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

manifold constraint transfer for visual structure driven optimization abstract in this paper we leverage the manifold structure of visual data in order to improve performance in general optimization problems subject to linear constraints as the main theoretical result we show that manifold constraints can be transferred from the data to the optimized variables if these are linearly correlated we also show that the resulting optimization problem can be solved with an efficient alternating direction method of multipliers that can consistently integrate the manifold constraints during the optimization process this leads to a simplification of the approach which instead of directly optimizing on the manifold we can iteratively recast the problem as the projection over the manifold via an embedding method the proposed method is extremely versatile since it can be applied to different problems including kernel ridge regression krr and sparse coding which have numerous applications in machine learning and computer vision in particular we apply the methods to different problems such as tracking object recognition and categorization showing a consistent increase of performance with respect to the state of the art

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

a second order cone programming approach for semi supervised learning semi supervised learning ssl involves the training of a decision rule from both labeled and unlabeled data in this paper we propose a novel ssl algorithm based on the multiple clusters per class assumption the proposed algorithm consists of two stages in the first stage we aim to capture the local cluster structure of the training data by using the k nearest neighbor knn algorithm to split the data into a number of disjoint subsets in the second stage a maximal margin classifier based on the second order cone programming socp is introduced to learn an inductive decision function from the obtained subsets globally for linear classification problems once the knn algorithm has been performed the proposed algorithm trains a classifier using only the first and second order moments of the subsets without considering individual data points since the number of subsets is usually much smaller than the number of training points the proposed algorithm is efficient for handling big data sets with a large amount of unlabeled data despite its simplicity the classification performance of the proposed algorithm is guaranteed by the maximal margin classifier we demonstrate the efficiency and effectiveness of the proposed algorithm on both synthetic and real world data sets

discriminative sparsity preserving projections for image recognition previous works have demonstrated that image classification performance can be significantly improved by manifold learning however performance of manifold learning heavily depends on the manual selection of parameters resulting in bad adaptability in real world applications in this paper we propose a new dimensionality reduction method called discriminative sparsity preserving projections dspp different from the existing sparse subspace algorithms which manually construct a penalty adjacency graph dspp employs sparse representation model to adaptively build both intrinsic adjacency graph and penalty graph with weight matrix and then integrates global within class structure into the discriminant manifold learning objective function for dimensionality reduction extensive experimental results on four image databases demonstrate the effectiveness of the proposed approach we analyzed the vertex points of penalty graph using sparse representation we adaptively constructed both penalty adjacency graph and intrinsic graph our method simultaneously considered the global and local geometric structure of data

probabilistic class structure regularized sparse representation graph for semi supervised hyperspectral image classification abstract graph based semi supervised learning ssl which performs well in hyperspectral image classification with a small amount of labeled samples has drawn a lot of attention in the past few years the key step of graph based ssl is to construct a good graph to represent original data structures among the existing graph construction methods sparse representation sr based methods have shown impressive performance on graph based ssl however most sr based methods fail to take into consideration the class structure of data in ssl we can obtain a probabilistic class structure which implies the probabilistic relationship between each sample and each class of the whole data by utilizing a small amount of labeled samples such class structure information can help sr model to yield a more discriminative coefficients which motivates us to exploit this class structure information in order to learn a discriminative graph in this paper we present a discriminative graph construction method called probabilistic class structure regularized sparse representation pcssr approach by incorporating the class structure information into the sr model pcssr can learn a discriminative graph from the data a class structure regularization is developed to make use of the probabilistic class structure and therefore to improve the discriminability of the graph we formulate our problem as a constrained sparsity minimization problem and solve it by the alternating direction method with adaptive penalty admap the experimental results on hyperion and aviris hyperspectral data show that our method outperforms state of the art

regularized coplanar discriminant analysis for dimensionality reduction abstract the dimensionality reduction methods based on linear embedding such as neighborhood preserving embedding npe sparsity preserving projections spp and collaborative representation based projections crp try to preserve a certain kind of linear representation for each sample after projection however in the transformed low dimensional space the linear relationship between the samples may be changed which cannot make the linear representation based classifiers such as sparse representation based classifier src to achieve higher recognition accuracy in this paper we propose a new linear dimensionality reduction algorithm called regularized coplanar discriminant analysis rcda to address this problem it simultaneously seeks a linear projection matrix and some linear representation coefficients that make the samples from the same class coplanar and the samples from different classes not coplanar the proposed regularization term balances the bias from the optimal linear representation and that from the class mean to avoid overfitting the training data and overcomes the matrix singularity in solving the linear representation coefficients an alternative optimization approach is proposed to solve the rcda model experiments are done on several benchmark face databases and hyperspectral image databases and results show that rcda can obtain better performance than other dimensionality reduction methods

a theory of algebraic cocycles we introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an eilenberg maclane space using these cocycles we develop a cohomology theory for complex algebraic varieties the theory is bigraded functorial and admits gysin maps it carries a natural cup product and a pairing to l homology chern classes of algebraic bundles are defined in the theory there is a natural transformation to singular integral cohomology theory that preserves cup products computations in special cases are carried out on a smooth variety it is proved that there are algebraic cocycles in each algebraic rational p p cohomology class in this announcement we present the outlines of a cohomology theory for algebraic varieties based on a new concept of an algebraic cocycle details will appear in fl our cohomology is a companion to the l homology theory recently studied in l f l f1 l f2 fm this homology is a bigraded theory based directly on the structure of the space of algebraic cycles it admits a natural transformation to integral homology that generalizes the usual map taking a cycle to its homology class our new cohomology theory is similarly bigraded and based on the structure of the space of algebraic cocycles it carries a ring structure coming from the complex join an elementary construction of projective geometry and it admits a natural transformation to integral cohomology chern classes are defined in the theory and transform under to the usual ones our definition of cohomology is very far from a duality construction on l homology nonetheless there is a natural and geometrically defined kronecker pairing between our morphic cohomology and l homology the foundation stone of our theory is the notion of an effective algebraic cocycle which is of some independent interest roughly speaking such a cocycle on a variety x with values in a projective variety y is a morphism from x to the space of cycles on y when x is normal this is equivalent by graphing to a cycle on x y with equidimensional fibres over x such cocycles abound in algebraic geometry and arise naturally in many circumstances the simplest perhaps is that of a flat morphism f x y whose corresponding cocycle associates to x x the pullback cycle f x many more arise naturally from synthetic constructions in projective geometry we show that every variety is rich in cocycles indeed if 1991 mathematics subject classification primary 14f99 14c05

