic that is the intraclass compactness graph the margin graph and inter class separability graph respectively in this method it is not necessary to convert the image matrix into high dimensional image vector so that much computational time would be saved in addition the proposed method preserves the manifold reconstruction relationships in the low dimensional subspace experimental results on the orl yale face and usps database show the effectiveness of the proposed method

laplacian regularized low rank representation and its applications low rank representation lrr has recently attracted a great deal of attention due to its pleasing efficacy in exploring low dimensional subspace structures embedded in data for a given set of observed data corrupted with sparse errors lrr aims at learning a lowest rank representation of all data jointly lrr has broad applications in pattern recognition computer vision and signal processing in the real world data often reside on low dimensional manifolds embedded in a high dimensional ambient space however the lrr method does not take into account the non linear geometric structures within data thus the locality and similarity information among data may be missing in the learning process to improve lrr in this regard we propose a general laplacian regularized low rank representation framework for data representation where a hypergraph laplacian regularizer can be readily introduced into i e a non negative sparse hyper laplacian regularized lrr model nshlrr by taking advantage of the graph regularizer our proposed method not only can represent the global low dimensional structures but also capture the intrinsic non linear geometric information in data the extensive experimental results on image clustering semi supervised image classification and dimensionality reduction tasks demonstrate the effectiveness of the proposed method

local graph embedding based on maximum margin criterion via fuzzy set abstract recently many algorithms based on locally graph embedding are proposed for dimensional reduction in nonlinear data however these algorithms are not effective when dealing with face images affected by variations in illumination conditions poses or perspectives and different facial expressions so distant data points are not deemphasized efficiently by locally graph embedding algorithms and it may degrade the performance of classification in order to solve the aforementioned problem this paper proposes a new efficient dimension reduction method local graph embedding method based on maximum margin criterion via fuzzy set for face recognition firstly the goal of this algorithm is preserved under nearest neighbor premise by constructing the fuzzy intrinsic graph and the fuzzy penalty graph secondly two novel fuzzy laplacian scatter matrices are calculated using fuzzy k nearest neighbor fknn in the proposed method finally maximum margin criterion mmc is used to avoid the small size sample problem the results of face recognition experiments on the orl yale and ar face databases demonstrate the effectiveness of our proposed method

face recognition using elasticfaces though principle component analysis pca and locality preserving projections lpps are two of the most popular linear methods for face recognition pca can only see the euclidean structure of the training set and lpp preserves the nonlinear submanifold structure hidden in the training set in this paper we propose the elastic preserving projections epps which by incorporating the merits of the local geometry and the global information of the training set epp outputs a sample subspace which simultaneously preserves the local geometrical structure and exploits the global information of the training set different from some other linear dimensionality reduction methods epp can be deemed as learning both the coordinates and the affinities between sample points furthermore the effectiveness of our proposed algorithm is analyzed theoretically and confirmed by some experiments on several well known face databases the obtained results indicate that epp significantly outperforms its other rival algorithms

supervised optimal locality preserving projection in the past few years the computer vision and pattern recognition community has witnessed a rapid growth of a new kind of feature extraction method the manifold learning methods which attempt to project the original data into a lower dimensional feature space by preserving the local neighborhood structure among these methods locality preserving projection lpp is one of the most promising feature extraction techniques unlike the unsupervised learning scheme of lpp this paper follows the supervised learning scheme i e it uses both local information and class information to model the similarity of the data based on novel similarity we propose two feature extraction algorithms supervised optimal locality preserving projection solpp and normalized laplacian based supervised optimal locality preserving projection nl solpp optimal here means that the extracted features via solpp or nl solpp are statistically uncorrelated and orthogonal we compare the proposed solpp and nl solpp with lpp orthogonal locality preserving projection olpp and uncorrelated locality preserving projection ulpp on publicly available data sets experimental results show that the proposed solpp and nl solpp achieve much higher recognition accuracy

