lle score a new filter based unsupervised feature selection method based on nonlinear manifold embedding and its application to image recognition the task of feature selection is to find the most representative features from the original high dimensional data because of the absence of the information of class labels selecting the appropriate features in unsupervised learning scenarios is much harder than that in supervised scenarios in this paper we investigate the potential of locally linear embedding lle which is a popular manifold learning method in feature selection task it is straightforward to apply the idea of lle to the graph preserving feature selection framework however we find that this straightforward application suffers from some problems for example it fails when the elements in the feature are all equal it does not enjoy the property of scaling invariance and cannot capture the change of the graph efficiently to solve these problems we propose a new filter based feature selection method based on lle in this paper which is named as lle score the proposed criterion measures the difference between the local structure of each feature and that of the original data our experiments of classification task on two face image data sets an object image data set and a handwriting digits data set show that lle score outperforms state of the art methods including data variance laplacian score and sparsity score

discriminative least squares regression for multiclass classification and feature selection this paper presents a framework of discriminative least squares regression lsr for multiclass classification and feature selection the core idea is to enlarge the distance between different classes under the conceptual framework of lsr first a technique called e dragging is introduced to force the regression targets of different classes moving along opposite directions such that the distances between classes can be enlarged then the e draggings are integrated into the lsr model for multiclass classification our learning framework referred to as discriminative lsr has a compact model form where there is no need to train two class machines that are independent of each other with its compact form this model can be naturally extended for feature selection this goal is achieved in terms of l2 1 norm of matrix generating a sparse learning model for feature selection the model for multiclass classification and its extension for feature selection are finally solved elegantly and efficiently experimental evaluation over a range of benchmark datasets indicates the validity of our method

semisupervised feature selection via spline regression for video semantic recognition to improve both the efficiency and accuracy of video semantic recognition we can perform feature selection on the extracted video features to select a subset of features from the high dimensional feature set for a compact and accurate video data representation provided the number of labeled videos is small supervised feature selection could fail to identify the relevant features that are discriminative to target classes in many applications abundant unlabeled videos are easily accessible this motivates us to develop semisupervised feature selection algorithms to better identify the relevant video features which are discriminative to target classes by effectively exploiting the information underlying the huge amount of unlabeled video data in this paper we propose a framework of video semantic recognition by semisupervised feature selection via spline regression rm s 2 rm fs 2 rm r two scatter matrices are combined to capture both the discriminative information and the local geometry structure of labeled and unlabeled training videos a within class scatter matrix encoding discriminative information of labeled training videos and a spline scatter output from a local spline regression encoding data distribution an ell 2 1 norm is imposed as a regularization term on the transformation matrix to ensure it is sparse in rows making it particularly suitable for feature selection to efficiently solve rm s 2 rm fs 2 rm r we develop an iterative algorithm and prove its convergency in the experiments three typical tasks of video semantic recognition such as video concept detection video classification and human action recognition are used to demonstrate that the proposed rm s 2 rm fs 2 rm r achieves better performance compared with the state of the art methods

spin and wedge representations of infinite dimensional lie algebras and groups abstract we suggest a purely algebraic construction of the spin representation of an infinite dimensional orthogonal lie algebra sections 1 and 2 and a corresponding group section 4 from this we deduce a construction of all level one highest weight representations of orthogonal affine lie algebras in terms of creation and annihilation operators on an infinite dimensional grassmann algebra section 3 we also give a similar construction of the level one representations of the general linear affine lie algebra in an infinite dimensional wedge space along these lines we construct the corresponding representations of the universal central extension of the group sln k t t 1 in spaces of sections of line bundles over infinite dimensional homogeneous spaces section 5

robust lp norm least squares support vector regression with feature selection lp norm least squares support vector regression lp lssvr is proposed for feature selection in regression using the absolute constraint and the lp norm regularization term lp lssvr performs robust against outliers lp lssvr ensures the useful features to be selected based on theoretical analysis lp lssvr only solves a series of linear equations leading to fast training speed in this paper we aim a novel algorithm called robust lp norm least squares support vector regression lp lssvr that is more robust than the traditional least squares support vector regression ls svr using the absolute constraint and the lp norm regularization term our lp lssvr performs robust against outliers moreover though the optimization problem is non convex the sparse solution of lp norm and the lower bonds for nonzero components technique ensure useful features selected by lp lssvr and it helps to find the local optimum of our lp lssvr experimental results show that although lp lssvr is more robust than least squares support vector regression ls svr and much faster than lp norm support vector regression lp svr and svr due to its equality constraint it is slower than ls svr and l1 norm support vector regression l1 svr it is as effective as lp svr l1 svr ls svr and svr in both feature selection and regression