random subspace based ensemble sparse representation a new random subspace based joint sparse representation model is proposed the sparse representations in multiple subspaces are integrated into an ensemble sparse representation the spectral clustering algorithm with random subspace based ensemble sparse representation is shown the semi supervised classification method with random subspace based ensemble sparse representation is described in this paper a new random subspace based ensemble sparse representation rs esr algorithm is proposed where the random subspace is introduced into sparse representation model for high dimensional data the random subspace method can not only reduce dimension of data but also make full use of effective information of data it is not like traditional dimensionality reduction methods that may lose some information of original data additionally a joint sparse representation model is emloyed to obtain the sparse representation of a sample set in the low dimensional random subspace then the sparse representations in multiple random subspaces are integrated as an ensemble sparse representation moreover the obtained rs esr is applied in classical clustering and semi supervised classification the experimental results on different real world data sets show the superiority of rs esr over traditional methods

low rank matrix factorization with adaptive graph regularizer in this paper we present a novel low rank matrix factorization algorithm with adaptive graph regularizer lmfagr we extend the recently proposed low rank matrix with manifold regularization mmf method with an adaptive regularizer different from mmf which constructs an affinity graph in advance lmfagr can simultaneously seek graph weight matrix and low dimensional representations of data that is graph construction and low rank matrix factorization are incorporated into a unified framework which results in an automatically updated graph rather than a predefined one the experimental results on some data sets demonstrate that the proposed algorithm outperforms the state of the art low rank matrix factorization methods

comparing k theories for complex varieties the semi topological k theory of a complex variety was defined in a recent paper by the authors with the expectation that it would prove to be a theory lying part way between the algebraic k theory of the variety and the topological k theory of the associated analytic space and thus would share properties with each of these other theories in this paper we realize these expectations by proving among other results that 1 the algebraic k theory with finite coefficients and the semi topological k theory with finite coefficients coincide on all projective complex varieties 2 semi topological k theory and topological k theory agree on certain types of generalized flag varieties and 3 assuming a result asserted by cohen and lima filho the semi topological k theory of any smooth projective variety becomes isomorphic to the topological k theory of the underlying analytic space once the bott element is inverted to illustrate the utility of our results we observe that a new proof of the quillen lichtenbaum conjecture for smooth complete curves is obtained as a corollary

robust and low rank representation for fast face identification with occlusions in this paper we propose an iterative method to address the face identification problem with block occlusions our approach utilizes a robust representation based on two characteristics in order to model contiguous errors e g block occlusion effectively the first fits to the errors a distribution described by a tailored loss function the second describes the error image as having a specific structure resulting in low rank in comparison with image size we will show that this joint characterization is effective for describing errors with spatial continuity our approach is computationally efficient due to the utilization of the alternating direction method of multipliers a special case of our fast iterative algorithm leads to the robust representation method which is normally used to handle non contiguous errors e g pixel corruption extensive results on representative face databases in constrained and unconstrained environments document the effectiveness of our method over existing robust representation methods with respect to both identification rates and computational time

robust nonnegative patch alignment for dimensionality reduction dimensionality reduction is an important method to analyze high dimensional data and has many applications in pattern recognition and computer vision in this paper we propose a robust nonnegative patch alignment for dimensionality reduction which includes a reconstruction error term and a whole alignment term we use correntropy induced metric to measure the reconstruction error in which the weight is learned adaptively for each entry for the whole alignment we propose locality preserving robust nonnegative patch alignment lp rna and sparsity preserviing robust nonnegative patch alignment sp rna which are unsupervised and supervised respectively in the lp rna we propose a locally sparse graph to encode the local geometric structure of the manifold embedded in high dimensional space in particular we select large p nearest neighbors for each sample then obtain the sparse representation with respect to these neighbors the sparse representation is used to build a graph which simultaneously enjoys locality sparseness and robustness in the sp rna we simultaneously use local geometric structure and discriminative information in which the sparse reconstruction coefficient is used to characterize the local geometric structure and weighted distance is used to measure the separability of different classes for the induced nonconvex objective function we formulate it into a weighted nonnegative matrix factorization based on half quadratic optimization we propose a multiplicative update rule to solve this function and show that the objective function converges to a local optimum several experimental results on synthetic and real data sets demonstrate that the learned representation is more discriminative and robust than most existing dimensionality reduction methods

the lack of a priori distinctions between learning algorithms this is the first of two papers that use off training set ots error to investigate the assumption free relationship between learning algorithms this first paper discusses the senses in which there are no a priori distinctions between learning algorithms the second paper discusses the senses in which there are such distinctions in this first paper it is shown loosely speaking that for any two algorithms a and b there are as many targets or priors over targets for which a has lower expected ots error than b as vice versa for loss functions like zero one loss in particular this is true if a is cross validation and b is anti cross validation choose the learning algorithm with largest cross validation error this paper ends with a discussion of the implications of these results for computational learning theory it is shown that one cannot say if empirical misclassification rate is low the vapnik chervonenkis dimension of your generalizer is small and the training set is large then with high probability your ots error is small other implications for membership queries algorithms and punting algorithms are also discussed