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

face recognition using laplacianfaces we propose an appearance based face recognition method called the laplacianface approach by using locality preserving projections lpp the face images are mapped into a face subspace for analysis different from principal component analysis pca and linear discriminant analysis lda which effectively see only the euclidean structure of face space lpp finds an embedding that preserves local information and obtains a face subspace that best detects the essential face manifold structure the laplacianfaces are the optimal linear approximations to the eigenfunctions of the laplace beltrami operator on the face manifold in this way the unwanted variations resulting from changes in lighting facial expression and pose may be eliminated or reduced theoretical analysis shows that pca lda and lpp can be obtained from different graph models we compare the proposed laplacianface approach with eigenface and fisherface methods on three different face data sets experimental results suggest that the proposed laplacianface approach provides a better representation and achieves lower error rates in face recognition

relations between gabor transforms and fractional fourier transforms and their applications for signal processing many useful relations between the gabor transform gt and the fractional fourier transform frft have been derived first we find that like the wigner distribution function wdf the frft is also equivalent to the rotation operation of the gt then we show that performing the scaled inverse fourier transform ift along an oblique line of the gt of f t can yield its frft since the gt is closely related to the frft we can use it for analyzing the characteristics of the frft compared with the wdf the gt does not have the cross term problem this advantage is important for the applications of filter design sampling and multiplexing in the frft domain moreover we find that if the gt is combined with the wdf the resultant operation called the gabor wigner transform gwt also has rotation relation with the frft we also derive the general form of the linear distribution that has rotation relation with the frft

positive semidefinite metric learning using boosting like algorithms the success of many machine learning and pattern recognition methods relies heavily upon the identification of an appropriate distance metric on the input data it is often beneficial to learn such a metric from the input training data instead of using a default one such as the euclidean distance in this work we propose a boosting based technique termed boostmetric for learning a quadratic mahalanobis distance metric learning a valid mahalanobis distance metric requires enforcing the constraint that the matrix parameter to the metric remains positive semidefinite semidefinite programming is often used to enforce this constraint but does not scale well and is not easy to implement boostmetric is instead based on the observation that any positive semidefinite matrix can be decomposed into a linear combination of trace one rank one matrices boostmetric thus uses rank one positive semidefinite matrices as weak learners within an efficient and scalable boosting based learning process the resulting methods are easy to implement efficient and can accommodate various types of constraints we extend traditional boosting algorithms in that its weak learner is a positive semidefinite matrix with trace and rank being one rather than a classifier or regressor experiments on various data sets demonstrate that the proposed algorithms compare favorably to those state of the art methods in terms of classification accuracy and running time

classification of symmetric positive definite matrices based on bilinear isometric riemannian embedding abstract because covariance features with the form of symmetric positive definite matrices lie on riemannian manifold classification on riemannian manifold could possess high performance in many applications unfortunately the applicability of classification methods developed on riemannian manifold is limited by their huge computational complexities particularly with the feature data on high dimensional riemannian manifold to alleviate the problem of computational cost in this paper a simple yet efficient dimensionality reduction algorithm bilinear isometric riemannian embedding is derived to construct a low dimensional embedding from high dimensional riemannian manifold to this end we model the bilinear isometric mapping to identify a low dimensional embedding that maximizes the preservation of riemannian geodesic distance a supervised classification method embedding discriminant analysis is then proposed based on the low dimensional embedding experimental results on image and electroencephalogram reveal that the proposed algorithms can efficiently extract the distance preserving embedding and obtain higher classification performance

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

approximate orthogonal sparse embedding for dimensionality reduction locally linear embedding lle is one of the most well known manifold learning methods as the representative linear extension of lle orthogonal neighborhood preserving projection onpp has attracted widespread attention in the field of dimensionality reduction in this paper a unified sparse learning framework is proposed by introducing the sparsity or l 1 norm learning which further extends the lle based methods to sparse cases theoretical connections between the onpp and the proposed sparse linear embedding are discovered the optimal sparse embeddings derived from the proposed framework can be computed by iterating the modified elastic net and singular value decomposition we also show that the proposed model can be viewed as a general model for sparse linear and nonlinear kernel subspace learning based on this general model sparse kernel embedding is also proposed for nonlinear sparse feature extraction extensive experiments on five databases demonstrate that the proposed sparse learning framework performs better than the existing subspace learning algorithm particularly in the cases of small sample sizes

discriminative multimanifold analysis for face recognition from a single training sample per person conventional appearance based face recognition methods usually assume that there are multiple samples per person mspp available for discriminative feature extraction during the training phase in many practical face recognition applications such as law enhancement e passport and id card identification this assumption however may not hold as there is only a single sample per person sspp enrolled or recorded in these systems many popular face recognition methods fail to work well in this scenario because there are not enough samples for discriminant learning to address this problem we propose in this paper a novel discriminative multimanifold analysis dmma method by learning discriminative features from image patches first we partition each enrolled face image into several nonoverlapping patches to form an image set for each sample per person then we formulate the sspp face recognition as a manifold manifold matching problem and learn multiple dmma feature spaces to maximize the manifold margins of different persons finally we present a reconstruction based manifold manifold distance to identify the unlabeled subjects experimental results on three widely used face databases are presented to demonstrate the efficacy of the proposed approach

