communicability and multipartite structures in complex networks at negative absolute temperatures we here present a method of clearly identifying multipartite subgraphs in a network the method is based on a recently introduced concept of the communicability which very clearly identifies communities in a complex network we here show that while the communicability at a positive temperature is useful in identifying communities the communicability at a negative temperature is useful in identifying multipartite subgraphs the latter quantity between two nodes is positive when the two nodes belong to the same subgraph and is negative when they do not the method is able to discover almost multipartite structures where intercommunity connections vastly outweigh intracommunity connections we illustrate the relevance of this work to real life food web and protein protein interaction networks

a generalized learning paradigm exploiting the structure of feedforward neural networks in this paper a general class of fast learning algorithms for feedforward neural networks is introduced and described the approach exploits the separability of each layer into linear and nonlinear blocks and consists of two steps the first step is the descent of the error functional in the space of the outputs of the linear blocks descent in the neuron space which can be performed using any preferred optimization strategy in the second step each linear block is optimized separately by using a least squares ls criterion to demonstrate the effectiveness of the new approach a detailed treatment of a gradient descent in the neuron space is conducted the main properties of this approach are the higher speed of convergence with respect to methods that employ an ordinary gradient descent in the weight space backpropagation bp better numerical conditioning and lower computational cost compared to techniques based on the hessian matrix the numerical stability is assured by the use of robust ls linear system solvers operating directly on the input data of each layer experimental results obtained in three problems are described which confirm the effectiveness of the new method

anti modularity and anti community detecting in complex networks abstract many networks of interest in sciences and social research can be divided naturally into anti communities the problem of detecting and characterizing such anti community structure has attracted recent attention in this paper we first define the anti modularity as a quantitative measure of anti community partitioning on a network we also theoretically and empirically show the reliability of anti modularity as a measurement of the quality of an anti community partitioning a label propagation algorithm lpad for anti community detection is proposed experimental results on synthetic and real world networks show that our algorithm lpad can obtain higher quality anti community partitioning than other methods

the reverse order law for the generalized inverse a 2 t s by using the ranks of matrices the necessary and sufficient condition is given for the reverse order law of the generalized inverse a 2 t s of matrix product a a 1a 2 a n to hold as the special cases similar results for moore penrose inverse a the weighted moore penrose inverse a m n drazin inverse a d and group inverse a g are also derived

stochastic blockmodels and community structure in networks stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks most blockmodels however ignore variation in vertex degree making them unsuitable for applications to real world networks which typically display broad degree distributions that can significantly affect the results here we demonstrate how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks we also propose a heuristic algorithm for community detection using this objective function or its non degree corrected counterpart and show that the degree corrected version dramatically outperforms the uncorrected one in both real world and synthetic networks

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

newton s method and quasi newton sqp method for general lc1 constrained optimization in this paper we study the second order sufficient and necessary conditions for lc 1 constrained optimization problems present newton methods and quasi newton sqp methods for this kind of problems and establish locally linear and superlinear convergence this work extends the classical theory of convex smooth minimization to general lc 1 constrained optimization

a new sure approach to image denoising interscale orthonormal wavelet thresholding this paper introduces a new approach to orthonormal wavelet image denoising instead of postulating a statistical model for the wavelet coefficients we directly parametrize the denoising process as a sum of elementary nonlinear processes with unknown weights we then minimize an estimate of the mean square error between the clean image and the denoised one the key point is that we have at our disposal a very accurate statistically unbiased mse estimate stein s unbiased risk estimate that depends on the noisy image alone not on the clean one like the mse this estimate is quadratic in the unknown weights and its minimization amounts to solving a linear system of equations the existence of this a priori estimate makes it unnecessary to devise a specific statistical model for the wavelet coefficients instead and contrary to the custom in the literature these coefficients are not considered random any more we describe an interscale orthonormal wavelet thresholding algorithm based on this new approach and show its near optimal performance both regarding quality and cpu requirement by comparing it with the results of three state of the art nonredundant denoising algorithms on a large set of test images an interesting fallout of this study is the development of a new group delay based parent child prediction in a wavelet dyadic tree