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

techniques computations and conjectures for semi topological k theory we establish the existence of an atiyah hirzebruch like spectral sequence relating the morphic cohomology groups of a smooth quasi projective complex variety to its semi topological k groups this spectral sequence is compatible with and indeed is built from the motivic spectral sequence that relates the motivic cohomology and algebraic k theory of varieties and it is also compatible with the classical atiyah hirzebruch spectral sequence in algebraic topology in the second part of this paper we use this spectral sequence in conjunction with another computational tool that we introduce namely a variation on the integral weight filtration of the borel moore singular homology of complex varieties introduced by h gillet and c soule to compute the semi topological k theory of a large class of varieties in particular we prove that for curves surfaces toric varieties projective rational three folds and related varieties the semi topological k groups and topological k groups are isomorphic in all degrees permitted by cohomological considerations we also formulate integral conjectures relating semi topological k theory to topological k theory analogous to more familiar conjectures namely the quillen lichtenbaum and beilinson lichtenbaum conjectures concerning mod n algebraic k theory and motivic cohomology in particular we prove a local vanishing result for morphic cohomology which enables us to formulate precisely a conjectural identification of morphic cohomology by a suslin our computations verify that these conjectures hold for the list of varieties above

learning a nonnegative sparse graph for linear regression previous graph based semisupervised learning g ssl methods have the following drawbacks 1 they usually predefine the graph structure and then use it to perform label prediction which cannot guarantee an overall optimum and 2 they only focus on the label prediction or the graph structure construction but are not competent in handling new samples to this end a novel nonnegative sparse graph nnsg learning method was first proposed then both the label prediction and projection learning were integrated into linear regression finally the linear regression and graph structure learning were unified within the same framework to overcome these two drawbacks therefore a novel method named learning a nnsg for linear regression was presented in which the linear regression and graph learning were simultaneously performed to guarantee an overall optimum in the learning process the label information can be accurately propagated via the graph structure so that the linear regression can learn a discriminative projection to better fit sample labels and accurately classify new samples an effective algorithm was designed to solve the corresponding optimization problem with fast convergence furthermore nnsg provides a unified perceptiveness for a number of graph based learning methods and linear regression methods the experimental results showed that nnsg can obtain very high classification accuracy and greatly outperforms conventional g ssl methods especially some conventional graph construction methods

supervised neighborhood graph construction for semi supervised classification graph based methods are among the most active and applicable approaches studied in semi supervised learning the problem of neighborhood graph construction for these methods is addressed in this paper neighborhood graph construction plays a key role in the quality of the classification in graph based methods several unsupervised graph construction methods have been proposed that have addressed issues such as data noise geometrical properties of the underlying manifold and graph hyper parameters selection in contrast in order to adapt the graph construction to the given classification task many of the recent graph construction methods take advantage of the data labels however these methods are not efficient since the hypothesis space of their possible neighborhood graphs is limited in this paper we first prove that the optimal neighborhood graph is a subgraph of a k nn graph for a large enough k which is much smaller than the total number of data points therefore we propose to use all the subgraphs of k nns graph as the hypothesis space in addition we show that most of the previous supervised graph construction methods are implicitly optimizing the smoothness functional with respect to the neighborhood graph parameters finally we provide an algorithm to optimize the smoothness functional with respect to the neighborhood graph in the proposed hypothesis space experimental results on various data sets show that the proposed graph construction algorithm mostly outperforms the popular k nn based construction and other state of the art methods

realistic action recognition via sparsely constructed gaussian processes realistic action recognition has been one of the most challenging research topics in computer vision the existing methods are commonly based on non probabilistic classification predicting category labels but not providing an estimation of uncertainty in this paper we propose a probabilistic framework using gaussian processes gps which can tackle regression problems with explicit uncertain models for action recognition a major challenge for gps when applied to large scale realistic data is that a large covariance matrix needs to be inverted during inference additionally from the manifold perspective the intrinsic structure of the data space is only constrained by a local neighborhood and data relationships with far distance usually can be ignored thus we design our gps covariance matrix via the proposed l1 construction and a local approximation la covariance weight updating method which are demonstrated to be robust to data noise automatically sparse and adaptive to the neighborhood extensive experiments on four realistic datasets i e ucf youtube ucf sports hollywood2 and hmdb51 show the competitive results of l1 gps compared with state of the art methods on action recognition tasks

subspace learning by l0 induced sparsity subspace clustering methods partition the data that lie in or close to a union of subspaces in accordance with the subspace structure such methods with sparsity prior such as sparse subspace clustering ssc elhamifar and vidal in ieee trans pattern anal mach intell 35 11 2765 2781 2013 with the sparsity induced by the ell 1 norm are demonstrated to be effective in subspace clustering most of those methods require certain assumptions e g independence or disjointness on the subspaces however these assumptions are not guaranteed to hold in practice and they limit the application of existing sparse subspace clustering methods in this paper we propose ell 0 induced sparse subspace clustering ell 0 ssc in contrast to the required assumptions such as independence or disjointness on subspaces for most existing sparse subspace clustering methods we prove that ell 0 ssc guarantees the subspace sparse representation a key element in subspace clustering for arbitrary distinct underlying subspaces almost surely under the mild i i d assumption on the data generation we also present the no free lunch theorem which shows that obtaining the subspace representation under our general assumptions can not be much computationally cheaper than solving the corresponding ell 0 sparse representation problem of ell 0 ssc a novel approximate algorithm named approximate ell 0 ssc a ell 0 ssc is developed which employs proximal gradient descent to obtain a sub optimal solution to the optimization problem of ell 0 ssc with theoretical guarantee the sub optimal solution is used to build a sparse similarity matrix upon which spectral clustering is performed for the final clustering results extensive experimental results on various data sets demonstrate the superiority of a ell 0 ssc compared to other competing clustering methods furthermore we extend ell 0 ssc to semi supervised learning by performing label propagation on the sparse similarity matrix learnt by a ell 0 ssc and demonstrate the effectiveness of the resultant semi supervised learning method termed ell 0 sparse subspace label propagation ell 0 sslp

label information guided graph construction for semi supervised learning in the literature most existing graph based semi supervised learning methods only use the label information of observed samples in the label propagation stage while ignoring such valuable information when learning the graph in this paper we argue that it is beneficial to consider the label information in the graph learning stage specifically by enforcing the weight of edges between labeled samples of different classes to be zero we explicitly incorporate the label information into the state of the art graph learning methods such as the low rank representation lrr and propose a novel semi supervised graph learning method called semi supervised low rank representation this results in a convex optimization problem with linear constraints which can be solved by the linearized alternating direction method though we take lrr as an example our proposed method is in fact very general and can be applied to any self representation graph learning methods experiment results on both synthetic and real data sets demonstrate that the proposed graph learning method can better capture the global geometric structure of the data and therefore is more effective for semi supervised learning tasks

