analysing images of curved surfaces a reflectance map makes the relationship between image intensity and surface orientation explicit trade offs between image intensity and surface orientation emerge which cannot be resolved locally in a single view existing methods for determining surface orientation from a single view embody assumptions about surface curvature the hessian matrix is introduced to represent surface curvature properties of surface curvature are expressed as properties of the hessian matrix for several classes of surface image analysis simplifies this result has already been established for planar surfaces forming trihedral corners similar simplification is demonstrated for developable surfaces and for the subclass of surfaces known as generalized cones these studies help to delineate shape information that can be determined from geometric measurements at object boundaries and shape information that can be determined from intensity measurements over sections of smoothly curved surface a novel technique called photometric stereo is discussed the idea of stereo is to obtain multiple images in order to determine the underlying scene precisely in photometric stereo the viewing direction is constant multiple images are obtained by varying the incident illumination it is shown that this provides sufficient information to determine surface orientation at each image point

hilbert space description on nonlinear discrete time dynamical systems it is shown that the linear recurrences of the form xn 1 xn where is analytic in xn can be brought down to a linear recurrence in hilbert space with the boson displacement operator

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

tensor representation learning based image patch analysis for text identification and recognition in this paper we introduce a novel framework for text identification and recognition called tensor representation learning based image patch analysis trl ipa unlike most of previous text identification approaches which can only be applied to binarized images trl ipa can be directly applied to gray level and color images trl ipa is built on a general formulation of the convergent tensor representation learning ctrl algorithms in the implementation of trl ipa image patches are represented in the form of tensors while low dimensional representations of these tensors are learned via a ctrl algorithm to identify text regions in new coming document images a random forest classifier is trained in the learned tensor subspace moreover the trl ipa framework can be straightforwardly applied to recognition problems such as handwritten digits recognition we conducted extensive experiments on ancient chinese arabic and cyrillic document images to evaluate trl ipa on text identification tasks experimental results demonstrate its effectiveness and robustness in addition recognition results on images of handwritten digits show its advantage over state of the art vector and tensor representation based approaches highlightsa novel model tensor representation learning based image patch analysis trl ipa is proposed for document understanding trl ipa is built on a general formulation of the convergent tensor representation learning ctrl algorithms the ctrl algorithms are theoretically guaranteed to converge to a local optimal solution of the learning problem extensive experiments demonstrate the superiority of trl ipa over related vector and tensor representation based approaches

higher rank support tensor machines for visual recognition this work addresses the two class classification problem within the tensor based large margin classification paradigm to this end we formulate the higher rank support tensor machines stms in which the parameters defining the separating hyperplane form a tensor tensorplane that is constrained to be the sum of rank one tensors subsequently we propose two extensions in which the separating tensorplanes take into consideration the spread of the training data along the different tensor modes more specifically we first propose the higher rank s s w stms that use the total or the within class covariance matrix in order to whiten the data and thus provide invariance to affine transformations second we propose the higher rank relative margin support tensor machines rmstms that bound from above the distance of the data samples from the separating tensorplane while maximizing the margin from it the corresponding optimization problem is solved in an iterative manner utilizing the candecomp parafac cp decomposition where at each iteration the parameters corresponding to the projections along a single tensor mode are estimated by solving a typical support vector machine svm type optimization problem the efficiency of the proposed method is illustrated on the problems of gait and action recognition where we report results that improve in some cases considerably the state of the art

ortho diffusion decompositions of graph based representation of images this paper proposes a new feature representation methodology for graph based data initially random walks on matrices of pairwise data similarities are considered a diffusion process is embedded into orthonormal decompositions of such matrices at various scales while enabling a data reduction mechanism as well at each scale the qr orthonormal decomposition algorithm alternating with diffusions and data reduction stages is applied recursively on the given graph based data representations the proposed methodology is used in extracting complex feature representations from images which are then used for image matching and in face recognition in the face recognition application both global appearance models and semantic representations of biometric features are considered both the correlation and the covariance of images of human faces are considered for the training stage when using global appearance models the proposed data representation is shown to be robust in face recognition applications when face images are represented in low resolution and when they are corrupted by noise highlightsthe ortho diffusion decompositions on graph representations of images are introduced correlation in the ortho diffusion space is used for optical flow estimation correlations covariance of ortho diffusion vectors is used for face recognition

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

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

clutter invariant atr one of the central problems in automated target recognition is to accommodate the infinite variety of clutter in real military environments the principle focus of our paper is on the construction of metric spaces where the metric measures the distance between objects of interest invariant to the infinite variety of clutter such metrics are formulated using second order random field models our results indicate that this approach significantly improves detection classification rates of targets in clutter

