fast and accurate binary response mixed model analysis via expectation propagation expectation propagation is a general prescription for approximation of integrals in statistical inference problems its literature is mainly concerned with bayesian inference scenarios however ex

a model framework for the enhancement of community detection in complex networks abstract community detection is an important data analysis problem in many different areas and how to enhance the quality of community detection in complicated real applications is still a challenge current community detection enhancement methods often take the enhancement as a preprocess of community detection they mainly focus on how to design the suitable topological similarity of nodes to adjust the original network but did not consider how to make use of this topological similarity more effectively in order to better utilize the similarity information we propose a model framework which integrates the enhancement into the whole community detection procedure first we calculate the structural similarity of nodes based on network topology second we present a stochastic model to describe the community memberships of nodes we then model the strong constraint based on structural similarity i e we make each node have the same community membership distribution with its most similar neighbors and then we model the weak constraint i e if two nodes have a high similarity we will make their community membership distributions close otherwise we will make them not close finally we present a nonnegative matrix factorization approach to learn the model parameters we evaluate our method on both synthetic and real world networks with ground truths and compare it with five comparable methods the experimental results demonstrate the superior performance of our new method over the competing ones for community detection and enhancement

identifying and ranking influential spreaders in complex networks with consideration of spreading probability abstract identifying the influential spreaders in complex network has great theoretical and practical significance in order to evaluate the spreading ability of the nodes some centrality measures are usually computed which include degree centrality dc betweenness centrality bc closeness centrality cc k shell centrality ks and local centrality lc however we observe that the performance of different centrality measures may change when these measures are used in a real network with different spreading probabilities specifically dc performs well for small spreading probabilities and lc is more suitable for larger ones to alleviate the sensitivity of these centrality measures to the spreading probability we modify lc and then integrate it with dc by considering the spreading probability we call the proposed measure hybrid degree centrality hc hc can take the advantages of dc or lc depending on the given spreading probability we use sir model to evaluate the performance of hc in both real networks and artificial networks experimental results show that hc performs robustly under different spreading probabilities compared with these known centrality measures such as dc lc bc cc and ks hc can evaluate the spreading ability of the nodes more accurately on most range of spreading probabilities furthermore we show that our method can better distinguish the spreading ability of nodes

generalized linear models with random effects salamander mating revisited in recent years much effort has been devoted to extending regression methodology to non gaussian data where responses are not independent these methods for dependent responses are suitable for data from longitudinal studies or nested designs however use of these methods for crossed designs seems to have serious limitations due to the intensive computations involved because of the intractable nature of the joint distribution in this paper we cast the problem in a bayesian framework and use a monte carlo method the gibbs sampler to avoid current computational limitations the flexibility of this approach is illustrated by analyzing the interesting salamander mating data reported by mccullagh and nelder 1989 generalized linear models 2nd edition london chapman and hall

community detection in networks based on minimum spanning tree and modularity abstract in this paper we propose a novel splitting and merging method for community detection in which a minimum spanning tree mst of dissimilarity between nodes in graph is employed in the splitting process edges with high dissimilarity in the mst are removed to construct small disconnected subgroups of nodes from the same community in the merging process subgroup pairs are iteratively merged to identify the final community structure maximizing the modularity the proposed method requires no parameter we provide a general framework for implementing such a method experimental results obtained by applying the method on computer generated networks and different real world networks show the effectiveness of the proposed method

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

modularity and community detection in bipartite networks the modularity of a network quantifies the extent relative to a null model network to which vertices cluster into community groups we define a null model appropriate for bipartite networks and use it to define a bipartite modularity the bipartite modularity is presented in terms of a modularity matrix b some key properties of the eigenspectrum of b are identified and used to describe an algorithm for identifying modules in bipartite networks the algorithm is based on the idea that the modules in the two parts of the network are dependent with each part mutually being used to induce the vertices for the other part into the modules we apply the algorithm to real world network data showing that the algorithm successfully identifies the modular structure of bipartite networks