graph embedding and extensions a general framework for dimensionality reduction a large family of algorithms supervised or unsupervised stemming from statistics or geometry theory has been designed to provide different solutions to the problem of dimensionality reduction despite the different motivations of these algorithms we present in this paper a general formulation known as graph embedding to unify them within a common framework in graph embedding each algorithm can be considered as the direct graph embedding or its linear kernel tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided furthermore the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms by utilizing this framework as a tool we propose a new supervised dimensionality reduction algorithm called marginal fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class while the penalty graph connects the marginal points and characterizes the interclass separability we show that mfa effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions real face recognition experiments show the superiority of our proposed mfa in comparison to lda also for corresponding kernel and tensor extensions

adaptive maximum margin analysis for image recognition abstract most existing discriminant manifold learning methods aim to maximize the margin among nearby data which is determined in the high dimensional original space as such they do not necessarily best maximize the margin between different classes in the low dimensional space which is a critically important property for image classification to handle this problem we propose an adaptive maximum margin analysis amma for feature extraction amma aims to seek a projection matrix that best maximize the margin which is calculated in the low dimensional space it uses sparse representation to adaptively construct the intrinsic and penalty graphs finally an iterative algorithm is developed to solve the projection matrix extensive experimental results on several image databases illustrate the effectiveness of the proposed approach

adaptive graph construction using data self representativeness for pattern classification graph construction from data constitutes a pre stage in many machine learning and computer vision tasks like semi supervised learning manifold learning and spectral clustering the influence of graph construction procedures on learning tasks and their related applications has only received limited study despite its critical impact on accuracy state of the art graphs are built via sparse coding adopting 1 regularization those graphs exhibit good performance in many computer vision applications however the locality and similarity among instances are not explicitly used in the coding scheme furthermore due to the use of 1 regularization these construction approaches can be computationally expensive in this paper we investigate graph construction using the data self representativeness property by incorporating a variant of locality constrained linear coding llc we introduce and derive four variants for graph construction these variants adopt a two phase llc tpllc compared with the recent 1 graphs our proposed objective function associated with three variants has an analytical solution and thus is more efficient a key element of the proposed methods is the second phase of coding that allows data closeness or locality to be naturally incorporated it performs a coding over some selected relevant samples and reinforces the individual regularization terms by exploiting the coefficients estimated in the first phase comprehensive experimental results using several benchmark datasets show that it can achieve or outperform existing state of the art results furthermore it is shown to be more efficient than the robust 1 graph construction schemes

lagrangian relaxation graph matching abstract graph matching is a fundamental problem in computer vision area graph matching problem that incorporates pair wise constraints can be formulated as an integer quadratic programming iqp problem with affine mapping constraint since it is known to be np hard approximate relaxation methods are usually required to find approximate solutions in this paper we present a new effective graph matching relaxation method called lagrangian relaxation graph matching lrgm which aims to generate a relaxation model by incorporating the affine mapping constraint into the matching objective optimization there are three main benefits of the proposed lrgm method 1 the nonnegative affine mapping constraint encoding one to one mapping is naturally incorporated in lrgm relaxation via lagrangian regularization 2 by further adding a l 1 norm constraint lrgm can generate a sparse solution empirically and thus returns a desired discrete solution for original iqp matching problem 3 an effective update algorithm is derived to solve the proposed lrgm model theoretically the converged solution can be proven to be karush kuhn tucker kkt optimal experimental results on both synthetic data and real world image datasets show the effectiveness and benefits of the proposed lrgm method

topological hypercovers and 1 realizations we show that if u is a hypercover of a topological space x then the natural map hocolim u x is a weak equivalence this fact is used to construct topological realization functors for the 1 homotopy theory of schemes over real and complex fields in an appendix we also prove a theorem about computing homotopy colimits of spaces that are not cofibrant

subspace clustering using a low rank constrained autoencoder the performance of subspace clustering is affected by data representation data representation for subspace clustering maps data from the original space into another space with the property of better separability many data representation methods have been developed in recent years typical among them are low rank representation lrr and an autoencoder lrr is a linear representation method that captures the global structure of data with low rank constraint alternatively an autoencoder nonlinearly maps data into a latent space using a neural network by minimizing the difference between the reconstruction and input to combine the advantages of an lrr globality and autoencoder self supervision based locality we propose a novel data representation method for subspace clustering the proposed method called low rank constrained autoencoder lrae forces the latent representation of the neural network to be of low rank and the low rank constraint is computed as a prior from the input space one major advantage of the lrae is that the learned data representation not only maintains the local features of the data but also preserves the underlying low rank global structure extensive experiments on several datasets for subspace clustering were conducted they demonstrated that the proposed lrae substantially outperformed state of the art subspace clustering methods

algebraic cycles on real varieties and z 2 equivariant homotopy theory in this paper the spaces of algebraic cycles on a real projective variety x are studied as z 2 spaces under the action of the galois group gal c r in particular the equivariant homotopy type of the group of algebraic p cycles zp pc is computed a version of lawson homology for real varieties is proposed the real lawson homology groups are computed for a class of real varieties

pilot aided ofdm channel estimation in the presence of the guard band in this letter pilot design and channel estimation are discussed for orthogonal frequency division multiplexing ofdm systems with guard subcarriers first we investigate the effects of guard band on channel estimation errors from this we propose pilot placement having a maximum distance between adjacent pilots except for the guard band and show that it achieves minimum channel estimation errors among partially equispaced pilots using equivalence of the toeplitz and circulant matrices also an efficient channel estimator is developed by introducing an extended channel and its finite impulse response fir approximation to overcome high numerical complexity caused by the presence of guard subcarriers and the use of a large number of subcarriers simulation results are presented for ofdm and orthogonal frequency division multiple access ofdma systems consistent with ieee 802 16a standards