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

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

semi supervised bilinear subspace learning recent research has demonstrated the success of tensor based subspace learning in both unsupervised and supervised configurations e g 2 d pca 2 d lda and dater in this correspondence we present a new semi supervised subspace learning algorithm by integrating the tensor representation and the complementary information conveyed by unlabeled data conventional semi supervised algorithms mostly impose a regularization term based on the data representation in the original feature space instead we utilize graph laplacian regularization based on the low dimensional feature space an iterative algorithm referred to as adaptive regularization based semi supervised discriminant analysis with tensor representation arsda t is also developed to compute the solution in addition to handling tensor data a vector based variant arsda v is also presented in which the tensor data are converted into vectors before subspace learning comprehensive experiments on the cmu pie and yale b databases demonstrate that arsda t brings significant improvement in face recognition accuracy over both conventional supervised and semi supervised subspace learning algorithms

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

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

multilinear supervised neighborhood embedding of a local descriptor tensor for scene object recognition in this paper we propose to represent an image as a local descriptor tensor and use a multilinear supervised neighborhood embedding msne for discriminant feature extraction which is able to be used for subject or scene recognition the contributions of this paper include 1 a novel feature extraction approach denoted as the histogram of orientation weighted with a normalized gradient nhog for local region representation which is robust to large illumination variation in an image 2 an image representation framework denoted as the local descriptor tensor which can effectively combine a moderate amount of local features together for image representation and be more efficient than the popular existing bag of feature model and 3 an msne analysis algorithm which can directly deal with the local descriptor tensor for extracting discriminant and compact features and at the same time preserve neighborhood structure in tensor feature space for subject scene recognition we demonstrate the performance advantages of our proposed approach over existing techniques on different types of benchmark database such as a scene data set i e ot8 face data sets i e yale and pie and view based object data sets coil 100 and eth 80

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

multi linear neighborhood preserving projection for face recognition this paper proposes a novel method of supervised and unsupervised multi linear neighborhood preserving projection mnpp for face recognition unlike conventional neighborhood preserving projections the mnpp method operates directly on tensorial data rather than vectors or matrices and solves problems of tensorial representation for multi dimensional feature extraction classification and recognition as opposed to traditional approaches such as npp and 2dnpp which derive only one subspace multiple interrelated subspaces are obtained in the mnpp method by unfolding the tensor over different tensorial directions the number of subspaces derived by mnpp is determined by the order of the tensor space this approach is used for face recognition and biometrical security classification problems involving higher order tensors the performance of our proposed and existing techniques is analyzed using three benchmark facial datasets orl ar and feret the obtained results show that the mnpp outperforms the standard approaches in terms of the error rate a new method for supervised and unsupervised dimensionality reduction problem work in embedded manifold to allow representation of multi dimensional images natural extension to 2 d 3 d or higher order tensors combine intrinsic geometry and discriminative information for face recognition avoid the small sample size and the curse of dimensionality problems

achieving robust face recognition from video by combining a weak photometric model and a learnt generic face invariant in spite of over two decades of intense research illumination and pose invariance remain prohibitively challenging aspects of face recognition for most practical applications the objective of this work is to recognize faces using video sequences both for training and recognition input in a realistic unconstrained setup in which lighting pose and user motion pattern have a wide variability and face images are of low resolution the central contribution is an illumination invariant which we show to be suitable for recognition from video of loosely constrained head motion in particular there are three contributions i we show how a photometric model of image formation can be combined with a statistical model of generic face appearance variation to exploit the proposed invariant and generalize in the presence of extreme illumination changes ii we introduce a video sequence re illumination algorithm to achieve fine alignment of two video sequences and iii we use the smoothness of geodesically local appearance manifold structure and a robust same identity likelihood to achieve robustness to unseen head poses we describe a fully automatic recognition system based on the proposed method and an extensive evaluation on 323 individuals and 1474 video sequences with extreme illumination pose and head motion variation our system consistently achieved a nearly perfect recognition rate over 99 7 on all four databases

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

analytical approach to initial value problems in nonlinear systems a method based on the equivalence between finite dimensional nonlinear and infinite dimensional linear systems of ordinary differential equations is presented in order to calculate the time dependent solutions of nonlinear physico chemical systems the solution is cast in the form of power series whose general term is known analytically

a low rank approximation based transductive support tensor machine for semisupervised classification in the fields of machine learning pattern recognition image processing and computer vision the data are usually represented by the tensors for the semisupervised tensor classification the existing transductive support tensor machine tstm needs to resort to iterative technique which is very time consuming in order to overcome this shortcoming in this paper we extend the concave convex procedure based transductive support vector machine cccp tsvm to the tensor patterns and propose a low rank approximation based tstm in which the tensor rank one decomposition is used to compute the inner product of the tensors theoretically concave convex procedure based tstm cccp tstm is an extension of the linear cccp tsvm to tensor patterns when the input patterns are vectors cccp tstm degenerates into the linear cccp tsvm a set of experiments is conducted on 23 semisupervised classification tasks which are generated from seven second order face data sets three third order gait data sets and two third order image data sets to illustrate the performance of the cccp tstm the results show that compared with cccp tsvm and tstm cccp tstm provides significant performance gain in terms of test accuracy and training speed

