on an integral type operator from the bloch space to mixed norm spaces let be a holomorphic self map of b and g h b such that g 0 0 where h b is the space of all holomorphic functions on the unit ball b of c n in this paper we investigate the following integral type operator d g f z 0 1 d f t z g t z d t t f h b where d f is the fractional derivative of f h b the boundedness and compactness of the operators d g between mixed norm spaces and bloch spaces in the unit ball are studied

manifold regularization a geometric framework for learning from labeled and unlabeled examples we propose a family of learning algorithms based on a new form of regularization that allows us to exploit the geometry of the marginal distribution we focus on a semi supervised framework that incorporates labeled and unlabeled data in a general purpose learner some transductive graph learning algorithms and standard methods including support vector machines and regularized least squares can be obtained as special cases we use properties of reproducing kernel hilbert spaces to prove new representer theorems that provide theoretical basis for the algorithms as a result in contrast to purely graph based approaches we obtain a natural out of sample extension to novel examples and so are able to handle both transductive and truly semi supervised settings we present experimental evidence suggesting that our semi supervised algorithms are able to use unlabeled data effectively finally we have a brief discussion of unsupervised and fully supervised learning within our general framework

extended cesaro operators on bergman spaces we define an extended cesaro operator tg with holomorphic symbol g in the unit ball b of cn for a large class of weights w we characterize those g for which tg is bounded or compact from bergman space lpa w b to lqa w b 0 p q in addition we obtain some results about equivalent norms the norm of point evaluation functionals and the interpolation sequences on lpa w b

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

fast nonnegative matrix factorization an active set like method and comparisons nonnegative matrix factorization nmf is a dimension reduction method that has been widely used for numerous applications including text mining computer vision pattern discovery and bioinformatics a mathematical formulation for nmf appears as a nonconvex optimization problem and various types of algorithms have been devised to solve the problem the alternating nonnegative least squares anls framework is a block coordinate descent approach for solving nmf which was recently shown to be theoretically sound and empirically efficient in this paper we present a novel algorithm for nmf based on the anls framework our new algorithm builds upon the block principal pivoting method for the nonnegativity constrained least squares problem that overcomes a limitation of the active set method we introduce ideas that efficiently extend the block principal pivoting method within the context of nmf computation our algorithm inherits the convergence property of the anls framework and can easily be extended to other constrained nmf formulations extensive computational comparisons using data sets that are from real life applications as well as those artificially generated show that the proposed algorithm provides state of the art performance in terms of computational speed

on an integral type operator from logarithmic bloch type and mixed norm spaces to bloch type spaces abstract this paper studies the boundedness and compactness of the following integral type operator recently introduced by this author p g f z 0 1 f t z g t z d t t z b where is a holomorphic self map of the unit ball b in c n and g is a holomorphic function on b such that g 0 0 from logarithmic bloch type and mixed norm spaces to bloch type spaces

iterated differentiation followed by composition from bloch type spaces to weighted bmoa spaces abstract let be a holomorphic self map of the open unit disk d and h d the class of holomorphic functions on d for n n 0 define an operator by c d n f f n f h d we characterize the boundedness and compactness of operator c d n from bloch type spaces to weighted bmoa spaces

graph regularized restricted boltzmann machine the restricted boltzmann machine rbm has received an increasing amount of interest in recent years it determines good mapping weights that capture useful latent features in an unsupervised manner the rbm and its generalizations have been successfully applied to a variety of image classification and speech recognition tasks however most of the existing rbm based models disregard the preservation of the data manifold structure in many real applications the data generally reside on a low dimensional manifold embedded in high dimensional ambient space in this brief we propose a novel graph regularized rbm to capture features and learning representations explicitly considering the local manifold structure of the data by imposing manifold based locality that preserves constraints on the hidden layer of the rbm the model ultimately learns sparse and discriminative representations the representations can reflect data distributions while simultaneously preserving the local manifold structure of data we test our model using several benchmark image data sets for unsupervised clustering and supervised classification problem the results demonstrate that the performance of our method exceeds the state of the art alternatives