face recognition by exploring information jointly in space scale and orientation information jointly contained in image space scale and orientation domains can provide rich important clues not seen in either individual of these domains the position spatial frequency and orientation selectivity properties are believed to have an important role in visual perception this paper proposes a novel face representation and recognition approach by exploring information jointly in image space scale and orientation domains specifically the face image is first decomposed into different scale and orientation responses by convolving multiscale and multi orientation gabor filters second local binary pattern analysis is used to describe the neighboring relationship not only in image space but also in different scale and orientation responses this way information from different domains is explored to give a good face representation for recognition discriminant classification is then performed based upon weighted histogram intersection or conditional mutual information with linear discriminant analysis techniques extensive experimental results on feret ar and frgc ver 2 0 databases show the significant advantages of the proposed method over the existing ones

sparse approximation to the eigensubspace for discrimination two dimensional 2 d image matrix based projection methods for feature extraction are widely used in many fields of computer vision and pattern recognition in this paper we propose a novel framework called sparse 2 d projections s2dp for image feature extraction different from the existing 2 d feature extraction methods s2dp iteratively learns the sparse projection matrix by using elastic net regression and singular value decomposition theoretical analysis shows that the optimal sparse subspace approximates the eigensubspace obtained by solving the corresponding generalized eigenequation with the s2dp framework many 2 d projection methods can be easily extended to sparse cases moreover when each row column of the image matrix is regarded as an independent high dimensional vector 1 d vector it is proven that the vector based eigensubspace is also approximated by the sparse subspace obtained by the same method used in this paper theoretical analysis shows that when compared with the vector based sparse projection learning methods s2dp greatly saves both computation and memory costs this property makes s2dp more tractable for real world applications experiments on well known face databases indicate the competitive performance of the proposed s2dp over some 2 d projection methods when facial expressions lighting conditions and time vary

rapid and brief communication two dimensional locality preserving projections 2dlpp with its application to palmprint recognition this paper proposes a novel algorithm for image feature extraction namely the two dimensional locality preserving projections 2dlpp which directly extracts the proper features from image matrices based on locality preserving criterion experimental results on the polyu palmprint database show the effectiveness of the proposed algorithm

discussion comment on two dimensional locality preserving projections 2dlpp with its application to palmprint recognition this paper proposes a novel algorithm for image feature extraction namely the two dimensional locality preserving projections 2dlpp which directly extracts the proper features from image matrices based on locality preserving criterion experimental results on the polyu palmprint database show the effectiveness of the proposed algorithm

rapid and brief communications a fourier lda approach for image recognition fourier transform and linear discrimination analysis lda are two commonly used techniques of image processing and recognition based on them we propose a fourier lda approach fla for image recognition it selects appropriate fourier frequency bands with favorable linear separability by using a two dimensional separability judgment then it extracts two dimensional linear discriminative features to perform the classification our experimental results on different image data prove that fla obtains better classification performance than other linear discrimination methods

relations between fractional operations and time frequency distributions and their applications the fractional fourier transform frft is a useful tool for signal processing it is the generalization of the fourier transform many fractional operations such as fractional convolution fractional correlation and the fractional hilbert transform are defined from it in fact the frft can be further generalized into the linear canonical transform lct and we can also use the lct to define several canonical operations in this paper we discuss the relations between the operations described above and some important time frequency distributions tfds such as the wigner distribution function wdf the ambiguity function af the signal correlation function and the spectrum correlation function first we systematically review the previous works in brief then some new relations are derived and listed in tables then we use these relations to analyze the applications of the frpt lct to fractional canonical filter design fractional canonical hilbert transform beam shaping and then we analyze the phase amplitude problems of the frft lct for phase amplitude problems we find as with the original fourier transform that in most cases the phase is more important than the amplitude for the frft lct we also use the wdf to explain why fractional canonical convolution can be used for space variant pattern recognition