symmetric subspace learning for image analysis subspace learning sl is one of the most useful tools for image analysis and recognition a large number of such techniques have been proposed utilizing a priori knowledge about the data in this paper new subspace learning techniques are presented that use symmetry constraints in their objective functions the rational behind this idea is to exploit the a priori knowledge that geometrical symmetry appears in several types of data such as images objects faces and so on experiments on artificial facial expression recognition face recognition and object categorization databases highlight the superiority and the robustness of the proposed techniques in comparison with standard sl techniques

backlund transformations for nonlinear evolution equations hilbert space approach abstract a new method of determining backlund transformations for nonlinear partial differential equations of the evolution type is introduced using the hilbert space approach the problem of finding backlund transformations is brought down to the solution of an abstract equation in hilbert space

fast computation of low rank matrix approximations given a matrix a it is often desirable to find a good approximation to a that has low rank we introduce a simple technique for accelerating the computation of such approximations when a has strong spectral features that is when the singular values of interest are significantly greater than those of a random matrix with size and entries similar to a our technique amounts to independently sampling and or quantizing the entries of a thus speeding up computation by reducing the number of nonzero entries and or the length of their representation our analysis is based on observing that the acts of sampling and quantization can be viewed as adding a random matrix n to a whose entries are independent random variables with zero mean and bounded variance since with high probability n has very weak spectral features we can prove that the effect of sampling and quantization nearly vanishes when a low rank approximation to a p n is computed we give high probability bounds on the quality of our approximation both in the frobenius and the 2 norm

fractal drums and phonons in binary glasses abstract the low frequency vibration spectrum of a surface fractal with a rigid fractal boundary presents a smaller density of states than an ordinary resonator such vibrations called fractinos should be present in partially phase separated glasses if one component is soft in addition the interfaces between the phase separated regions are fractal diffusion fronts which are mass fractals close to percolation cluster hulls it is proposed that the fractons which have claimed to exist in these non fractal materials are the vibrations of these internal interfaces

systems of ordinary differential equations with nonlinear superposition principles abstract this work is concerned with the derivation of superposition rules which express the general solution of ordinary differential equations x x t x r n t r in terms of a finite number of particular solutions the point of departure is lie s criterion according to which such a rule exists if and only if the vector fields x t generate a finite dimensional lie algebra we provide three different constructive methods for deriving superposition rules and apply them to systems of coupled riccati equations of the projective and conformal types based respectively on the lie algebra sl n 1 r and o p 1 n p 1

uncorrelated multilinear discriminant analysis with regularization and aggregation for tensor object recognition this paper proposes an uncorrelated multilinear discriminant analysis umlda framework for the recognition of multidimensional objects known as tensor objects uncorrelated features are desirable in recognition tasks since they contain minimum redundancy and ensure independence of features the umlda aims to extract uncorrelated discriminative features directly from tensorial data through solving a tensor to vector projection the solution consists of sequential iterative processes based on the alternating projection method and an adaptive regularization procedure is incorporated to enhance the performance in the small sample size sss scenario a simple nearest neighbor classifier is employed for classification furthermore exploiting the complementary information from differently initialized and regularized umlda recognizers an aggregation scheme is adopted to combine them at the matching score level resulting in enhanced generalization performance while alleviating the regularization parameter selection problem the umlda based recognition algorithm is then empirically shown on face and gait recognition tasks to outperform four multilinear subspace solutions mpca dater gtda tr1da and four linear subspace solutions bayesian lda ulda r jd lda

recovery guarantees for exemplar based clustering for a certain class of distributions we prove that the linear programming relaxation of k medoids clustering a variant of k means clustering where means are replaced by exemplars from within the dataset distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn and the separation distance between any two balls are sufficiently large our results hold in the nontrivial regime where the separation distance is small enough that points drawn from different balls may be closer to each other than points drawn from the same ball in this case clustering by thresholding pairwise distances between points can fail we also exhibit numerical evidence of high probability recovery in a substantially more permissive regime

ordinal distance metric learning for image ranking recently distance metric learning dml has attracted much attention in image retrieval but most previous methods only work for image classification and clustering tasks in this brief we focus on designing ordinal dml algorithms for image ranking tasks by which the rank levels among the images can be well measured we first present a linear ordinal mahalanobis dml model that tries to preserve both the local geometry information and the ordinal relationship of the data then we develop a nonlinear dml method by kernelizing the above model considering of real world image data with nonlinear structures to further improve the ranking performance we finally derive a multiple kernel dml approach inspired by the idea of multiple kernel learning that performs different kernel operators on different kinds of image features extensive experiments on four benchmarks demonstrate the power of the proposed algorithms against some related state of the art methods