on a product type operator from weighted bergman orlicz space to some weighted type spaces let d z c z 1 be the open unit disk an analytic self map of d and an analytic function on d let d be the differentiation operator and w the weighted composition operator the boundedness and compactness of the product type operator dw from the weighted bergman orlicz space to the bers type space weighted bloch space and weighted zygmund space on d are characterized

adaptive method for nonsmooth nonnegative matrix factorization nonnegative matrix factorization nmf is an emerging tool for meaningful low rank matrix representation in nmf explicit constraints are usually required such that nmf generates desired products or factorizations especially when the products have significant sparseness features it is known that the ability of nmf in learning sparse representation can be improved by embedding a smoothness factor between the products motivated by this result we propose an adaptive nonsmooth nmf ans nmf method in this paper in our method the embedded factor is obtained by using a data related approach so it matches well with the underlying products implying a superior faithfulness of the representations besides due to the usage of an adaptive selection scheme to this factor the sparseness of the products can be separately constrained leading to wider applicability and interpretability furthermore since the adaptive selection scheme is processed through solving a series of typical linear programming problems it can be easily implemented simulations using computer generated data and real world data show the advantages of the proposed ans nmf method over the state of the art methods

concept factorization with adaptive neighbors for document clustering in this paper a novel concept factorization cf method called cf with adaptive neighbors cfans is proposed the idea of cfan is to integrate an ans regularization constraint into the cf decomposition the goal of cfan is to extract the representation space that maintains geometrical neighborhood structure of the data similar to the existing graph regularized cf cfan builds a neighbor graph weights matrix the key difference is that the cfan performs dimensionality reduction and finds the neighbor graph weights matrix simultaneously an efficient algorithm is also derived to solve the proposed problem we apply the proposed method to the problem of document clustering on the 20 newsgroups reuters 21578 and tdt2 document data sets our experiments demonstrate the effectiveness of the method

spectral properties of the alignment matrices in manifold learning local methods for manifold learning generate a collection of local parameterizations which is then aligned to produce a global parameterization of the underlying manifold the alignment procedure is carried out through the computation of a partial eigendecomposition of a so called alignment matrix in this paper we present an analysis of the eigenstructure of the alignment matrix giving both necessary and sufficient conditions under which the null space of the alignment matrix recovers the global parameterization we show that the gap in the spectrum of the alignment matrix is proportional to the square of the size the precise definition of the size is given in section sec sp of the overlap of the local parameterizations thus deriving a quantitative measure of how stably the null space can be computed numerically we also give a perturbation analysis of the null space of the alignment matrix when the computation of the local parameterizations is subject to error our analysis provides insights into the behaviors and performance of local manifold learning algorithms

low rank matrix approximation with manifold regularization this paper proposes a new model of low rank matrix factorization that incorporates manifold regularization to the matrix factorization superior to the graph regularized nonnegative matrix factorization this new regularization model has globally optimal and closed form solutions a direct algorithm for data with small number of points and an alternate iterative algorithm with inexact inner iteration for large scale data are proposed to solve the new model a convergence analysis establishes the global convergence of the iterative algorithm the efficiency and precision of the algorithm are demonstrated numerically through applications to six real world datasets on clustering and classification performance comparison with existing algorithms shows the effectiveness of the proposed method for low rank factorization in general

on blog to qlogp pullbacks abstract we characterize the boundedness and the compactness of composition operators acting on the weighted bloch space b log generalizing previous results and answering to a question of r yoneda

generalized product type operators from weighted bergman orlicz spaces to bloch orlicz spaces let d be the open unit disk in the complex plane an analytic self map of d and an analytic function on d let dn be the nth differentiation operator and w the weighted composition operator in this paper the boundedness and compactness of the generalized product type operators dnw and w dn from weighted bergman orlicz spaces to bloch orlicz spaces are characterized

extended cesaro operators between bloch type spaces in the unit ball of cn abstract in this paper we characterize those holomorphic symbols in the unit ball of c n for which the induced extended cesaro operator t b b respectively b 0 b 0 is bounded or compact where and are normal functions on 0 1 in addition we obtain some properties of those spaces b and b 0

