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

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

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

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

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

on the global regularity of generalized leray alpha type models abstract we generalize leray alpha type models studied in cheskidov et al 2005 1 and linshiz and titi 2007 4 via fractional laplacians and employ besov space techniques to obtain global regularity results with the logarithmically supercritical dissipation

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

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

global wellposedness of defocusing critical nonlinear schrodinger equation in the radial case is globally wellposed in time more precisely we obtain a unique solution u u ch1 0 such that for all time u t depends continuously on the data in fact the dependence is even real analytic here moreover there is scattering for t the same statement holds for radial data h s 1 and proves in particular global existence of classical solutions in the radially symmetric case also this issue was open thus this is the analogue for nls of the result for the wave equation with quintic nonlinearity obtained by m struwe str in the radial case and by m grillakis gr s s in general in the case of the wave equation the proof is based on the following two different facts

global well posedness and scattering for the energy critical nonlinear schrodinger equation in r 3 we obtain global well posedness scattering and global l 10 spacetime bounds for energy class solutions to the quintic defocusing schrodinger equa tion in r 1 3 which is energy critical in particular this establishes global existence of classical solutions our work extends the results of bourgain 4 and grillakis 20 which handled the radial case the method is similar in spirit to the induction on energy strategy of bourgain 4 but we perform the induction analysis in both frequency space and physical space simultaneously and replace the morawetz inequality by an interaction variant first used in 12 13 the principal advantage of the interaction morawetz estimate is that it is not localized to the spatial origin and so is better able to handle nonradial solutions in particular this interaction estimate together with an almost conservation argument controlling the movement of l 2 mass in fre quency space rules out the possibility of energy concentration

on scattering for the quintic defocusing nonlinear schrodinger equation on r t2 we consider the problem of large data scattering for the quintic nonlinear schrodinger equation on r t2 this equation is critical both at the level of energy and mass most notably we exhibit a new type of profile a large scale profile that controls the asymptotic behavior of the solutions 2014 wiley periodicals inc

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

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

horseshoes for diffeomorphisms preserving hyperbolic measures we give extensions of katok s horseshoe constructions comment on related results and provide a self contained proof we consider either a c 1 alpha diffeomorphism preserving a hyperbolic measure or a c 1 diffeomorphism preserving a hyperbolic measure whose support admits a dominated splitting

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

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

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

dispersion of small amplitude solutions of the generalized korteweg de vries equation abstract we study the long time behavior of small solutions of the initial value problem for the generalized korteweg de vries equation t u x 3 u x f u 0 gkdv u x 0 g x for the case where f w w s with s 1 4 23 57 3 8625 our results imply that if g l11 g l22 is sufficiently small then sup r 1 t 1 3 u t l in particular the solution tends to zero in the supremum norm the proofs make use of duhamel s formula and dispersion estimates for the linear propagator as well as chain and leibniz rules for fractional derivatives of compositions d f u lp and products d fg lp 0

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

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

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

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

scattering above energy norm of solutions of a loglog energy supercritical schrodinger equation with radial data abstract we prove global well posedness and scattering of h k h k r n h 1 r n solutions of the loglog energy supercritical schrodinger equation i t u u u 4 n 2 u log c log 10 u 2 0 c c n n 3 4 with radial data u 0 u 0 h k h k r n h 1 r n k n 2 this is achieved roughly speaking by extending bourgain s argument in bourgain 1999 1 see also grillakis 2000 5 and tao s argument in tao 2005 10 in high dimensions

global well posedness and scattering for the defocusing energy critical nonlinear schrodinger equation in r1 4 we obtain global well posedness scattering uniform regularity and global l6t x spacetime bounds for energy space solutions to the defocusing energy critical nonlinear schrodinger equation in a 4 our arguments closely follow those of colliander keel et al though our derivation of the frequency localized interaction morawetz estimate is somewhat simpler as a consequence our method yields a better bound on the l6t x norm

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