tensor decomposition for signal processing and machine learning tensors or multiway arrays are functions of three or more indices i j k ldots similar to matrices two way arrays which are functions of two indices r c for row column tensors have a rich history stretching over almost a century and touching upon numerous disciplines but they have only recently become ubiquitous in signal and data analytics at the confluence of signal processing statistics data mining and machine learning this overview article aims to provide a good starting point for researchers and practitioners interested in learning about and working with tensors as such it focuses on fundamentals and motivation using various application examples aiming to strike an appropriate balance of breadth and depth that will enable someone having taken first graduate courses in matrix algebra and probability to get started doing research and or developing tensor algorithms and software some background in applied optimization is useful but not strictly required the material covered includes tensor rank and rank decomposition basic tensor factorization models and their relationships and properties including fairly good coverage of identifiability broad coverage of algorithms ranging from alternating optimization to stochastic gradient statistical performance analysis and applications ranging from source separation to collaborative filtering mixture and topic modeling classification and multilinear subspace learning

decentralized dimensionality reduction for distributed tensor data across sensor networks this paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks the main contributions of this paper are as follows first conventional centralized methods which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode are not suitable for the network environment here we relax the simultaneous processing manner into the one vector by one vector ovbov manner i e determining the projection vectors pvs related to each tensor mode one by one second we prove that in the ovbov manner each pv can be determined without modifying any tensor data which simplifies corresponding computations third we cast the decentralized pv determination problem as a set of subproblems with consensus constraints so that it can be solved in the network environment only by local computations and information communications among neighboring nodes fourth we introduce the null space and transform the pv determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint which can be solved by the lagrange multiplier method finally experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks

bilinear lanczos components for fast dimensionality reduction and feature extraction matrix based methods such as generalized low rank approximations of matrices glram have gained wide attention from researchers in pattern recognition and machine learning communities in this paper a novel concept of bilinear lanczos components blc is introduced to approximate the projection vectors obtained from eigen based methods without explicit computing eigenvectors of the matrix this new method sequentially reduces the reconstruction error for a frobenius norm based optimization criterion and the resulting approximation performance is thus improved during successive iterations in addition a theoretical clue for selecting suitable dimensionality parameters without losing classification information is presented in this paper the blc approach realizes dimensionality reduction and feature extraction by using a small number of lanczos components extensive experiments on face recognition and image classification are conducted to evaluate the efficiency and effectiveness of the proposed algorithm results show that the new approach is competitive with the state of the art methods while it has a much lower training cost

exploring sparseness and self similarity for action recognition we propose that the dynamics of an action in video data forms a sparse self similar manifold in the space time volume which can be fully characterized by a linear rank decomposition inspired by the recurrence plot theory we introduce the concept of joint self similarity volume joint ssv to model this sparse action manifold and hence propose a new optimized rank 1 tensor approximation of the joint ssv to obtain compact low dimensional descriptors that very accurately characterize an action in a video sequence we show that these descriptor vectors make it possible to recognize actions without explicitly aligning the videos in time in order to compensate for speed of execution or differences in video frame rates moreover we show that the proposed method is generic in the sense that it can be applied using different low level features such as silhouettes tracked points histogram of oriented gradients and so forth therefore our method does not necessarily require explicit tracking of features in the space time volume our experimental results on five public data sets demonstrate that our method produces promising results and outperforms many baseline methods

target detection based on a dynamic subspace for hyperspectral target detection it is usually the case that only part of the targets pixels can be used as target signatures so can we use them to construct the most proper background subspace for detecting all the probable targets in this paper a dynamic subspace detection dsd method which establishes a multiple detection framework is proposed in each detection procedure blocks of pixels are calculated by the random selection and the succeeding detection performance distribution analysis manifold analysis is further used to eliminate the probable anomalous pixels and purify the subspace datasets and the remaining pixels construct the subspace for each detection procedure the final detection results are then enhanced by the fusion of target occurrence frequencies in all the detection procedures experiments with both synthetic and real hyperspectral images hsi evaluate the validation of our proposed dsd method by using several different state of the art methods as the basic detectors with several other single detectors and multiple detection methods as comparable methods improved receiver operating characteristic curves and better separability between targets and backgrounds by the dsd methods are illustrated the dsd methods also perform well with the covariance based detectors showing their efficiency in selecting covariance information for detection the dynamic subspace detection theory is a useful background statistics estimation our method can find the most suitable pixels to construct detectors targets can be further distinguished by a fusion of all the detection procedures