fractional fourier transform wigner distribution and filter design for stationary and nonstationary random processes in this paper we derive the relationship among the fractional fourier transform frft the linear canonical transform lct and the stationary and nonstationary random processes we find many interesting properties for example if we perform the frft for a stationary process although the result is no longer stationary the amplitude of the autocorrelation function is still independent of time we also find that the lct of a white noise is still a white one for the frft of a stationary process the ambiguity function af is a tilted line and the wigner distribution function wdf is invariant along a certain direction we also define the fractional stationary random process and find that a nonstationary random process can be expressed by a summation of fractional stationary random processes in addition after performing the filter designed in the frft domain for a white noise we can use the segment length of the axis on the wdf plane to estimate the power of the noise and use the area circled by cutoff lines to estimate its energy thus in communication to reduce the effect of the white noise the area of the wdf of the transmitted signal should be as small as possible

low rank embedding for robust image feature extraction robustness to noises outliers and corruptions is an important issue in linear dimensionality reduction since the sample specific corruptions and outliers exist the class special structure or the local geometric structure is destroyed and thus many existing methods including the popular manifold learning based linear dimensionality methods fail to achieve good performance in recognition tasks in this paper we focus on the unsupervised robust linear dimensionality reduction on corrupted data by introducing the robust low rank representation lrr thus a robust linear dimensionality reduction technique termed low rank embedding lre is proposed in this paper which provides a robust image representation to uncover the potential relationship among the images to reduce the negative influence from the occlusion and corruption so as to enhance the algorithm s robustness in image feature extraction lre searches the optimal lrr and optimal subspace simultaneously the model of lre can be solved by alternatively iterating the argument lagrangian multiplier method and the eigendecomposition the theoretical analysis including convergence analysis and computational complexity of the algorithms is presented experiments on some well known databases with different corruptions show that lre is superior to the previous methods of feature extraction and therefore it indicates the robustness of the proposed method the code of this paper can be downloaded from http www scholat com laizhihui

stability of the euler maclaurin methods for neutral differential equations with piecewise continuous arguments abstract this paper deals with the stability analysis of the euler maclaurin methods for neutral differential equations with piecewise continuous arguments u t au t i 0 n a i u i t the stability regions of the euler maclaurin methods are determined the conditions under which the analytic stability region is contained in the numerical stability region are obtained and some numerical experiments are given

stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type this paper is concerned with the numerical properties of q methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments using two q methods namely the one leg q method and the linear q method the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained and the conditions of oscillations for the q methods are also obtained it is proved that oscillations of the analytic solution are preserved by the q methods furthermore the relationships between stability and oscillations are revealed some numerical experiments are presented to illustrate our results

quadratic projection based feature extraction with its application to biometric recognition this paper presents a novel quadratic projection based feature extraction framework where a set of quadratic matrices is learned to distinguish each class from all other classes we formulate quadratic matrix learning qml as a standard semidefinite programming sdp problem however the conventional interior point sdp solvers do not scale well to the problem of qml for high dimensional data to solve the scalability of qml we develop an efficient algorithm termed dualqml based on the lagrange duality theory to extract nonlinear features to evaluate the feasibility and effectiveness of the proposed framework we conduct extensive experiments on biometric recognition experimental results on three representative biometric recognition tasks including face palmprint and ear recognition demonstrate the superiority of the dualqml based feature extraction algorithm compared to the current state of the art algorithms highlightsa novel quadratic projection based feature extraction framework is developed a set of quadratic matrices is learnt to distinguish each class from other classes quadratic matrix learning qml is formulated as an sdp problem an efficient algorithm is developed to solve qml based on lagrange duality theory experiments on biometric recognition show the effectiveness of our algorithm

constrained nonnegative matrix factorization for image representation nonnegative matrix factorization nmf is a popular technique for finding parts based linear representations of nonnegative data it has been successfully applied in a wide range of applications such as pattern recognition information retrieval and computer vision however nmf is essentially an unsupervised method and cannot make use of label information in this paper we propose a novel semi supervised matrix decomposition method called constrained nonnegative matrix factorization cnmf which incorporates the label information as additional constraints specifically we show how explicitly combining label information improves the discriminating power of the resulting matrix decomposition we explore the proposed cnmf method with two cost function formulations and provide the corresponding update solutions for the optimization problems empirical experiments demonstrate the effectiveness of our novel algorithm in comparison to the state of the art approaches through a set of evaluations based on real world applications

oscillatory and asymptotic properties of nonlinear first order neutral differential equations with piecewise constant argument in the paper the asymptotic behaviour of the nonoscillating solutions of nonlinear first order neutral differential equations with piecewise constant argument is considered and sufficient conditions for oscillation of all solutions are obtained