composition operators from bloch type spaces into qk type spaces supposeis an analytic map of the unit disk d into itself x is a banach space of analytic functions on d define the composition operator c cf f for all f x in this paper the boundedness and compactness of the composition operators from bloch spaces into qk p q and qk 0 p q spaces are discussed where 0 keywords composition operator analytic function bspace k carleson measure compact k carleson measure

stabilisation of second order nonlinear equations with variable delay for a wide class of second order nonlinear non autonomous models we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal allows to stabilise unstable motions of the system the delays are variable which leads to more flexible controls permitting delay perturbations only delay bounds are significant for stabilisation by a delayed control the results are applied to the sunflower equation which has an infinite number of equilibrium points

compact composition operators on the bloch space necessary and sufficient conditions are given for a composition operator cof f o q to be compact on the bloch space w and on the little bloch space o weakly compact composition operators on o are shown to be compact if q e o is a conformal mapping of the unit disk d into itself whose image q d approaches the unit circle t only in a finite number of nontangential cusps then co is compact on 7o on the other hand if there is a point of t n q d at which q d does not have a cusp then co is not compact

products of volterra type operator and composition operator from h and bloch spaces to zygmund spaces the boundedness and compactness of the products of volterra type operators and composition operators from the space of bounded analytic functions and the bloch space to the zygmund space are discussed in this paper

products of integral type operators and composition operators between bloch type spaces a complete picture on the boundedness and compactness of the products of integral type operators and composition operators between bloch type spaces of holomorphic functions on the unit disk is given in this paper

compact differences of weighted composition operators from weighted bergman spaces to weighted type spaces abstract we characterize the compactness of differences of weighted composition operators from the weighted bergman space a p 0 1 to the weighted type space h v of analytic functions on the open unit disk d in terms of inducing symbols 1 2 d d and u 1 u 2 d c for the case 1

cesaro operators on hardy spaces in the unit ball this article establishes the boundedness of the generalized cesaro operator on holomorphic hardy spaces in the unit ball the approach consists in writing the generalized cesaro operator as a composition of certain integral operators

enhancing low rank subspace clustering by manifold regularization recently low rank representation lrr method has achieved great success in subspace clustering sc which aims to cluster the data points that lie in a union of low dimensional subspace given a set of data points lrr seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself however lrr only considers the global euclidean structure while the local manifold structure which is often important for many real applications is ignored in this paper to exploit the local manifold structure of the data a manifold regularization characterized by a laplacian graph has been incorporated into lrr leading to our proposed laplacian regularized lrr laplrr an efficient optimization procedure which is based on alternating direction method of multipliers admm is developed for laplrr experimental results on synthetic and real data sets are presented to demonstrate that the performance of lrr has been enhanced by using the manifold regularization

generalized composition operators on zygmund spaces and bloch type spaces the boundedness and compactness of the generalized composition operator on zygmund spaces and bloch type spaces are investigated in this paper

asymptotic expansion for the initial value problem of the sunflower equation abstract in this paper we consider the initial value problem ivp for the sunflower equation ex t ax t b sin x t e 0 with x t t t e 0 x 0 y0 we prove that the solution of the above mentioned ivp has an asymptotic expansion uniformly valid on e for e sufficiently small

predicting ct image from mri data through feature matching with learned nonlinear local descriptors attenuation correction for positron emission tomography pet magnetic resonance mr hybrid imaging systems and dose planning for mr based radiation therapy remain challenging due to insufficient high energy photon attenuation information we present a novel approach that uses the learned nonlinear local descriptors and feature matching to predict pseudo computed tomography pct images from t1 weighted and t2 weighted magnetic resonance imaging mri data the nonlinear local descriptors are obtained by projecting the linear descriptors into the nonlinear high dimensional space using an explicit feature map and low rank approximation with supervised manifold regularization the nearest neighbors of each local descriptor in the input mr images are searched in a constrained spatial range of the mr images among the training dataset then the pct patches are estimated through k nearest neighbor regression the proposed method for pct prediction is quantitatively analyzed on a dataset consisting of paired brain mri and ct images from 13 subjects our method generates pct images with a mean absolute error mae of 75 25 18 05 hounsfield units a peak signal to noise ratio of 30 87 1 15 db a relative mae of 1 56 0 5 in pet attenuation correction and a dose relative structure volume difference of 0 055 0 107 in d 98 as compared with true ct the experimental results also show that our method outperforms four state of the art methods