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

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

detection and segmentation of generic shapes based on affine modeling of energy in eigenspace this paper presents a novel approach for detection and segmentation of man made generic shapes in cluttered images the set of shapes to be detected are members of affine transformed versions of basic geometric shapes such as rectangles circles etc the shape set is represented by its vectorial edge map transformed over a wide range of affine parameters we use vectorial boundary instead of regular boundary to improve the robustness to noise background clutter and partial occlusion our approach consists of a detection stage and a verification stage in the detection stage we first derive the energy from the principal eigenvectors of the set next an a posteriori probability map of energy distribution is computed from the projection of the edge map representation in a vectorial eigen space local peaks of the posterior probability map are located and indicate candidate detections we use energy probability based detection since we find that the underlying distribution is not gaussian and resembles a hypertoroid in the verification stage each candidate is verified using a fast search algorithm based on a novel representation in angle space and the corresponding pose information of the detected shape is obtained the angular representation used in the verification stage yields better results than a euclidean distance representation experiments are performed in various interfering distortions and robust detection and segmentation are achieved

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

multiple rank multi linear svm for matrix data classification matrices or more generally multi way arrays tensors are common forms of data that are encountered in a wide range of real applications how to classify this kind of data is an important research topic for both pattern recognition and machine learning in this paper by analyzing the relationship between two famous traditional classification approaches i e svm and stm a novel tensor based method i e multiple rank multi linear svm mrmlsvm is proposed different from traditional vector based and tensor based methods multiple rank left and right projecting vectors are employed to construct decision boundary and establish margin function we reveal that the rank of transformation can be regarded as a tradeoff parameter to balance the capacity of learning and generalization in essence we also proposed an effective approach to solve the proposed non convex optimization problem the convergence behavior initialization computational complexity and parameter determination problems are analyzed compared with vector based classification methods mrmlsvm achieves higher accuracy and has lower computational complexity compared with traditional supervised tensor based methods mrmlsvm performs better for matrix data classification promising experimental results on various kinds of data sets are provided to show the effectiveness of our method highlightswe have proposed a novel method i e mrmlsvm for matrix data classification we have revealed the essence of mrmlsvm from the view of learning theory we have provided an effective way to solve the proposed non convex problem our proposed approach is a common model and mrmlsvm is just an instance

a least squares framework for component analysis over the last century component analysis ca methods such as principal component analysis pca linear discriminant analysis lda canonical correlation analysis cca locality preserving projections lpp and spectral clustering sc have been extensively used as a feature extraction step for modeling classification visualization and clustering ca techniques are appealing because many can be formulated as eigen problems offering great potential for learning linear and nonlinear representations of data in closed form however the eigen formulation often conceals important analytic and computational drawbacks of ca techniques such as solving generalized eigen problems with rank deficient matrices e g small sample size problem lacking intuitive interpretation of normalization factors and understanding commonalities and differences between ca methods this paper proposes a unified least squares framework to formulate many ca methods we show how pca lda cca lpp sc and its kernel and regularized extensions correspond to a particular instance of least squares weighted kernel reduced rank regression ls wkrrr the ls wkrrr formulation of ca methods has several benefits 1 provides a clean connection between many ca techniques and an intuitive framework to understand normalization factors 2 yields efficient numerical schemes to solve ca techniques 3 overcomes the small sample size problem 4 provides a framework to easily extend ca methods we derive weighted generalizations of pca lda sc and cca and several new ca techniques

incremental nonlinear dimensionality reduction by manifold learning understanding the structure of multidimensional patterns especially in unsupervised cases is of fundamental importance in data mining pattern recognition and machine learning several algorithms have been proposed to analyze the structure of high dimensional data based on the notion of manifold learning these algorithms have been used to extract the intrinsic characteristics of different types of high dimensional data by performing nonlinear dimensionality reduction most of these algorithms operate in a batch mode and cannot be efficiently applied when data are collected sequentially in this paper we describe an incremental version of isomap one of the key manifold learning algorithms our experiments on synthetic data as well as real world images demonstrate that our modified algorithm can maintain an accurate low dimensional representation of the data in an efficient manner

occurrence of secular terms in the carleman embedding secular terms occur in many perturbative solutions of nonlinear equation systems in this work an investigation is made of which cases they may occur in as the result of the application of the linear carleman embedding to a system of nonlinear equations the solution for the embedded system is written in a form that makes it convenient to see how these terms originate their occurrence for the general case is discussed and the results are exemplified by working out the henon heiles system