a variational maximization maximization algorithm for generalized linear mixed models with crossed random effects we present a variational maximization maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects e g item response models with random items random raters or random occasion specific effects the method is based on a factorized variational approximation of the latent variable distribution given observed variables which creates a lower bound of the log marginal likelihood the lower bound is maximized with respect to the factorized distributions as well as model parameters with the proposed algorithm a high dimensional intractable integration is translated into a two dimensional integration problem we incorporate an adaptive gauss hermite quadrature method in conjunction with the variational method in order to increase computational efficiency numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the laplace approximation

accuracy and precision of methods for community identification in weighted networks based on brief review of approaches for community identification and measurement for sensitivity characterization the accuracy and precision of several approaches for detecting communities in weighted networks are investigated in weighted networks the community structure should take both links and link weights into account and the partition of networks should be evaluated by weighted modularity q w the results reveal that link weight has important effects on communities especially in dense networks potts model and weighted extremal optimization weo algorithm work well on weighted networks then potts model and weo algorithms are used to detect communities in rhesus monkey network the results gives nice understanding for real community structure

community detection in complex networks by dynamical simplex evolution we benchmark the dynamical simplex evolution dse method with several of the currently available algorithms to detect communities in complex networks by comparing correctly identified nodes for different levels of fuzziness of random networks composed of well defined communities the potential benefits of the dse method to detect hierarchical substructures in complex networks are discussed

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

an efficient community detection method based on rank centrality abstract community detection is a very important problem in social network analysis classical clustering approach k means has been shown to be very efficient to detect communities in networks however k means is quite sensitive to the initial centroids or seeds especially when it is used to detect communities to solve this problem in this study we propose an efficient algorithm k rank which selects the top k nodes with the highest rank centrality as the initial seeds and updates these seeds by using an iterative technique like k means then we extend k rank to partition directed weighted networks and to detect overlapping communities the empirical study on synthetic and real networks show that k rank is robust and better than the state of the art algorithms including k means bgll lpa infomap and oslom

properties of highly clustered networks we propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient among other things our results indicate that increased clustering leads to a decrease in the size of the giant component of the network we also study susceptible infective recovered type epidemic processes within the model and find that clustering decreases the size of epidemics but also decreases the epidemic threshold making it easier for diseases to spread in addition clustering causes epidemics to saturate sooner meaning that they infect a near maximal fraction of the network for quite low transmission rates

fuzzy overlapping community detection based on local random walk and multidimensional scaling a b s t r a c t a fuzzy overlapping community is an important kind of overlapping community in which each node belongs to each community to different extents it exists in many real networks but how to identify a fuzzy overlapping community is still a challenging task in this work the concept of local random walk and a new distance metric are introduced based on the new distance measurement the dissimilarity index between each node of a network is calculated firstly then in order to keep the original node distance as much as possible the network structure is mapped into low dimensional space by the multidimensional scaling mds finally the fuzzy c means clustering is employed to find fuzzy communities in a network the experimental results show that the proposed algorithm is effective and efficient to identify the fuzzy overlapping communities in both artificial networks and real world networks

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

community detection in complex networks using density based clustering algorithm and manifold learning abstract like clustering analysis community detection aims at assigning nodes in a network into different communities fdp is a recently proposed density based clustering algorithm which does not need the number of clusters as prior input and the result is insensitive to its parameter however fdp cannot be directly applied to community detection due to its inability to recognize the community centers in the network to solve the problem a new community detection method named isofdp is proposed in this paper first we use isomap technique to map the network data into a low dimensional manifold which can reveal diverse pair wised similarity then fdp is applied to detect the communities in the network an improved partition density function is proposed to select the proper number of communities automatically we test our method on both synthetic and real world networks and the results demonstrate the effectiveness of our algorithm over the state of the art methods