ensemble manifold regularized sparse low rank approximation for multiview feature embedding in computer vision and pattern recognition researches the studied objects are often characterized by multiple feature representations with high dimensionality thus it is essential to encode that multiview feature into a unified and discriminative embedding that is optimal for a given task to address this challenge this paper proposes an ensemble manifold regularized sparse low rank approximation emr slra algorithm for multiview feature embedding the emr slra algorithm is based on the framework of least squares component analysis in particular the low dimensional feature representation and the projection matrix are obtained by the low rank approximation of the concatenated multiview feature matrix by considering the complementary property among multiple features emr slra simultaneously enforces the ensemble manifold regularization on the output feature embedding in order to further enhance its robustness against the noise the group sparsity is introduced into the objective formulation to impose direct noise reduction on the input multiview feature matrix since there is no closed form solution for emr slra this paper provides an efficient emr slra optimization procedure to obtain the output feature embedding experiments on the pattern recognition applications confirm the effectiveness of the emr slra algorithm compare with some other multiview feature dimensionality reduction approaches highlightsthis paper proposes a novel emr slra algorithm for multiview feature embedding the least squares component analysis is generalized to multiview version the ensemble manifold regularization is enforced to explore the complementarity the group sparsity is introduced to promote the robustness against the noise an efficient iterative procedure is developed to solve emr slra

on an integral type operator from iterated logarithmic bloch spaces into bloch type spaces let h b denote the space of all holomorphic functions on the open unit ball b of c n let f f 1 f n be a holomorphic self map of b and email protected h b such that g 0 0 in this paper we study the boundedness and compactness of the following integral type operator recently introduced by xiangling zhu and the second authori f gf z email protected 0 1rf f tz g tz dtt email protected b from the iterated logarithmic bloch spaces into the bloch type spaces for the case when f z z we also obtain a sufficient and necessary condition for the boundedness of this operator from the iterated logarithmic bloch space into the little bloch type space

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

lmi based stability for singularly perturbed nonlinear impulsive differential systems with delays of small parameter abstract in this paper a class of singularly perturbed nonlinear impulsive delay differential systems is considered where the time delays include a small parameter based on lyapunov krasovskii functional and free weighting matrix method some novel delay dependent global asymptotic stability results are derived in terms of linear matrix inequalities lmis which can be easily solved using efficient convex optimization algorithms the results show that the system stability is very sensitive to the singular perturbation and the small parameter in time delays a numerical example is given to show the effectiveness of the proposed results

nonnegative ranks decompositions and factorizations of nonnegative matrices the nonnegative rank of a nonnegative matrix is the smallest number of nonnegative rank one matrices into which the matrix can be decomposed additively such decompositions are useful in diverse scientific disciplines we obtain characterizations and bounds and show that the nonnegative rank can be computed exactly over the reals by a finite algorithm

extended cesaro operators between different hardy spaces abstract let h p denote the hardy space of holomorphic functions on the unit ball b this note gives some sufficient and necessary conditions for the boundedness and compactness of the following extended cesaro operators t g f z 0 1 f tz r g tz dt t and l g f z 0 1 r f tz g tz dt t where z b and g is a fixed holomorphic map on b acting from the space h p into the space h q for the case p q our results extend and simplify some one dimensional results

bounded superposition operators between bloch orlicz and α bloch spaces we characterize all entire functions that transform a bloch orlicz space into the bloch space by superposition

graph regularized nonnegative matrix factorization for data representation matrix factorization techniques have been frequently applied in information retrieval computer vision and pattern recognition among them nonnegative matrix factorization nmf has received considerable attention due to its psychological and physiological interpretation of naturally occurring data whose representation may be parts based in the human brain on the other hand from the geometric perspective the data is usually sampled from a low dimensional manifold embedded in a high dimensional ambient space one then hopes to find a compact representation which uncovers the hidden semantics and simultaneously respects the intrinsic geometric structure in this paper we propose a novel algorithm called graph regularized nonnegative matrix factorization gnmf for this purpose in gnmf an affinity graph is constructed to encode the geometrical information and we seek a matrix factorization which respects the graph structure our empirical study shows encouraging results of the proposed algorithm in comparison to the state of the art algorithms on real world problems