maxwell s equations in a periodic structure consider a diffraction of a beam of particles in r3 when the dielectric coefficient is a constant cl above a surface s and a constant e2 below a surface s and the magnetic permeability is constant throughout rii s is assumed to be periodic in the xl direction and of the form x1 f1 s x3 f3 s x2 arbitrary we prove that there exists a unique solution to the time harmonic maxwell equations in r 3 having the form of refracted waves for x3 1 and of transmitted waves for x3 1 if and only if there exists a unique solution to a certain system of two coupled fredholm equations thus in particular for all the e s except for a discrete number there exists a unique solution to the maxwell equations introduction in this paper we consider the maxwell equations for time harmonic solutions in the entire space r3 with piecewise constant dielectric coefficient having jump across a periodic surface the magnetic permeability u is assumed to be constant whereas the dielectric coefficient e is given by e 8 above a surface s x3 f xl and e e2 below the surface s e and 82 are different constants if s is a half space x3 0 then the solution eo ho can be computed explicitly we assume in this paper that s is periodic i e f xl l f xl vx1 e r l 0 we wish to find a solution e h such that e eo and h ho are superpositions of transmitted waves 0 1 in x3 a where a maxlfl in 1 7 we assume that f e c2 and we reduce the solution of the maxwell equations to a fredholm system of four integral equations in 8 we reduce it further to a fredholm system of two integral equations thus for all but a discrete sequence of values of the physical parameters there exists a unique solution to the integral equations yielding a solution of the maxwell equations received by the editors january 25 1989 1980 mathematics subject classification 1985 revision primary 78a10 78a45 secondary 35p25 47a40

linearization transformations for non linear dynamical systems hilbert space approach abstract a new method for the linearization of non linear dynamical systems with both a finite and an infinite number of degrees of freedom is introduced using the hilbert space approach the problem of finding the linearization transformations is reduced to the solution of abstract linear equations in hilbert space

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

gender classification from unaligned facial images using support subspaces rough face alignments result in suboptimal performance of face identification in this study we present an approach for identifying the gender based on facial images without proper face alignments instead of just using only the detected face patch for identification a set of patches is randomly cropped around the face detection region each patch set is represented by a linear subspace and compared with other linear subspaces by measuring their canonical correlations a similarity matrix comprised of the canonical correlations is then incorporated into an indefinite kernel support vector machine svm formulation the number of support vectors which we call support subspaces can be decided automatically hence we can avoid the dimension selection problem observed in our previous work our experimental results demonstrate that the proposed approach outperforms state of the art methods

discriminant nonnegative tensor factorization algorithms nonnegative matrix factorization nmf has proven to be very successful for image analysis especially for object representation and recognition nmf requires the object tensor with valence more than one to be vectorized this procedure may result in information loss since the local object structure is lost due to vectorization recently in order to remedy this disadvantage of nmf methods nonnegative tensor factorizations ntf algorithms that can be applied directly to the tensor representation of object collections have been introduced in this paper we propose a series of unsupervised and supervised ntf methods that is we extend several nmf methods using arbitrary valence tensors moreover by incorporating discriminant constraints inside the ntf decompositions we present a series of discriminant ntf methods the proposed approaches are tested for face verification and facial expression recognition where it is shown that they outperform other popular subspace approaches

uncorrelated multilinear principal component analysis for unsupervised multilinear subspace learning this paper proposes an uncorrelated multilinear principal component analysis umpca algorithm for unsupervised subspace learning of tensorial data it should be viewed as a multilinear extension of the classical principal component analysis pca framework through successive variance maximization umpca seeks a tensor to vector projection tvp that captures most of the variation in the original tensorial input while producing uncorrelated features the solution consists of sequential iterative steps based on the alternating projection method in addition to deriving the umpca framework this work offers a way to systematically determine the maximum number of uncorrelated multilinear features that can be extracted by the method umpca is compared against the baseline pca solution and its five state of the art multilinear extensions namely two dimensional pca 2dpca concurrent subspaces analysis csa tensor rank one decomposition trod generalized pca gpca and multilinear pca mpca on the tasks of unsupervised face and gait recognition experimental results included in this paper suggest that umpca is particularly effective in determining the low dimensional projection space needed in such recognition tasks

experimental observation of local modes in fractal drums abstract it is shown that fractal boundary conditions drastically alter the properties of wave excitations in space the low frequency vibration modes of soap bubbles deposited on a fractal contour are observed there exist localized modes the vibrations have a singular behavior along the boundary consequently fractal resonators are necessarily non linear resonators and have special damping properties

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

local linear discriminant analysis framework using sample neighbors the linear discriminant analysis lda is a very popular linear feature extraction approach the algorithms of lda usually perform well under the following two assumptions the first assumption is that the global data structure is consistent with the local data structure the second assumption is that the input data classes are gaussian distributions however in real world applications these assumptions are not always satisfied in this paper we propose an improved lda framework the local lda llda which can perform well without needing to satisfy the above two assumptions our llda framework can effectively capture the local structure of samples according to different types of local data structure our llda framework incorporates several different forms of linear feature extraction approaches such as the classical lda and principal component analysis the proposed framework includes two llda algorithms a vector based llda algorithm and a matrix based llda mllda algorithm mllda is directly applicable to image recognition such as face recognition our algorithms need to train only a small portion of the whole training set before testing a sample they are suitable for learning large scale databases especially when the input data dimensions are very high and can achieve high classification accuracy extensive experiments show that the proposed algorithms can obtain good classification results