noise robust semi supervised learning via fast sparse coding this paper presents a novel noise robust graph based semi supervised learning algorithm to deal with the challenging problem of semi supervised learning with noisy initial labels inspired by the successful use of sparse coding for noise reduction we choose to give new l1 norm formulation of laplacian regularization for graph based semi supervised learning since our l1 norm laplacian regularization is explicitly defined over the eigenvectors of the normalized laplacian matrix we formulate graph based semi supervised learning as an l1 norm linear reconstruction problem which can be efficiently solved by sparse coding furthermore by working with only a small subset of eigenvectors we develop a fast sparse coding algorithm for our l1 norm semi supervised learning finally we evaluate the proposed algorithm in noise robust image classification the experimental results on several benchmark datasets demonstrate the promising performance of the proposed algorithm highlightswe propose novel semi supervised learning based on fast sparse coding our algorithm achieves promising results in noise robust image classification our algorithm can readily be extended to many other challenging problems

prime discriminant simplicial complex the structure representation of data distribution plays an important role in understanding the underlying mechanism of generating data in this paper we propose the prime discriminant simplicial complex pdsc by utilizing persistent homology to capture such structures assuming that each class is represented with a prime simplicial complex we classify unlabeled samples based on the nearest projection distances from the samples to the simplicial complexes we also extend the extrapolation ability of these complexes with a projection constraint term experiments in simulated and practical datasets indicate that compared with several published algorithms the proposed pdsc approaches achieve promising performance without losing structure representation

ber minimized ofdm systems with channel independent precoders we consider the minimization of uncoded bit error rate ber for the orthogonal frequency division multiplexing ofdm system with an orthogonal precoder we analyze the ber performance of precoded ofdm systems with zero forcing and minimum mean squared error mmse receivers in the case of mmse receivers we show that for quadrature phase shift keying qpsk there exists a class of optimal precoders that are channel independent examples of this class include the discrete fourier transform dft matrix and the hadamard matrix when the precoder is the dft matrix the resulting optimal transceiver becomes the single carrier system with cyclic prefix sc cp system we also show that the worst solution corresponds to the conventional ofdm system the conventional ofdm system has the largest ber in the case of zero forcing receivers the design of optimal transceiver depends on the signal to noise ratio snr for higher snr solutions of optimal precoders are the same as those of mmse receivers

learning with ell 1 graph for image analysis the graph construction procedure essentially determines the potentials of those graph oriented learning algorithms for image analysis in this paper we propose a process to build the so called directed 1 graph in which the vertices involve all the samples and the ingoing edge weights to each vertex describe its 1 norm driven reconstruction from the remaining samples and the noise then a series of new algorithms for various machine learning tasks e g data clustering subspace learning and semi supervised learning are derived upon the 1 graphs compared with the conventional k nearest neighbor graph and ball graph the 1 graph possesses the advantages 1 greater robustness to data noise 2 automatic sparsity and 3 adaptive neighborhood for individual datum extensive experiments on three real world datasets show the consistent superiority of 1 graph over those classic graphs in data clustering subspace learning and semi supervised learning tasks

generalization as search abstract the problem of concept learning or forming a general description of a class of objects given a set of examples and non examples is viewed here as a search problem existing programs that generalize from examples are characterized in terms of the classes of search strategies that they employ several classes of search strategies are then analyzed and compared in terms of their relative capabilities and computational complexities

harnack thom theorem for higher cycle groups and picard varieties we generalize the harnack thom theorem to relate the ranks of the lawson homology groups with 22 coefficients of a real quasiprojective variety with the ranks of its reduced real lawson homology groups in the case of zero cycle group we recover the classical harnack thom theorem and generalize the classical version to include real quasiprojective varieties we use weil s construction of picard varieties to construct reduced real picard groups and milnor s construction of universal bundles to construct some weak models of classifying spaces of some cycle groups these weak models are used to produce long exact sequences of homotopy groups which are the main tool in computing the homotopy groups of some cycle groups of divisors we obtain some congruences involving the picard number of a nonsingular real projective variety and the rank of its reduced real lawson homology groups of divisors

convex sparse spectral clustering single view to multi view spectral clustering sc is one of the most widely used methods for data clustering it first finds a low dimensional embedding u of data by computing the eigenvectors of the normalized laplacian matrix and then performs k means on text u top to get the final clustering result in this paper we observe that in the ideal case text u text u top should be block diagonal and thus sparse therefore we propose the sparse sc ssc method that extends the sc with sparse regularization on text u text u top to address the computational issue of the nonconvex ssc model we propose a novel convex relaxation of ssc based on the convex hull of the fixed rank projection matrices then the convex ssc model can be efficiently solved by the alternating direction method of multipliers furthermore we propose the pairwise ssc that extends ssc to boost the clustering performance by using the multi view information of data experimental comparisons with several baselines on real world datasets testify to the efficacy of our proposed methods

vanishing theorems for real algebraic cycles we establish the analogue of the friedlander mazur conjecture for teh s reduced lawson homology groups of real varieties which says that the reduced lawson homology of a real quasi projective variety x vanishes in homological degrees larger than the dimension of x in all weights as an application we obtain a vanishing of homotopy groups of the mod 2 topological groups of averaged cycles and a characterization in a range of indices of dos santos real lawson homology as the homotopy groups of the topological group of averaged cycles we also establish an equivariant poincare duality between equivariant friedlander walker real morphic cohomology and dos santos real lawson homology we use this together with an equivariant extension of the mod 2 beilinson lichtenbaum conjecture to compute some real lawson homology groups in terms of bredon cohomology

mtc a fast and robust graph based transductive learning method despite the great success of graph based transductive learning methods most of them have serious problems in scalability and robustness in this paper we propose an efficient and robust graph based transductive classification method called minimum tree cut mtc which is suitable for large scale data motivated from the sparse representation of graph we approximate a graph by a spanning tree exploiting the simple structure we develop a linear time algorithm to label the tree such that the cut size of the tree is minimized this significantly improves graph based methods which typically have a polynomial time complexity moreover we theoretically and empirically show that the performance of mtc is robust to the graph construction overcoming another big problem of traditional graph based methods extensive experiments on public data sets and applications on web spam detection and interactive image segmentation demonstrate our method s advantages in aspect of accuracy speed and robustness