modularity maximization using completely positive programming abstract community detection is one of the most prominent problems of social network analysis in this paper a novel method for modularity maximization mm for community detection is presented which exploits the alternating direction augmented lagrangian adal method for maximizing a generalized form of newman s modularity function we first transform newman s modularity function into a quadratic program and then use completely positive programming cpp to map the quadratic program to a linear program which provides the globally optimal maximum modularity partition in order to solve the proposed cpp problem a closed form solution using the adal merged with a rank minimization approach is proposed the performance of the proposed method is evaluated on several real world data sets used for benchmarks community detection simulation results shows the proposed technique provides outstanding results in terms of modularity value for crisp partitions

multiresolution community detection for megascale networks by information based replica correlations we use a potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph our multiresolution algorithm calculates correlations among multiple copies replicas of the same graph over a range of resolutions significant multiresolution structures are identified by strongly correlated replicas the average normalized mutual information the variation in information and other measures in principle give a quantitative estimate of the best resolutions and indicate the relative strength of the structures in the graph because the method is based on information comparisons it can in principle be used with any community detection model that can examine multiple resolutions our approach may be extended to other optimization problems as a local measure our potts model avoids the resolution limit that affects other popular models with this model our community detection algorithm has an accuracy that ranks among the best of currently available methods using it we can examine graphs over 40 ifmmode times else texttimes fi 10 6 nodes and more than 1 ifmmode times else texttimes fi 10 9 edges we further report that the multiresolution variant of our algorithm can solve systems of at least 200 text 000 nodes and 10 ifmmode times else texttimes fi 10 6 edges on a single processor with exceptionally high accuracy for typical cases we find a superlinear scaling o l 1 3 for community detection and o l 1 3 text text log text n for the multiresolution algorithm where l is the number of edges and n is the number of nodes in the system

advanced modularity specialized label propagation algorithm for detecting communities in networks abstract a modularity specialized label propagation algorithm lpam for detecting network communities was recently proposed this promising algorithm offers some desirable qualities however lpam favors community divisions where all communities are similar in total degree and thus it is prone to get stuck in poor local maxima in the modularity space to escape local maxima we employ a multistep greedy agglomerative algorithm msg that can merge multiple pairs of communities at a time combining lpam and msg we propose an advanced modularity specialized label propagation algorithm lpam experiments show that lpam successfully detects communities with higher modularity values than ever reported in two commonly used real world networks moreover lpam offers a fair compromise between accuracy and speed

laplace s approximation for nonlinear mixed models summary an approximation to laplace s method for integrals is applied to marginal distributions of data arising from models in which both fixed and random effects enter nonlinearly the approach provides alternative derivations of some recent algorithms for fitting such models and it has direct ties with gaussian restricted maximum likelihood and the accompanying mixed model equations

community detection by fuzzy clustering abstract how to measure the similarity between nodes is of great importance for fuzzy clustering when we use the approach to uncover communities in complex networks in this paper we first measure the similarity between nodes in a network based on edge centralities and model the network as a fuzzy relation then two fuzzy transitive rules rule i and rule ii are applied on the relation respectively by which the similarity information can be transferred from one node to another in the network until the relation reaches a stable state by choosing different thresholds our method finally can partition the network into several non overlapping subgroups we compare our method with some state of the art methods on the lfr benchmark and real world networks we find that our method based on rule i can correctly identify communities when the similarity between nodes of same groups is greater than that of different groups while it is just opposite to rule ii our method achieves better results than the state of the art methods when the pre planted communities of the random networks are vaguer

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

community structure and scale free collections of erdős renyi graphs community structure plays a significant role in the analysis of social networks and similar graphs yet this structure is little understood and not well captured by most models we formally define a community to be a subgraph that is internally highly connected and has no deeper substructure we use tools of combinatorics to show that any such community must contain a dense erd ifmmode mbox h o else h o fi s r enyi er subgraph based on mathematical arguments we hypothesize that any graph with a heavy tailed degree distribution and community structure must contain a scale free collection of dense er subgraphs these theoretical observations corroborate well with empirical evidence from this we propose the block two level erd ifmmode mbox h o else h o fi s r enyi bter model and demonstrate that it accurately captures the observable properties of many real world social networks

detection of community structures in networks via global optimization abstract we present an analysis of communality structure in networks based on the application of simulated annealing techniques in this case we use as cost function the already introduced modularity q 1 which is based on the relative number of links within a commune against the number of links that would correspond in case the links were distributed randomly we compare the results of our approach against other methodologies based on betweenness analysis and show that in all cases a better community structure can be attained