the branching rules of conformal embeddings after recalling the main properties of a conformal embedding of lie algebras g id p which is defined by the equality of the sugawara central charges on both sides we launch a systematic study of their branching rules the bulk of the paper is devoted to the proof of a general formula in the case suim su m n su m at the end we give some applications to the con struction of modular invariant partition functions

a construction of the c 1 modular invariant partition functions decomposition theorems for certain representations of kac moody algebras which are needed for the construction of modular invariant unitary conformal models are proved it is shown that allc 1 modular invariant models can then be recovered from gauged free fermionic models including the exceptional cases

compound rank k projections for bilinear analysis in many real world applications data are represented by matrices or high order tensors despite the promising performance the existing 2 d discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection making the model less flexible in this paper we propose a novel compound rank k projection crp algorithm for bilinear analysis the crp deals with matrices directly without transforming them into vectors and it therefore preserves the correlations within the matrix and decreases the computation complexity different from the existing 2 d discriminant analysis algorithms objective function values of crp increase monotonically in addition the crp utilizes multiple rank k projection models to enable a larger search space in which the optimal solution can be found in this way the discriminant ability is enhanced we have tested our approach on five data sets including uuim cvl pointing 04 usps and coil20 experimental results show that the performance of our proposed crp performs better than other algorithms in terms of classification accuracy

on finite subgroups of su 2 simple lie algebras and the mckay correspondence the question is considered of how the restriction n where n is irreducible for all n and is a finite subgroup of su 2 decomposes into irreducibles for any arbitrary n unk it is announced that using the mckay correspondence the problem has an elegant solution in terms of the coxeter element for the associated lie algebra and that the numbers involved come in a beautiful way from the root structure

on the approximability of minimizing nonzero variables or unsatisfied relations in linear systems we investigate the computational complexity of two closely related classes of combinatorial optimization problems for linear systems which arise in various fields such as machine learning operations research and pattern recognition in the first class min ulr one wishes given a possibly infeasible system of linear relations to find a solution that violates as few relations as possible while satisfying all the others in the second class min rvls the linear system is supposed to be feasible and one looks for a solution with as few nonzero variables as possible for both min ulr and min rvls the four basic types of relational operators and are considered while min rvls with equations was mentioned to be np hard in garey and johnson 1979 we established in amaldi 1992 amaldi and kann 1995 that min ulr with equalities and inequalities are np hard even when restricted to homogeneous systems with bipolar coefficients the latter problems have been shown hard to approximate in arora et al 1993 in this paper we determine strong bounds on the approximability of various variants of min rvls and min ulr including constrained ones where the variables are restricted to take binary values or where some relations are mandatory while others are optional the various np hard versions turn out to have different approximability properties depending on the type of relations and the additional constraints but none of them can be approximated within any constant factor unless p np particular attention is devoted to two interesting special cases that occur in discriminant analysis and machine learning in particular we disprove a conjecture of van horn and martinez 1992 regarding the existence of a polynomial time algorithm to design linear classifiers or perceptrons that involve a close to minimum number of features

snr of generalized diversity selection combining with nonidentical rayleigh fading statistics a closed form expression for the average signal to noise ratio snr of generalized diversity selection combining using the m largest in instantaneous snr diversity signals for arbitrary m assuming that the rayleigh fading statistics on each diversity branch are identically independently distributed i i d already exists in the literature in this paper a similar closed form expression but for nonidentically distributed statistics is derived this expression specializes to known results such as the average snrs of maximal ratio combining with either i i d or non i i d diversity statistics and that of conventional selection combining csc with i i d diversity statistics in addition it provides for the first time a simple closed form solution to the combined snr of csc with non i i d diversity statistics further the closed form solution for the snr of selecting the m largest diversity signals has negligible computational complexity

average level crossing rate and average outage duration of generalized selection combining the paper presents an analytical methodology for the evaluation of the average level crossing rate and the average outage duration of generalized selection combining more specifically it presents a general approach when this scheme is employed over independent but not necessarily identically distributed fading channels the general approach is then specialized to independent identically distributed rayleigh fading paths selected numerical examples and plots are also provided and discussed

on holomorphic factorization of wzw and coset models it is shown how coupling to gauge fields can be used to explain the basic facts concerning holomorphic factorization of the wzw model of two dimensional conformal field theory which previously have been understood primarily by using conformal field theory ward identities we also consider in a similar vein the holomorphic factorization ofg h coset models we discuss theg g model as a topological field theory and comment on a conjecture by spiegelglas