latent semantic learning with structured sparse representation for human action recognition this paper proposes a novel latent semantic learning method for extracting high level latent semantics from a large vocabulary of abundant mid level features i e visual keywords with structured sparse representation which can help to bridge the semantic gap in the challenging task of human action recognition to discover the manifold structure of mid level features we develop a graph based spectral embedding approach to latent semantic learning with the graph over mid level features being constructed using sparse representation moreover we define new l 1 norm hypergraph regularization to induce extra structured sparsity into sparse representation for graph construction due to the nice properties sparsity and noise robustness of such structured sparse representation our graph construction can capture dominant and robust relationships among mid level features which are crucial for the success of latent semantic learning in action recognition unlike the traditional latent semantic analysis based on topic models our latent semantic learning method can explore the manifold structure of mid level features in both graph construction and spectral embedding which results in compact but discriminative high level features the experimental results on the commonly used kth action dataset and unconstrained youtube action dataset show the promising performance of our method

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

a collaborative representation based projections method for feature extraction in graph embedding based methods we usually need to manually choose the nearest neighbors and then compute the edge weights using the nearest neighbors via l2 norm e g lle it is difficult and unstable to manually choose the nearest neighbors in high dimensional space so how to automatically construct a graph is very important in this paper first we give a l2 graph like l1 graph l2 graph calculates the edge weights using the total samples avoiding manually choosing the nearest neighbors second a l2 graph based feature extraction method is presented called collaborative representation based projections crp like spp crp aims to preserve the collaborative representation based reconstruction relationship of data crp utilizes a l2 norm graph to characterize the local compactness information crp maximizes the ratio between the total separability information and the local compactness information to seek the optimal projection matrix crp is much faster than spp since crp calculates the objective function with l2 norm while spp calculate the objective function with l1 norm experimental results on feret ar yale face databases and the polyu finger knuckle print database demonstrate that crp works well in feature extraction and leads to a good recognition performance we give a l2 norm graph based on collaborative representation we propose a collaborative representation based projections crp for feature extraction crp is a rayleigh quotient form and can be calculated via generalized eigenvalue decomposition

robust subspace segmentation via nonconvex low rank representation a nonconvex formulation to determine the low rank representation from contaminated data is proposed we provide a proximal iteratively reweighed algorithm for solving the nonconvex model the proposed nonconvex model can recover the underlying low rank structure of subspaces in spite of noisy corruptions recently low rank representation lrr has been successfully applied to explore subspace segmentation of data in this paper we propose a nonconvex formulation to determine the lrr from contaminated data unlike in traditional methods which directly utilize the nuclear norm to approximate the rank function and penalize noise using the 2 1 norm our method introduces the ky fan p k norm and the 2 q norm to better approximate the rank minimization problem and enhance the robustness against noise an efficient algorithm is derived for solving the novel objective function and this is followed by a rigorous theoretical proof of the convergence extensive experiments on face datasets clearly demonstrate that the proposed methods are more robust to illumination variations corruptions and occlusions

on the selection of the redundant carrier positions in uw ofdm unique word uw ofdm is a new multicarrier technique that was recently proposed in m huemer c hofbauer and j b huber the potential of unique words in ofdm proc inowo hamburg germany sep 2010 pp 140 144 in this technique the guard interval that contains a priori known samples is part of the fft interval to be able to construct the uw ofdm signal some carriers must be sacrificed to transmit redundant information these carriers are called the redundant carriers it turns out that the average redundant energy needed strongly depends on the positions of the redundant carriers in this paper we look for the redundant carrier placement that minimizes the average redundant energy however this optimization is a np hard problem therefore we reformulate the optimization problem and implement a branch and bound b b algorithm to find the optimum the results of the b b search algorithm are compared to a theoretical lower bound and with the results for two low cost redundant carrier placements i e the quasi uniform qu distribution h steendam the quasi uniform redundant carrier placement for uw ofdm vehicular technology conf fall 2012 quebec canada sep 2012 for the case where no guard bands are present and the maximum distance md distribution in case forbidden guard bands are present we show in this paper that when the full band is available for redundant carriers both the redundant carrier placement found with the b b algorithm and the qu distribution result in a redundant energy that is very close to the theoretical lower bound although the b b slightly outperforms the qu distribution this implies that the qu distribution is a good low cost solution to the redundant carrier placement problem in the case of no guard bands however when there are forbidden guard bands in which the redundant carriers cannot be placed the qu distribution can no longer be used in that case the results of the b b algorithm are compared to that of the md distribution we show in this paper that the proposed b b algorithm outperforms the md distribution in the sense that it needs noticeably lower redundant energy

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

a unified framework for representation based subspace clustering of out of sample and large scale data under the framework of spectral clustering the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points some recent works build the graph using sparse low rank and ell 2 norm based representation and have achieved the state of the art performance however these methods have suffered from the following two limitations first the time complexities of these methods are at least proportional to the cube of the data size which make those methods inefficient for solving the large scale problems second they cannot cope with the out of sample data that are not used to construct the similarity graph to cluster each out of sample datum the methods have to recalculate the similarity graph and the cluster membership of the whole data set in this paper we propose a unified framework that makes the representation based subspace clustering algorithms feasible to cluster both the out of sample and the large scale data under our framework the large scale problem is tackled by converting it as the out of sample problem in the manner of sampling clustering coding and classifying furthermore we give an estimation for the error bounds by treating each subspace as a point in a hyperspace extensive experimental results on various benchmark data sets show that our methods outperform several recently proposed scalable methods in clustering a large scale data set

principal graph and structure learning based on reversed graph embedding many scientific datasets are of high dimension and the analysis usually requires retaining the most important structures of data principal curve is a widely used approach for this purpose however many existing methods work only for data with structures that are mathematically formulated by curves which is quite restrictive for real applications a few methods can overcome the above problem but they either require complicated human made rules for a specific task with lack of adaption flexibility to different tasks or cannot obtain explicit structures of data to address these issues we develop a novel principal graph and structure learning framework that captures the local information of the underlying graph structure based on reversed graph embedding as showcases models that can learn a spanning tree or a weighted undirected ell 1 graph are proposed and a new learning algorithm is developed that learns a set of principal points and a graph structure from data simultaneously the new algorithm is simple with guaranteed convergence we then extend the proposed framework to deal with large scale data experimental results on various synthetic and six real world datasets show that the proposed method compares favorably with baselines and can uncover the underlying structure correctly