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

semi supervised clustering algorithm for community structure detection in complex networks abstract discovering a community structure is fundamental for uncovering the links between structure and function in complex networks in this paper we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization snmf and the maximum optimization of modularity density based on this equivalence we develop a new algorithm named the so called snmf ss by combining snmf and a semi supervised clustering approach previous nmf based algorithms often suffer from the restriction of measuring network topology from only one perspective but our algorithm uses a semi supervised mechanism to get rid of the restriction the algorithm is illustrated and compared with spectral clustering and nmf by using artificial examples and other classic real world networks experimental results show the significance of the proposed approach particularly in the cases when community structure is obscure

spectral analysis of deformed random networks we study spectral behavior of sparsely connected random networks under the random matrix framework subnetworks without any connection among them form a network having perfect community structure as connections among the subnetworks are introduced the spacing distribution shows a transition from the poisson statistics to the gaussian orthogonal ensemble statistics of random matrix theory the eigenvalue density distribution shows a transition to the wigner s semicircular behavior for a completely deformed network the range for which spectral rigidity measured by the dyson mehta ensuremath delta 3 statistics follows the gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure the spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure whereas the density distribution and the ensuremath delta 3 statistics remain identical to the undeformed network on the other hand the ensuremath delta 3 statistics is useful for the larger deformation strengths finally we analyze the spectrum of a protein protein interaction network for helicobacter and compare the spectral behavior with those of the model networks

spectral methods for community detection and graph partitioning we consider three distinct and well studied problems concerning network structure community detection by modularity maximization community detection by statistical inference and normalized cut graph partitioning each of these problems can be tackled using spectral algorithms that make use of the eigenvectors of matrix representations of the network we show that with certain choices of the free parameters appearing in these spectral algorithms the algorithms for all three problems are in fact identical and hence that at least within the spectral approximations used here there is no difference between the modularity and inference based community detection methods or between either and graph partitioning

maximum likelihood algorithms for generalized linear mixed models abstract maximum likelihood algorithms are described for generalized linear mixed models i show how to construct a monte carlo version of the em algorithm propose a monte carlo newton raphson algorithm and evaluate and improve the use of importance sampling ideas calculation of the maximum likelihood estimates is feasible for a wide variety of problems where they were not previously i also use the newton raphson algorithm as a framework to compare maximum likelihood to the joint maximization or penalized quasi likelihood methods and explain why the latter can perform poorly

a community detection method based on local similarity and degree clustering information community detection is of great importance to understand the structures and functions of networks in this paper a novel algorithm is proposed based on local similarity and degree clustering information local similarity is employed to measure the similarity between nodes and their neighbors in order to form communities within which nodes are closely connected degree clustering information a hybrid criterion combining local neighborhood ratio with degree ratio make a large number of nodes with low degree to embrace a small amount of nodes with high degree furthermore each node in small scale communities has the duty to try to connect the nodes with high degree to expand communities and finally the optimal community structure can be obtained simulation results on real and artificial networks show that the proposed algorithm has the excellent performance in terms of accuracy

community detection in complex networks by density based clustering abstract we proposed a method to find the community structure in a complex network by density based clustering physical topological distance is introduced in density based clustering for determining a distance function of specific influence functions according to the distribution of the data the community structures are uncovered the method keeps a better connection mode of the community structure than the existing algorithms in terms of modularity which can be viewed as a basic characteristic of community detection in the future moreover experimental results indicate that the proposed method is efficient and effective to be used for community detection of medium and large networks