conformal embeddings rank level duality and exceptional modular invariants we compute the branching rules of the conformal embeddingsso 4nk 1 sp 2n k sp 2k n andso rq 1 so r q so q r forrq even using this we prove that the affine algebrassp 2n k andsp 2k n have the sames matrix and modular invariants as a second application we show how the triality ofso 8 leads to an exceptional modular invariant forsu 2 at level 16 and for allso q 4 at level 8

an mgf based performance analysis of generalized selection combining over rayleigh fading channels using the notion of the spacing between ordered exponential random variables a performance analysis of the generalized selection combining gsc diversity scheme over rayleigh fading channels is presented and compared with that of the conventional maximal ratio combining and selection combining schemes starting with the moment generating function mgf of the gsc output signal to noise ratio snr we derive closed form expressions for the average combined snr outage probability and average error probability of a wide variety of modulation schemes operating over independently identically distributed i i d diversity paths because of their simple form these expressions readily allow numerical evaluation for cases of practical interest the results are also extended to the case of non i i d diversity paths

effective discriminative feature selection with nontrivial solution feature selection and feature transformation the two main ways to reduce dimensionality are often presented separately in this paper a feature selection method is proposed by combining the popular transformation based dimensionality reduction method linear discriminant analysis lda and sparsity regularization we impose row sparsity on the transformation matrix of lda through ell 2 1 norm regularization to achieve feature selection and the resultant formulation optimizes for selecting the most discriminative features and removing the redundant ones simultaneously the formulation is extended to the ell 2 p norm regularized case which is more likely to offer better sparsity when 0 thus the formulation is a better approximation to the feature selection problem an efficient algorithm is developed to solve the ell 2 p norm based optimization problem and it is proved that the algorithm converges when 0 systematical experiments are conducted to understand the work of the proposed method promising experimental results on various types of real world data sets demonstrate the effectiveness of our algorithm

top k feature selection framework using robust 0 1 integer programming feature selection fs which identifies the relevant features in a data set to facilitate subsequent data analysis is a fundamental problem in machine learning and has been widely studied in recent years most fs methods rank the features in order of their scores based on a specific criterion and then select the k top ranked features where k is the number of desired features however these features are usually not the top k features and may present a suboptimal choice to address this issue we propose a novel fs framework in this article to select the exact top k features in the unsupervised semisupervised and supervised scenarios the new framework utilizes the l0 2 norm as the matrix sparsity constraint rather than its relaxations such as the l1 2 norm since the l0 2 norm constrained problem is difficult to solve we transform the discrete l0 2 norm based constraint into an equivalent 0 1 integer constraint and replace the 0 1 integer constraint with two continuous constraints the obtained top k fs framework with two continuous constraints is theoretically equivalent to the l0 2 norm constrained problem and can be optimized by the alternating direction method of multipliers admm unsupervised and semisupervised fs methods are developed based on the proposed framework and extensive experiments on real world data sets are conducted to demonstrate the effectiveness of the proposed fs framework

adaptive unsupervised feature selection with structure regularization feature selection is one of the most important dimension reduction techniques for its efficiency and interpretation since practical data in large scale are usually collected without labels and labeling these data are dramatically expensive and time consuming unsupervised feature selection has become a ubiquitous and challenging problem without label information the fundamental problem of unsupervised feature selection lies in how to characterize the geometry structure of original feature space and produce a faithful feature subset which preserves the intrinsic structure accurately in this paper we characterize the intrinsic local structure by an adaptive reconstruction graph and simultaneously consider its multiconnected components multicluster structure by imposing a rank constraint on the corresponding laplacian matrix to achieve a desirable feature subset we learn the optimal reconstruction graph and selective matrix simultaneously instead of using a predetermined graph we exploit an efficient alternative optimization algorithm to solve the proposed challenging problem together with the theoretical analyses on its convergence and computational complexity finally extensive experiments on clustering task are conducted over several benchmark data sets to verify the effectiveness and superiority of the proposed unsupervised feature selection algorithm