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

recurrent neural networks for computing weighted moore penrose inverse1this project is supported by the national nature science foundation of china doctoral point foundation of china and youth science foundation of universities in shanghai of china 1 three recurrent neural networks are presented for computing the weighted moore penrose inverse of rank deficient matrices the first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of weighted moore penrose inverse under the condition of zero initial states the second recurrent neural network consists of an array of neurons corresponding to a weighted moore penrose inverse matrix with decaying self connections and constant connections in each row or column the third recurrent neural network consists of two layers of neuron arrays corresponding respectively to a weighted moore penrose inverse and a lagrangian matrix with constant connections

reverse order laws for 1 2 3 generalized inverses in this paper we present purely algebraic necessary and sufficient conditions for reverse order laws to hold for 1 2 3 and 1 2 4 generalized inverses on the set of matrices

vsnr a wavelet based visual signal to noise ratio for natural images this paper presents an efficient metric for quantifying the visual fidelity of natural images based on near threshold and suprathreshold properties of human vision the proposed metric the visual signal to noise ratio vsnr operates via a two stage approach in the first stage contrast thresholds for detection of distortions in the presence of natural images are computed via wavelet based models of visual masking and visual summation in order to determine whether the distortions in the distorted image are visible if the distortions are below the threshold of detection the distorted image is deemed to be of perfect visual fidelity vsnr infin and no further analysis is required if the distortions are suprathreshold a second stage is applied which operates based on the low level visual property of perceived contrast and the mid level visual property of global precedence these two properties are modeled as euclidean distances in distortion contrast space of a multiscale wavelet decomposition and vsnr is computed based on a simple linear sum of these distances the proposed vsnr metric is generally competitive with current metrics of visual fidelity it is efficient both in terms of its low computational complexity and in terms of its low memory requirements and it operates based on physical luminances and visual angle rather than on digital pixel values and pixel based dimensions to accommodate different viewing conditions

maximum likelihood orientation estimation of 1 d patterns in laguerre gauss subspaces a method for measuring the orientation of linear 1 d patterns based on a local expansion with laguerre gauss circular harmonic lg ch functions is presented it lies on the property that the polar separable lg ch functions span the same space as the 2 d cartesian separable hermite gauss 2 d hg functions exploiting the simple steerability of the lg ch functions and the peculiar block linear relationship among the two expansion coefficients sets maximum likelihood ml estimates of orientation and cross section parameters of 1 d patterns are obtained projecting them in a proper subspace of the 2 d hg family it is shown in this paper that the conditional ml solution derived by elimination of the cross section parameters surprisingly yields the same asymptotic accuracy as the ml solution for known cross section parameters the accuracy of the conditional ml estimator is compared to the one of state of art solutions on a theoretical basis and via simulation trials a thorough proof of the key relationship between the lg ch and the 2 d hg expansions is also provided

a modularity based spectral method for simultaneous community and anti community detection abstract in a graph or complex network communities and anti communities are node sets whose modularity attains extremely large values positive and negative respectively we consider the simultaneous detection of communities and anti communities by looking at spectral methods based on various matrix based definitions of the modularity of a vertex set invariant subspaces associated to extreme eigenvalues of these matrices provide indications on the presence of both kinds of modular structure in the network the localization of the relevant invariant subspaces can be estimated by looking at particular matrix angles based on frobenius inner products

on network bipartivity systems with two types of agents with a preference for heterophilous interaction produces networks that are more or less close to bipartite we propose two measures quantifying the notion of bipartivity the two measures one well known and natural but computationally intractable one computationally less complex but also less intuitive are examined on model networks that continuously interpolates between bipartite graphs and graphs with many odd circuits we find that the bipartivity measures increase as we tune the control parameters of the test networks to intuitively increase the bipartivity and thus conclude that the measures are quite relevant we also measure and discuss the values of our bipartivity measures for empirical social networks constructed from professional collaborations internet communities and field surveys here we find as expected that networks arising from romantic online interaction have high and professional collaboration networks have low bipartivity values in some other cases probably due to low average degree of the network the bipartivity measures cannot distinguish between romantic and friendship oriented interaction

image denoising using scale mixtures of gaussians in the wavelet domain we describe a method for removing noise from digital images based on a statistical model of the coefficients of an overcomplete multiscale oriented basis neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables a gaussian vector and a hidden positive scalar multiplier the latter modulates the local variance of the coefficients in the neighborhood and is thus able to account for the empirically observed correlation between the coefficient amplitudes under this model the bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable we demonstrate through simulations with images contaminated by additive white gaussian noise that the performance of this method substantially surpasses that of previously published methods both visually and in terms of mean squared error