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

iterative subspace analysis based on feature line distance nearest feature line based subspace analysis is first proposed in this paper compared with conventional methods the newly proposed one brings better generalization performance and incremental analysis the projection point and feature line distance are expressed as a function of a subspace which is obtained by minimizing the mean square feature line distance moreover by adopting stochastic approximation rule to minimize the objective function in a gradient manner the new method can be performed in an incremental mode which makes it working well upon future data experimental results on the feret face database and the uci satellite image database demonstrate the effectiveness

mr ntd manifold regularization nonnegative tucker decomposition for tensor data dimension reduction and representation with the advancement of data acquisition techniques tensor multidimensional data objects are increasingly accumulated and generated for example multichannel electroencephalographies multiview images and videos in these applications the tensor objects are usually nonnegative since the physical signals are recorded as the dimensionality of tensor objects is often very high a dimension reduction technique becomes an important research topic of tensor data from the perspective of geometry high dimensional objects often reside in a low dimensional submanifold of the ambient space in this paper we propose a new approach to perform the dimension reduction for nonnegative tensor objects our idea is to use nonnegative tucker decomposition ntd to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects to preserve geometric information in tensor data we employ a manifold regularization term for the core tensors constructed in the tucker decomposition an algorithm called manifold regularization ntd mr ntd is developed to solve the common projection matrices and core tensors in an alternating least squares manner the convergence of the proposed algorithm is shown and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects respectively these theoretical results show that the proposed algorithm can be efficient extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed mr ntd algorithm

kernel self optimization learning for kernel based feature extraction and recognition kernel learning is becoming an important research topic in the area of machine learning and it has wide applications in pattern recognition computer vision image and signal processing kernel learning provides a promising solution to nonlinear problems including nonlinear feature extraction classification and clustering however in kernel based systems the problem of the kernel function and its parameters remains to be solved methods of choosing parameters from a discrete set of values have been presented in previous studies but these methods do not change the data distribution structure in the kernel based mapping space accordingly performance is not improved because the current kernel optimization does not change the data distribution based on this problem this paper presents a uniform framework for kernel self optimization with the ability to adjust the data structure the data dependent kernel is extended and applied to kernel learning and optimization equations with two criteria for measuring data discrimination are used to solve the optimal parameter values some experiments are performed to evaluate the performance in popular kernel learning methods including kernel principal components analysis kpca kernel discriminant analysis kda and kernel locality preserving projection klpp these evaluations show that the framework of kernel self optimization is feasible for enhancing kernel based learning methods

face recognition using ipca ica algorithm in this paper a fast incremental principal non gaussian directions analysis algorithm called ipca ica is introduced this algorithm computes the principal components of a sequence of image vectors incrementally without estimating the covariance matrix so covariance free and at the same time transforming these principal components to the independent directions that maximize the non gaussianity of the source two major techniques are used sequentially in a real time fashion in order to obtain the most efficient and independent components that describe a whole set of human faces database this procedure is done by merging the runs of two algorithms based on principal component analysis pca and independent component analysis ica running sequentially this algorithm is applied to face recognition problem simulation results on different databases showed high average success rate of this algorithm compared to others

a linear support higher order tensor machine for classification there has been growing interest in developing more effective learning machines for tensor classification at present most of the existing learning machines such as support tensor machine stm involve nonconvex optimization problems and need to resort to iterative techniques obviously it is very time consuming and may suffer from local minima in order to overcome these two shortcomings in this paper we present a novel linear support higher order tensor machine shtm which integrates the merits of linear c support vector machine c svm and tensor rank one decomposition theoretically shtm is an extension of the linear c svm to tensor patterns when the input patterns are vectors shtm degenerates into the standard c svm a set of experiments is conducted on nine second order face recognition datasets and three third order gait recognition datasets to illustrate the performance of the proposed shtm the statistic test shows that compared with stm and c svm with the rbf kernel shtm provides significant performance gain in terms of test accuracy and training speed especially in the case of higher order tensors

mode kn factor analysis for image ensembles in this corespondence we study the extra factor estimation problem with the assumption that the training image ensemble is expressed as an nth order tensor with the nth dimension characterizing all features for an image and other dimensions for different extra factors such as illuminations poses and identities to overcome the local minimum issue of conventional algorithms designed for this problem we present a novel statistical learning framework called mode kn factor analysis for obtaining a closed form solution to estimating the extra factors of any test image in the learning stage for the kth k ne n dimension of the data tensor the mode kn patterns are constructed by concatenating the feature dimension and the kth extra factor dimension and then a mode kn factor analysis model is learnt based on the mode kn patterns unfolded from the original data tensor in the inference stage for a test image the mode classification of the kth dimension is performed within a probabilistic framework the advantages of mode kn factor analysis over conventional tensor analysis algorithms are twofold 1 a closed form solution instead of iterative sub optimal solution as conventionally is derived for estimating the extra factor mode of any test image and 2 the classification capability is enhanced by interacting with the process of synthesizing data of all other modes in the k th dimension experiments on the pointing 04 and cmu pie databases for pose and illumination estimation both validate the superiority of the proposed algorithm over conventional algorithms for extra factor estimation