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

differences of generalized composition operators on the bloch space abstract the boundedness and compactness of the differences of two generalized composition operators on the bloch space in the unit disk are investigated in this paper

on new bloch type spaces we introduce a new bloch type space so called the logarithmic bloch type space b l o g b a d on the unit disc d as the space of all holomorphic functions f on d such thatsupz d 1 z alne b a1 z b f z 0 and b 0 and present some basic properties of the space a necessary and a sufficient condition for a function with hadamard gaps to belong to the logarithmic bloch type space are given as well as some applications of these results to a composition operator

low rank matrix factorization with multiple hypergraph regularizer this paper presents a novel low rank matrix factorization method named multihmmf which incorporates multiple hypergraph manifold regularization to the low rank matrix factorization in order to effectively exploit high order information among the data samples the hypergraph is introduced to model the local structure of the intrinsic manifold specifically multiple hypergraph regularization terms are separately constructed to consider the local invariance the optimal intrinsic manifold is constructed by linearly combining multiple hypergraph manifolds then the regularization term is incorporated into a truncated singular value decomposition framework resulting in a unified objective function so that matrix factorization is changed into an optimization problem alternating optimization is used to solve the optimization problem with the result that the low dimensional representation of data space is obtained the experimental results of image clustering demonstrate that the proposed method outperforms state of the art data representation methods we propose a novel low rank matrix factorization method we incorporate multiple hypergraph manifold regularization to the matrix factorization we adopt alternating optimization to solve the optimization problem

background foreground modeling based on spatiotemporal sparse subspace clustering background estimation and foreground segmentation are important steps in many high level vision tasks many existing methods estimate background as a low rank component and foreground as a sparse matrix without incorporating the structural information therefore these algorithms exhibit degraded performance in the presence of dynamic backgrounds photometric variations jitter shadows and large occlusions we observe that these backgrounds often span multiple manifolds therefore constraints that ensure continuity on those manifolds will result in better background estimation hence we propose to incorporate the spatial and temporal sparse subspace clustering into the robust principal component analysis rpca framework to that end we compute a spatial and temporal graph for a given sequence using motion aware correlation coefficient the information captured by both graphs is utilized by estimating the proximity matrices using both the normalized euclidean and geodesic distances the low rank component must be able to efficiently partition the spatiotemporal graphs using these laplacian matrices embedded with the rpca objective function these laplacian matrices constrain the background model to be spatially and temporally consistent both on linear and nonlinear manifolds the solution of the proposed objective function is computed by using the linearized alternating direction method with adaptive penalty optimization scheme experiments are performed on challenging sequences from five publicly available datasets and are compared with the 23 existing state of the art methods the results demonstrate excellent performance of the proposed algorithm for both the background estimation and foreground segmentation

manifold regularized discriminative nonnegative matrix factorization with fast gradient descent nonnegative matrix factorization nmf has become a popular data representation method and has been widely used in image processing and pattern recognition problems this is because the learned bases can be interpreted as a natural parts based representation of data and this interpretation is consistent with the psychological intuition of combining parts to form a whole for practical classification tasks however nmf ignores both the local geometry of data and the discriminative information of different classes in addition existing research results show that the learned basis is unnecessarily parts based because there is neither explicit nor implicit constraint to ensure the representation parts based in this paper we introduce the manifold regularization and the margin maximization to nmf and obtain the manifold regularized discriminative nmf md nmf to overcome the aforementioned problems the multiplicative update rule mur can be applied to optimizing md nmf but it converges slowly in this paper we propose a fast gradient descent fgd to optimize md nmf fgd contains a newton method that searches the optimal step length and thus fgd converges much faster than mur in addition fgd includes mur as a special case and can be applied to optimizing nmf and its variants for a problem with 165 samples in r1600 fgd converges in 28 s while mur requires 282 s we also apply fgd in a variant of md nmf and experimental results confirm its efficiency experimental results on several face image datasets suggest the effectiveness of md nmf