unsupervised feature selection by regularized self representation by removing the irrelevant and redundant features feature selection aims to find a compact representation of the original feature with good generalization ability with the prevalence of unlabeled data unsupervised feature selection has shown to be effective in alleviating the curse of dimensionality and is essential for comprehensive analysis and understanding of myriads of unlabeled high dimensional data motivated by the success of low rank representation in subspace clustering we propose a regularized self representation rsr model for unsupervised feature selection where each feature can be represented as the linear combination of its relevant features by using l 2 1 norm to characterize the representation coefficient matrix and the representation residual matrix rsr is effective to select representative features and ensure the robustness to outliers if a feature is important then it will participate in the representation of most of other features leading to a significant row of representation coefficients and vice versa experimental analysis on synthetic and real world data demonstrates that the proposed method can effectively identify the representative features outperforming many state of the art unsupervised feature selection methods in terms of clustering accuracy redundancy reduction and classification accuracy highlightsa regularized self representation rsr model is proposed for unsupervised feature selection an iterative reweighted least squares algorithm is proposed to solve the rsr model the proposed method shows superior performance to state of the art

ser and outage of threshold based hybrid selection maximal ratio combining over generalized fading channels the average symbol error rate and outage probability of threshold based hybrid selection maximal ratio combining t hs mrc in generalized fading environments are analyzed a t hs mrc combiner chooses the combined branches according to a predetermined normalized threshold and the strength of the instantaneous signal to noise ratio snr of each branch therefore the number of combined branches is a random variable rather than a fixed number as in conventional hybrid selection maximal ratio combining h s mrc using the moment generating function method a unified analysis of t hs mrc over various slow and frequency nonselective fading channels is presented both independent identically distributed and independent nonidentically distributed diversity branches are considered the derivation allows different m ary linear modulation schemes the theory is illustrated using coherent m ary phase shift keying in nakagami m fading as an example it is shown that previous published results are incorrect

a compact performance analysis of generalized selection combining with independent but nonidentically distributed rayleigh fading paths we derive a compact expression for the moment generating function mgf of the output of a generalized selection combiner for independent but nonidentically distributed rayleigh fading paths which is then used to derive a single integral expression for the symbol error probability of for example m psk because of the simple product form of the mgf and its ability to be expressed as a partial fraction expansion we are then able to invert this function to derive the probability density function and cumulative distribution function of the combiner output from which the outage probability can then be evaluated in closed form an example of the latter is given for an exponentially decaying power delay profile

quantum field theories in one and two dimensions axiomes pour les theories de champ quantiques theories quantiques du champ a une dimension theories quantiques du champ chirales a 2 dimensions

sparse subspace clustering algorithm theory and applications many real world problems deal with collections of high dimensional data such as images videos text and web documents dna microarray data and more often such high dimensional data lie close to low dimensional structures corresponding to several classes or categories to which the data belong in this paper we propose and study an algorithm called sparse subspace clustering to cluster data points that lie in a union of low dimensional subspaces the key idea is that among the infinitely many possible representations of a data point in terms of other points a sparse representation corresponds to selecting a few points from the same subspace this motivates solving a sparse optimization program whose solution is used in a spectral clustering framework to infer the clustering of the data into subspaces since solving the sparse optimization program is in general np hard we consider a convex relaxation and show that under appropriate conditions on the arrangement of the subspaces and the distribution of the data the proposed minimization program succeeds in recovering the desired sparse representations the proposed algorithm is efficient and can handle data points near the intersections of subspaces another key advantage of the proposed algorithm with respect to the state of the art is that it can deal directly with data nuisances such as noise sparse outlying entries and missing entries by incorporating the model of the data into the sparse optimization program we demonstrate the effectiveness of the proposed algorithm through experiments on synthetic data as well as the two real world problems of motion segmentation and face clustering

subspace clustering guided unsupervised feature selection unsupervised feature selection ufs aims to reduce the time complexity and storage burden improve the generalization ability of learning machines by removing the redundant irrelevant and noisy features due to the lack of training labels most existing ufs methods generate the pseudo labels by spectral clustering matrix factorization or dictionary learning and convert ufs to a supervised problem the learned clustering labels reflect the data distribution with respect to classes and therefore are vital to the ufs performance in this paper we proposed a novel subspace clustering guided unsupervised feature selection scufs method the clustering labels of the training samples are learned by representation based subspace clustering and features that can well preserve the cluster labels are selected scufs can well learn the data distribution in that it uncovers the underlying multi subspace structure of the data and iteratively learns the similarity matrix and clustering labels experimental results on benchmark datasets for unsupervised feature selection show that scufs outperforms the state of the art ufs methods highlightsa novel subspace clustering guided unsupervised feature selection scufs model is proposed scufs learns a similarity graph by self representation of samples and can uncover the underlying multi subspace structure of data the iterative updating of similarity graph and pseudo label matrix can learn a more accurate data distribution