multiplicative perturbations of matrices and the generalized triple reverse order law for the moore penrose inverse abstract for a matrix a let a denote its moore penrose inverse a matrix m is called a multiplicative perturbation of t c m n if m e t f for some e c m m and f c n n based on the alternative expression for m as m e t t t f t t the generalized triple reverse order law for the moore penrose inverse is obtained as m f t t y y t z z l r 1 e t t where y y t z z l r 1 is the weighted moore penrose inverse for certain matrices y z l and r associated to the triple t e f furthermore it is proved that this weighted moore penrose inverse in the resulting expression for m can be really replaced with t if e t t e t t t t f t t f t t in the special case that rank m rank t or m is a weak perturbation of t a simplified version of m as well as m m and m m is also derived

reverse order laws in c algebras abstract in this paper we offer purely algebraic necessary and sufficient conditions for reverse order laws for generalized inverses in c algebras extending rank conditions for matrices and range conditions for hilbert space operators

generalized modularity matrices various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems in this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral type algorithms for community detection

no reference image quality assessment in the spatial domain we propose a natural scene statistic based distortion generic blind no reference nr image quality assessment iqa model that operates in the spatial domain the new model dubbed blind referenceless image spatial quality evaluator brisque does not compute distortion specific features such as ringing blur or blocking but instead uses scene statistics of locally normalized luminance coefficients to quantify possible losses of naturalness in the image due to the presence of distortions thereby leading to a holistic measure of quality the underlying features used derive from the empirical distribution of locally normalized luminances and products of locally normalized luminances under a spatial natural scene statistic model no transformation to another coordinate frame dct wavelet etc is required distinguishing it from prior nr iqa approaches despite its simplicity we are able to show that brisque is statistically better than the full reference peak signal to noise ratio and the structural similarity index and is highly competitive with respect to all present day distortion generic nr iqa algorithms brisque has very low computational complexity making it well suited for real time applications brisque features may be used for distortion identification as well to illustrate a new practical application of brisque we describe how a nonblind image denoising algorithm can be augmented with brisque in order to perform blind image denoising results show that brisque augmentation leads to performance improvements over state of the art methods a software release of brisque is available online http live ece utexas edu research quality brisque release zip for public use and evaluation

a no reference objective image sharpness metric based on the notion of just noticeable blur jnb this work presents a perceptual based no reference objective image sharpness blurriness metric by integrating the concept of just noticeable blur into a probability summation model unlike existing objective no reference image sharpness blurriness metrics the proposed metric is able to predict the relative amount of blurriness in images with different content results are provided to illustrate the performance of the proposed perceptual based sharpness metric these results show that the proposed sharpness metric correlates well with the perceived sharpness being able to predict with high accuracy the relative amount of blurriness in images with different content

automatic parameter selection for denoising algorithms using a no reference measure of image content across the field of inverse problems in image and video processing nearly all algorithms have various parameters which need to be set in order to yield good results in practice usually the choice of such parameters is made empirically with trial and error if no ground truth reference is available some analytical methods such as cross validation and stein s unbiased risk estimate sure have been successfully used to set such parameters however these methods tend to be strongly reliant on restrictive assumptions on the noise and also computationally heavy in this paper we propose a no reference metric q which is based upon singular value decomposition of local image gradient matrix and provides a quantitative measure of true image content i e sharpness and contrast as manifested in visually salient geometric features such as edges in the presence of noise and other disturbances this measure 1 is easy to compute 2 reacts reasonably to both blur and random noise and 3 works well even when the noise is not gaussian the proposed measure is used to automatically and effectively set the parameters of two leading image denoising algorithms ample simulated and real data experiments support our claims furthermore tests using the tid2008 database show that this measure correlates well with subjective quality evaluations for both blur and noise distortions

hybrid no reference natural image quality assessment of noisy blurry jpeg2000 and jpeg images in this paper we propose a new image quality assessment method based on a hybrid of curvelet wavelet and cosine transforms called hybrid no reference hnr model from the properties of natural scene statistics the peak coordinates of the transformed coefficient histogram of filtered natural images occupy well defined clusters in peak coordinate space which makes nr possible compared to other methods hnr has three benefits 1 it is an nr method applicable to arbitrary images without compromising the prediction accuracy of full reference methods 2 as far as we know it is the only general nr method well suited for four types of filters noise blur jpeg2000 and jpeg compression and 3 it can classify the filter types of the image and predict filter levels even when the image is results from the application of two different filters we tested hnr on very intensive video image database our image library and laboratory for image video engineering a public library results are compared to the state of the art methods including peak snr structural similarity visual information fidelity and so on