cluster ensembles a knowledge reuse framework for combining multiple partitions this paper introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings we first identify several application scenarios for the resultant knowledge reuse framework that we call cluster ensembles the cluster ensemble problem is then formalized as a combinatorial optimization problem in terms of shared mutual information in addition to a direct maximization approach we propose three effective and efficient techniques for obtaining high quality combiners consensus functions the first combiner induces a similarity measure from the partitionings and then reclusters the objects the second combiner is based on hypergraph partitioning the third one collapses groups of clusters into meta clusters which then compete for each object to determine the combined clustering due to the low computational costs of our techniques it is quite feasible to use a supra consensus function that evaluates all three approaches against the objective function and picks the best solution for a given situation we evaluate the effectiveness of cluster ensembles in three qualitatively different application scenarios i where the original clusters were formed based on non identical sets of features ii where the original clustering algorithms worked on non identical sets of objects and iii where a common data set is used and the main purpose of combining multiple clusterings is to improve the quality and robustness of the solution promising results are obtained in all three situations for synthetic as well as real data sets

maximum likelihood estimation of limited and discrete dependent variable models with nested random effects abstract gauss hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models unfortunately the estimates are biased for large cluster sizes and or intraclass correlations we show that adaptive quadrature largely overcomes these problems we then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables the models can include several nested random effects intercepts and coefficients representing unobserved heterogeneity at different levels of a hierarchical dataset the required multivariate integrals are evaluated efficiently using spherical quadrature rules simulations show that adaptive quadrature performs well in a wide range of situations

community detection algorithms a comparative analysis uncovering the community structure exhibited by real networks is a crucial step toward an understanding of complex systems that goes beyond the local organization of their constituents many algorithms have been proposed so far but none of them has been subjected to strict tests to evaluate their performance most of the sporadic tests performed so far involved small networks with known community structure and or artificial graphs with a simplified structure which is very uncommon in real systems here we test several methods against a recently introduced class of benchmark graphs with heterogeneous distributions of degree and community size the methods are also tested against the benchmark by girvan and newman proc natl acad sci u s a 99 7821 2002 and on random graphs as a result of our analysis three recent algorithms introduced by rosvall and bergstrom proc natl acad sci u s a 104 7327 2007 proc natl acad sci u s a 105 1118 2008 blondel et al j stat mech theory exp 2008 p10008 and ronhovde and nussinov phys rev e 80 016109 2009 have an excellent performance with the additional advantage of low computational complexity which enables one to analyze large systems

multilevel covariance component models summary a straightforward extension to the multilevel linear model with nested covariance components is described this allows the specification and efficient estimation of a very general mixed linear model with both crossed and nested covariance components goldstein 1986 describes the analysis of the multilevel mixed effects linear model with random coefficients where the variance and covariance components have a nested structure across levels the purpose of the present note is to show how a simple extension to the formulae in that paper can accommodate cross classifications of the components within any level of the nesting thus enabling quite general covariance component models to be specified and efficient parameter estimates obtained for simplicity the 3 level model is used with the extension to 4 or more levels being straightforward we write the random part of the 3 level model as

k means type algorithms a generalized convergence theorem and characterization of local optimality the k means algorithm is a commonly used technique in cluster analysis in this paper several questions about the algorithm are addressed the clustering problem is first cast as a nonconvex mathematical program then a rigorous proof of the finite convergence of the k means type algorithm is given for any metric it is shown that under certain conditions the algorithm may fail to converge to a local minimum and that it converges under differentiability conditions to a kuhn tucker point finally a method for obtaining a local minimum solution is given