unsupervised multi class co segmentation via joint cut over l_ 1 manifold hyper graph of discriminative image regions this paper systematically advocates a robust and efficient unsupervised multi class co segmentation approach by leveraging underlying subspace manifold propagation to exploit the cross image coherency it can combat certain image co segmentation difficulties due to viewpoint change partial occlusion complex background transient illumination and cluttering texture patterns our key idea is to construct a powerful hyper graph joint cut framework which incorporates mid level image regions based intra image feature representation and l 1 manifold graph based inter image coherency exploration for local image region generation we propose a bi harmonic distance distribution difference metric to govern the super pixel clustering in a bottom up way it not only affords drastic data reduction but also gives rise to discriminative and structure meaningful feature representation as for the inter image coherency we leverage multi type features involved l 1 graph to detect the underlying local manifold from cross image regions as a result the implicit supervising information could be encoded into the unsupervised hyper graph joint cut framework we conduct extensive experiments and make comprehensive evaluations with other state of the art methods over various benchmarks including icoseg msrc and oxford flower all the results demonstrate the superiorities of our method in terms of accuracy robustness efficiency and versatility

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

quaternionic algebraic cycles and reality in this paper we compute the equivariant homotopy type of spaces of algebraic cycles on real brauer severi varieties under the action of the galois group gal c r appropriate stabilizations of these spaces yield two equivariant spectra the first one classifies dupont seymour s quaternionic k theory and the other one classifies an equivariant cohomology theory 3 which is a natural recipient of characteristic classes kh x 3 x for quaternionic bundles over real spaces x

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

multiple kernel sparse representations for supervised and unsupervised learning in complex visual recognition tasks it is typical to adopt multiple descriptors which describe different aspects of the images for obtaining an improved recognition performance descriptors that have diverse forms can be fused into a unified feature space in a principled manner using kernel methods sparse models that generalize well to the test data can be learned in the unified kernel space and appropriate constraints can be incorporated for application in supervised and unsupervised learning in this paper we propose to perform sparse coding and dictionary learning in the multiple kernel space where the weights of the ensemble kernel are tuned based on graph embedding principles such that class discrimination is maximized in our proposed algorithm dictionaries are inferred using multiple levels of 1d subspace clustering in the kernel space and the sparse codes are obtained using a simple levelwise pursuit scheme empirical results for object recognition and image clustering show that our algorithm outperforms existing sparse coding based approaches and compares favorably to other state of the art methods

from local similarities to global coding a framework for coding applications feature coding has received great attention in recent years as a building block of many image processing algorithms in particular the importance of the locality assumption in coding approaches has been studied in many previous works we review this assumption and claim that using the similarity of data points to a more global set of anchor points does not necessarily weaken the coding method as long as the underlying structure of the anchor points is considered we propose to capture the underlying structure by assuming a random walker over the anchor points we also show that our method is a fast approximation to the diffusion map kernel experiments on various data sets show that with a knowledge of the underlying structure of anchor points different state of the art coding algorithms may boost their performance in different learning tasks by utilizing the proposed method

semi supervised double sparse graphs based discriminant analysis for dimensionality reduction abstract discriminant analysis da is a well known dimensionality reduction tool in pattern classification with enough efficient labeled samples the optimal projections could be found by maximizing the between class scatter variance meanwhile minimizing the within class scatter variance however the acquisition of label information is difficult in practice so semi supervised discriminant analysis has attracted much attention in recent years where both few labeled samples and many unlabeled samples are utilized during learning process sparse graph learned by sparse representation contains local structure information about data and is widely employed in dimensionality reduction in this paper semi supervised double sparse graphs sdsg based dimensionality reduction is proposed which considers both the positive and negative structure relationship of data points by using double sparse graphs aiming to explore the discriminant information among unlabeled samples joint k nearest neighbor selection strategy is proposed to select pseudo labeled samples which contain some precise discriminant information in the following procedures the data subset consisting of labeled samples and pseudo labeled samples are used instead of the original data based on two different criterions two sdsg based discriminant analysis methods are designed and denoted by sdsg dda distance based da and sdsg rda reconstruction based da which also use different strategies to reduce the effect of pseudo labels inaccuracy finally the experimental results both on uci datasets and hyperspectral images validate the effectiveness and advantage of the proposed methods compared with some classical dimensionality reduction methods

acquiring linear subspaces for face recognition under variable lighting previous work has demonstrated that the image variation of many objects human faces in particular under variable lighting can be effectively modeled by low dimensional linear spaces even when there are multiple light sources and shadowing basis images spanning this space are usually obtained in one of three ways a large set of images of the object under different lighting conditions is acquired and principal component analysis pca is used to estimate a subspace alternatively synthetic images are rendered from a 3d model perhaps reconstructed from images under point sources and again pca is used to estimate a subspace finally images rendered from a 3d model under diffuse lighting based on spherical harmonics are directly used as basis images in this paper we show how to arrange physical lighting so that the acquired images of each object can be directly used as the basis vectors of a low dimensional linear space and that this subspace is close to those acquired by the other methods more specifically there exist configurations of k point light source directions with k typically ranging from 5 to 9 such that by taking k images of an object under these single sources the resulting subspace is an effective representation for recognition under a wide range of lighting conditions since the subspace is generated directly from real images potentially complex and or brittle intermediate steps such as 3d reconstruction can be completely avoided nor is it necessary to acquire large numbers of training images or to physically construct complex diffuse harmonic light fields we validate the use of subspaces constructed in this fashion within the context of face recognition

structure constrained low rank representation benefiting from its effectiveness in subspace segmentation low rank representation lrr and its variations have many applications in computer vision and pattern recognition such as motion segmentation image segmentation saliency detection and semisupervised learning it is known that the standard lrr can only work well under the assumption that all the subspaces are independent however this assumption cannot be guaranteed in real world problems this paper addresses this problem and provides an extension of lrr named structure constrained lrr sc lrr to analyze the structure of multiple disjoint subspaces which is more general for real vision data we prove that the relationship of multiple linear disjoint subspaces can be exactly revealed by sc lrr with a predefined weight matrix as a nontrivial byproduct we also illustrate that sc lrr can be applied for semisupervised learning the experimental results on different types of vision problems demonstrate the effectiveness of our proposed method