tensor distance based multilinear locality preserved maximum information embedding this brief paper presents a unified framework for tensor based dimensionality reduction dr with a new tensor distance td metric and a novel multilinear locality preserved maximum information embedding mlpmie algorithm different from traditional euclidean distance which is constrained by the orthogonality assumption td measures the distance between data points by considering the relationships among different coordinates to preserve the natural tensor structure in low dimensional space mlpmie directly works on the high order form of input data and iteratively learns the transformation matrices in order to preserve the local geometry and to maximize the global discrimination simultaneously mlpmie keeps both local and global structures in a manifold model by integrating td into tensor embedding td mlpmie performs tensor based dr through the whole learning procedure and achieves stable performance improvement on various standard datasets

formulating robust linear regression estimation as a one class lda criterion discriminative hat matrix linear discriminant analysis such as fisher s criterion is a statistical learning tool traditionally devoted to separating a training dataset into two or even several classes by the way of linear decision boundaries in this paper we show that this tool can formalize the robust linear regression problem as a robust estimator will do more precisely we develop a one class fischer s criterion in which the maximization provides both the regression parameters and the separation of the data in two classes typical data and atypical data or outliers this new criterion is built on the statistical properties of the subspace decomposition of the hat matrix from this angle we improve the discriminative properties of the hat matrix which is traditionally used as outlier diagnostic measure in linear regression naturally we call this new approach discriminative hat matrix the proposed algorithm is fully nonsupervised and needs only the initialization of one parameter synthetic and real datasets are used to study the performance both in terms of regression and classification of the proposed approach we also illustrate its potential application to image recognition and fundamental matrix estimation in computer vision

symmetries and first integrals for dissipative systems the connection between symmetries time independent and time dependent first integrals for autonomous systems of first order ordinary differential equations is discussed several new results which have been obtained by applying a reduce package are reported

hilbert space description of classical dynamical systems ii abstract it is shown that classical dynamical systems can be described by a hilbert space schrodinger like equation with the hamiltonian a non hermitian one expressed in terms of bose creation and annihilation operators the presented formalism includes the carleman embedding as the special case

efficient image classification via multiple rank regression the problem of image classification has aroused considerable research interest in the field of image processing traditional methods often convert an image to a vector and then use a vector based classifier in this paper a novel multiple rank regression model mrr for matrix data classification is proposed unlike traditional vector based methods we employ multiple rank left projecting vectors and right projecting vectors to regress each matrix data set to its label for each category the convergence behavior initialization computational complexity and parameter determination are also analyzed compared with vector based regression methods mrr achieves higher accuracy and has lower computational complexity compared with traditional supervised tensor based methods mrr performs better for matrix data classification promising experimental results on face object and hand written digit image classification tasks are provided to show the effectiveness of our method

tensor learning for regression in this paper we exploit the advantages of tensorial representations and propose several tensor learning models for regression the model is based on the canonical parallel factor decomposition of tensors of multiple modes and allows the simultaneous projections of an input tensor to more than one direction along each mode two empirical risk functions are studied namely the square loss and e insensitive loss functions the former leads to higher rank tensor ridge regression trr and the latter leads to higher rank support tensor regression str both formulated using the frobenius norm for regularization we also use the group sparsity norm for regularization favoring in that way the low rank decomposition of the tensorial weight in that way we achieve the automatic selection of the rank during the learning process and obtain the optimal rank trr and str experiments conducted for the problems of head pose human age and 3 d body pose estimations using real data from publicly available databases verified not only the superiority of tensors over their vector counterparts but also the efficiency of the proposed algorithms

mpca multilinear principal component analysis of tensor objects this paper introduces a multilinear principal component analysis mpca framework for tensor object feature extraction objects of interest in many computer vision and pattern recognition applications such as 2d 3d images and video sequences are naturally described as tensors or multilinear arrays the proposed framework performs feature extraction by determining a multilinear projection that captures most of the original tensorial input variation the solution is iterative in nature and it proceeds by decomposing the original problem to a series of multiple projection subproblems as part of this work methods for subspace dimensionality determination are proposed and analyzed it is shown that the mpca framework discussed in this work supplants existing heterogeneous solutions such as the classical principal component analysis pca and its 2d variant 2d pca finally a tensor object recognition system is proposed with the introduction of a discriminative tensor feature selection mechanism and a novel classification strategy and applied to the problem of gait recognition results presented here indicate mpca s utility as a feature extraction tool it is shown that even without a fully optimized design an mpca based gait recognition module achieves highly competitive performance and compares favorably to the state of the art gait recognizers