generalized composition operators from f p q s spaces to bloch type spaces abstract let h b denote the space of all holomorphic functions on the unit ball b of c n let be a holomorphic self map of b and g h b such that g 0 0 in this paper we investigate the boundedness and compactness of the generalized composition operator c g f z 0 1 r f tz g tz dt t which map from f p q s and f0 p q s to bloch type space b in the unit ball

dual graph regularized latent low rank representation for subspace clustering low rank representation lrr has received considerable attention in subspace segmentation due to its effectiveness in exploring low dimensional subspace structures embedded in data to preserve the intrinsic geometrical structure of data a graph regularizer has been introduced into lrr framework for learning the locality and similarity information within data however it is often the case that not only the high dimensional data reside on a non linear low dimensional manifold in the ambient space but also their features lie on a manifold in feature space in this paper we propose a dual graph regularized lrr model dglrr by enforcing preservation of geometric information in both the ambient space and the feature space the proposed method aims for simultaneously considering the geometric structures of the data manifold and the feature manifold furthermore we extend the dglrr model to include non negative constraint leading to a parts based representation of data experiments are conducted on several image data sets to demonstrate that the proposed method outperforms the state of the art approaches in image clustering

composition operators on bloch orlicz type spaces abstract in this paper we use young s functions to define the bloch orlicz spaces as a generalization of bloch spaces we study continuity boundedness from below and compactness of composition operators on bloch orlicz spaces

composition operators from logarithmic bloch spaces to weighted bloch spaces we characterize the analytic self maps f of the unit disk d in c that induce continuous composition operators c f from the log bloch space b l o g d to m bloch spaces b m d in terms of the sequence of quotients of the m bloch semi norm of the nth power of f and the log bloch semi norm of the nth power f n of the identity function on d where m d 0 is continuous and bounded we also obtain an expression that is equivalent to the essential norm of c f between these spaces thus characterizing f such that c f is compact after finding a pairwise norm equivalent family of log bloch type spaces that are defined on the unit ball b n of c n and include the log bloch space we obtain an extension of our boundedness compactness essential norm results for c f acting on b l o g to the case when c f acts on these more general log bloch type spaces

characterizations of α bloch spaces on the unit ball abstract we obtain a characterization of the bloch space for any 0 in the unit ball of c n in terms of f z f w z w moreover a new characterization for the bloch space is given

on the iterated logarithmic bloch space on the unit ball abstract we introduce a new space of analytic functions on the unit ball the so called iterated logarithmic bloch space b log k and study some of its properties among other features we study the boundedness and compactness of weighted composition operators on the unit disk as well as of a recently introduced integral type operator on the unit ball with i domain the iterated logarithmic bloch space b log k or the little iterated logarithmic bloch space b log k 0 and ii range the bloch type space b or the little bloch type space b 0 or the weighted space h or the little weighted space h 0

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

on a new operator from the logarithmic bloch space to the bloch type space on the unit ball abstract we study the boundedness and compactness of a recently introduced operator denoted by p g which is a kind of the product of composition and integral operators on the unit ball b c n from the logarithmic bloch space b log and the little logarithmic bloch space b log 0 to the bloch type space b or the little bloch type space b 0

weighted composition operators between weighted bergman spaces and hardy spaces on the unit ball of cn abstract in this paper we study the weighted composition operators w f f between weighted bergman spaces and hardy spaces on the unit ball of c n we characterize the boundedness and the compactness of the weighted composition operators w a p a q 0 q p 1 and w h p b h q b 0 q p

principal manifolds and nonlinear dimensionality reduction via tangent space alignment we present a new algorithm for manifold learning and nonlinear dimensionality reduction based on a set of unorganized data points sampled with noise from a parameterized manifold the local geometry of the manifold is learned by constructing an approximation for the tangent space at each data point and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold we also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases we illustrate our algorithm using curves and surfaces both in two dimensional three dimensional 2d 3d euclidean spaces and in higher dimensional euclidean spaces we also address several theoretical and algorithmic issues for further research and improvements