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

elastic net hypergraph learning for image clustering and semi supervised classification graph model is emerging as a very effective tool for learning the complex structures and relationships hidden in data in general the critical purpose of graph oriented learning algorithms is to construct an informative graph for image clustering and classification tasks in addition to the classical k nearest neighbor and r neighborhood methods for graph construction l 1 graph and its variants are emerging methods for finding the neighboring samples of a center datum where the corresponding ingoing edge weights are simultaneously derived by the sparse reconstruction coefficients of the remaining samples however the pairwise links of l 1 graph are not capable of capturing the high order relationships between the center datum and its prominent data in sparse reconstruction meanwhile from the perspective of variable selection the l 1 norm sparse constraint regarded as a lasso model tends to select only one datum from a group of data that are highly correlated and ignore the others to simultaneously cope with these drawbacks we propose a new elastic net hypergraph learning model which consists of two steps in the first step the robust matrix elastic net model is constructed to find the canonically related samples in a somewhat greedy way achieving the grouping effect by adding the l 2 penalty to the l 1 constraint in the second step hypergraph is used to represent the high order relationships between each datum and its prominent samples by regarding them as a hyperedge subsequently hypergraph laplacian matrix is constructed for further analysis new hypergraph learning algorithms including unsupervised clustering and multi class semi supervised classification are then derived extensive experiments on face and handwriting databases demonstrate the effectiveness of the proposed method

rational isomorphisms between k theories and cohomology theories the well known isomorphism relating the rational algebraic k theory groups and the rational motivic cohomology groups of a smooth variety over a field of characteristic 0 is shown to be realized by a map the segre map of infinite loop spaces moreover the associated chern character map on rational homotopy groups is shown to be a ring isomorphism a technique is introduced that establishes a useful general criterion for a natural transformation of functors on quasi projective complex varieties to induce a homotopy equivalence of semi topological singular complexes since semi topological k theory and morphic cohomology can be formulated as the semi topological singular complexes associated to algebraic k theory and motivic cohomology this criterion provides a rational isomorphism between the semi topological k theory groups and the morphic cohomology groups of a smooth complex variety consequences include a riemann roch theorem for the chern character on semi topological k theory and an interpretation of the topological filtration on singular cohomology groups in k theoretic terms

low rank preserving embedding abstract in this paper we consider the problem of linear dimensionality reduction with the novel technique of low rank representation which is a promising tool of discovering subspace structures of given data existing approaches based on graph embedding usually capture structure of data via stacking the local structure of each datum such as neighborhood graph l1 graph and l2 graph yet they lack explicit discrimination between those local structures and suffer from corrupted samples to this end we propose a new linear dimensionality reduction method by virtue of the lowest rank representation lrr of data which is dubbed low rank preserving embedding lrpe different from the traditional routes lrpe achieves all data self representations jointly and can thus extract the global structure of a data set as a whole the global low rank constraint explicitly enforces the lrr matrix to be block diagonal form so that the samples with a similar intrinsic structure which are more likely to be from the same class are described by a similar set of bases hence lrpe is discriminative even if no class labels are provided benefiting from the robust lrr lrpe is also robust to various noises and errors in data besides we rewritten all related methods into a unified formulation followed by a detailed solution and clear comparisons finally we conduct extensive experiments on publicly available data sets for data visualization and classification the inspiring experimental results show the effectiveness the cheap computation and the robustness of the proposed method

joint sparse representation and embedding propagation learning a framework for graph based semisupervised learning in this paper we propose a novel graph based semisupervised learning framework called joint sparse representation and embedding propagation learning jsrepl the idea of jsrepl is to join epl with sparse representation to perform label propagation like most of graph based semisupervised propagation learning algorithms jsrepl also constructs weights graph matrix from given data different from classical approaches which build weights graph matrix and estimate the labels of unlabeled data in sequence jsrepl simultaneously builds weights graph matrix and estimates the labels of unlabeled data we also propose an efficient algorithm to solve the proposed problem the proposed method is applied to the problem of semisupervised image clustering using the orl yale pie and yaleb data sets our experiments demonstrate the effectiveness of our proposed algorithm

an image segmentation method based on network clustering model abstract network clustering phenomena are ubiquitous in nature and human society in this paper a method involving a network clustering model is proposed for mass segmentation in mammograms first the watershed transform is used to divide an image into regions and features of the image are computed then a graph is constructed from the obtained regions and features the network clustering model is applied to realize clustering of nodes in the graph compared with two classic methods the algorithm based on the network clustering model performs more effectively in experiments

learning locality constrained collaborative representation for robust face recognition abstract the models of low dimensional manifold and sparse representation are two well known concise models that suggest that each data can be described by a few characteristics manifold learning is usually investigated for dimension reduction by preserving some expected local geometric structures from the original space into a low dimensional one the structures are generally determined by using pairwise distance e g euclidean distance alternatively sparse representation denotes a data point as a linear combination of the points from the same subspace in practical applications however the nearby points in terms of pairwise distance may not belong to the same subspace and vice versa consequently it is interesting and important to explore how to get a better representation by integrating these two models together to this end this paper proposes a novel coding algorithm called locality constrained collaborative representation lccr which introduce a kind of local consistency into coding scheme to improve the discrimination of the representation the locality term derives from a biologic observation that the similar inputs have similar codes the objective function of lccr has an analytical solution and it does not involve local minima the empirical studies based on several popular facial databases show that lccr is promising in recognizing human faces with varying pose expression and illumination as well as various corruptions and occlusions