new support vector algorithms we propose a new class of support vector algorithms for regression and classification in these algorithms a parameter lets one effectively control the number of support vectors while this can be useful in its own right the parameterization has the additional benefit of enabling us to eliminate one of the other free parameters of the algorithm the accuracy parameter epsilon in the regression case and the regularization constant c in the classification case we describe the algorithms give some theoretical results concerning the meaning and the choice of and report experimental results

when is b a a generalized inverse of ab in practice factorizations of a generalized inverse often arise from factorizations of the matrix which is to be inverted in addition to full rank factorizations normal factorizations and singular value decompositions svd there are other factorizations of particular matrices that are natural to certain problems for instance in statistics answers to questions like when is b a a generalized inverse of ab may thus be a computational tool besides they are of significant interest because they provide us with insights into the g inversion of matrix products

the reverse order law revisited abstract necessary and sufficient conditions are given for the triple reverse order law abc c b a to hold some special cases are considered

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

penalized versions of the newman girvan modularity and their relation to normalized cuts and k means clustering two penalized balanced and normalized versions of the newman girvan modularity are introduced and estimated by the non negative eigenvalues of the modularity and normalized modularity matrix respectively in this way the partition of the vertices that maximizes the modularity can be obtained by applying the k means algorithm for the representatives of the vertices based on the eigenvectors belonging to the largest positive eigenvalues of the modularity or normalized modularity matrix the proper dimension depends on the number of the structural eigenvalues of positive sign while dominating negative eigenvalues indicate an anticommunity structure the balance between the negative and the positive eigenvalues determines whether the underlying graph has a community anticommunity or randomlike structure

a detail based method for linear full reference image quality prediction in this paper a novel full reference method is proposed for image quality assessment using the combination of two separate metrics to measure the perceptually distinct impact of detail losses and of spurious details to this purpose the gradient of the impaired image is locally decomposed as a predicted version of the original gradient plus a gradient residual it is assumed that the detail attenuation identifies the detail loss whereas the gradient residuals describe the spurious details it turns out that the perceptual impact of detail losses is roughly linear with the loss of the positional fisher information while the perceptual impact of the spurious details is roughly proportional to a logarithmic measure of the signal to residual ratio the affine combination of these two metrics forms a new index strongly correlated with the empirical differential mean opinion score dmos for a significant class of image impairments as verified for three independent popular databases the method allowed alignment and merging of dmos data coming from these different databases to a common dmos scale by affine transformations unexpectedly the dmos scale setting is possible by the analysis of a single image affected by additive noise

the representation and approximation for the weighted moore penrose inverse we present a unified representation theorem for the weighted moore penrose inverse specific expressions and computational procedures for the weighted moore penrose inverse can be uniformly derived

two dimensional approach to full reference image quality assessment based on positional structural information a method for full reference visual quality assessment based on the 2 d combination of two diverse metrics is described the first metric is a measure of structural information loss based on the fisher information about the position of the structures in the observed images the second metric acts as a categorical indicator of the type of distortion that images underwent these two metrics constitute the inner state of a virtual cognitive model viewed as a system whose output is the automatic visual quality estimate the use of a 2 d metric fills the intrinsic incompleteness of methods based on a single metric while providing consistent response across different image impairment factors and blind distortion classification capability with a modest computational overhead the high accuracy and robustness of the method are demonstrated through cross validation experiments

triple reverse order law for weighted generalized inverses in this paper we present a new triple reverse order law of weighted generalized inverses which does not involve the calculation of any generalized inverse our result is an important improvement of the existing reverse order law of weighted generalized inverse

maximum likelihood localization of 2 d patterns in the gauss laguerre transform domain theoretic framework and preliminary results usual approaches to localization i e joint estimation of position orientation and scale of a bidimensional pattern employ suboptimum techniques based on invariant signatures which allow for position estimation independent of scale and orientation in this paper a maximum likelihood method for pattern localization working in the gauss laguerre transform glt domain is presented the glt is based on an orthogonal family of circular harmonic functions with specific radial profiles which permits optimum joint estimation of position and scale rotation parameters looking at the maxima of a gauss laguerre likelihood map the fisher information matrix for any given pattern is given and the theoretical asymptotic accuracy of the parameter estimates is calculated through the cramer rao lower bound application of the ml estimation method is discussed and an example is provided