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

modularity functions maximization with nonnegative relaxation facilitates community detection in networks abstract we show here that the problem of maximizing a family of quantitative functions encompassing both the modularity q measure and modularity density d measure for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity laplacian instead of using traditional spectral relaxation we apply additional nonnegative constraint into this graph clustering problem and design efficient algorithms to optimize the new objective with the explicit nonnegative constraint our solutions are very close to the ideal community indicator matrix and can directly assign nodes into communities the near orthogonal columns of the solution can be reformulated as the posterior probability of corresponding node belonging to each community therefore the proposed method can be exploited to identify the fuzzy or overlapping communities and thus facilitates the understanding of the intrinsic structure of networks experimental results show that our new algorithm consistently sometimes significantly outperforms the traditional spectral relaxation approaches

analysis of weighted networks the connections in many networks are not merely binary entities either present or not but have associated weights that record their strengths relative to one another recent studies of networks have by and large steered clear of such weighted networks which are often perceived as being harder to analyze than their unweighted counterparts here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph allowing us to apply standard techniques for unweighted graphs to weighted ones as well we give a number of examples of the method including an algorithm for detecting community structure in weighted networks and a simple proof of the maximum flow minimum cut theorem

benchmark graphs for testing community detection algorithms community structure is one of the most important features of real networks and reveals the internal organization of the nodes many algorithms have been proposed but the crucial issue of testing i e the question of how good an algorithm is with respect to others is still open standard tests include the analysis of simple artificial graphs with a built in community structure that the algorithm has to recover however the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks here we introduce a class of benchmark graphs that account for the heterogeneity in the distributions of node degrees and of community sizes we use this benchmark to test two popular methods of community detection modularity optimization and potts model clustering the results show that the benchmark poses a much more severe test to algorithms than standard benchmarks revealing limits that may not be apparent at a first analysis

a class of improved algorithms for detecting communities in complex networks abstract detecting communities in complex networks is of considerable importance for understanding both the structure and function of the networks here we propose a class of improved algorithms for community detection by combining the betweenness algorithm of girvan and newman with the edge weight defined by the edge clustering coefficient the improved algorithms are tested on some artificial and real world networks and the results show that they can detect communities of networks more effectively in both unweighted and weighted cases in addition the technique for improving the betweenness algorithm in this paper thanks to its compatibility can directly be applied to various detection algorithms

column generation algorithms for exact modularity maximization in networks finding modules or clusters in networks currently attracts much attention in several domains the most studied criterion for doing so due to newman and girvan phys rev e 69 026113 2004 is modularity maximization many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality there are few exact algorithms prominent among which is a paper by xu et al eur phys j b 60 231 2007 modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of grotschel and wakabayashi math program 45 59 1989 applied we propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming performance of the four resulting algorithms is compared on problems from the literature instances with up to 512 entities are solved exactly moreover the computing time of previously solved problems are reduced substantially

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

revealing network communities with a nonlinear programming method the detection of network communities has attracted significant research attention lately to discover such structures a mathematical measure known as modularity is often used for optimization unfortunately the optimization is np hard and approximated solutions have to be sought for large networks in this paper we propose a nonlinear programming method for optimization that is based on the augmented lagrangian technique we further identify the inherent connection between the proposed method and positive semi definite programming and its low rank reduction which helps to justify the performance of the method compared with previously published approaches the proposed method is empirically efficient and effective at detecting underlying network communities

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

robustness of community structure in networks the discovery of community structure is a common challenge in the analysis of network data many methods have been proposed for finding community structure but few have been proposed for determining whether the structure found is statistically significant or whether conversely it could have arisen purely as a result of chance in this paper we show that the significance of community structure can be effectively quantified by measuring its robustness to small perturbations in network structure we propose a suitable method for perturbing networks and a measure of the resulting change in community structure and use them to assess the significance of community structure in a variety of networks both real and computer generated

detecting one mode communities in bipartite networks by bipartite clustering triangular abstract in this paper an algorithm is proposed to detect one mode community structures in bipartite networks and to deduce which one mode community structures are weighted after analyzing the topological properties in bipartite networks bipartite clustering triangular is introduced first bipartite networks are projected into two weighted one mode networks by bipartite clustering triangular then all the maximal sub graphs from two one mode weighted networks are extracted and the maximal sub graphs are merged together using a weighted clustering threshold in addition the proposed algorithm successfully finds overlapping vertices between one mode communities experimental results using some real world network data shows that the performance of the proposed algorithm is satisfactory

maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm summary two new implementations of the em algorithm are proposed for maximum likelihood fitting of generalized linear mixed models both methods use random independent and identically distributed sampling to construct monte carlo approximations at the e step one approach involves generating random samples from the exact conditional distribution of the random effects given the data by rejection sampling using the marginal distribution as a candidate the second method uses a multivariate t importance sampling approximation in many applications the two methods are complementary rejection sampling is more efficient when sample sizes are small whereas importance sampling is better with larger sample sizes monte carlo approximation using random samples allows the monte carlo error at each iteration to be assessed by using standard central limit theory combined with taylor series methods specifically we construct a sandwich variance estimate for the maximizer at each approximate e step this suggests a rule for automatically increasing the monte carlo sample size after iterations in which the true em step is swamped by monte carlo error in contrast techniques for assessing monte carlo error have not been developed for use with alternative implementations of monte carlo em algorithms utilizing markov chain monte carlo e step approximations three different data sets including the infamous salamander data of mccullagh and nelder are used to illustrate the techniques and to compare them with the alternatives the results show that the methods proposed can be considerably more efficient than those based on markov chain monte carlo algorithms however the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension

a practical method for calculating largest lyapunov exponents from small data sets detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest lyapunov exponent lyapunov exponents quantify the exponential divergence of initially close state space trajectories and estimate the amount of chaos in a system we present a new method for calculating the largest lyapunov exponent from an experimental time series the method follows directly from the definition of the largest lyapunov exponent and is accurate because it takes advantage of all the available data we show that the algorithm is fast easy to implement and robust to changes in the following quantities embedding dimension size of data set reconstruction delay and noise level furthermore one may use the algorithm to calculate simultaneously the correlation dimension thus one sequence of computations will yield an estimate of both the level of chaos and the system complexity

identification of overlapping community structure in complex networks using fuzzy c means clustering abstract identification of overlapping communities clusters in a complex network is a general problem in data mining of network data sets in this paper we devise a novel algorithm to identify overlapping communities in complex networks by the combination of a new modularity function based on generalizing ng s q function an approximation mapping of network nodes into euclidean space and fuzzy c means clustering experimental results indicate that the new algorithm is efficient at detecting both good clusterings and the appropriate number of clusters

semi supervised community detection based on discrete potential theory abstract in recent studies of the complex network most of the community detection methods only consider the network topological structure without background information this leads to a relatively low accuracy in this paper a novel semi supervised community detection algorithm is proposed based on the discrete potential theory it effectively incorporates individual labels the labels of corresponding communities to guide the community detection process for achieving better accuracy specifically a number of vertices with user defined labels are first identified to act as unit elementary charges which can generate different electrostatic fields then community detection can be translated into a potential transmission problem by formulating the problem using combinational dirichlet labels of those unlabeled vertices can be determined by the labels for which the greatest potential is calculated finally a better community partition can be obtained our extensive numerical experiments in both artificial and real networks lead to two key observations first individual labels play an important role in community detection and second our proposed semi supervised community detection algorithm outperforms existing counterparts in both accuracy and time complexity especially for obscure networks

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

criterions for locally dense subgraphs abstract community detection is one of the most investigated problems in the field of complex networks although several methods were proposed there is still no precise definition of communities as a step toward a definition i highlight two necessary properties of communities separation and internal cohesion the latter being a new concept i propose a local method of community detection based on two dimensional local optimization which i tested on common benchmarks and on the word association database

distance dissimilarity index and network community structure we address the question of finding the community structure of a complex network in an earlier effort h zhou phys rev e 67 041908 2003 the concept of network random walking is introduced and a distance measure defined here we calculate based on this distance measure the dissimilarity index between nearest neighboring vertices of a network and design an algorithm to partition these vertices into communities that are hierarchically organized each community is characterized by an upper and a lower dissimilarity threshold the algorithm is applied to several artificial and real world networks and excellent results are obtained in the case of artificially generated random modular networks this method outperforms the algorithm based on the concept of edge betweenness centrality for yeast s protein protein interaction network we are able to identify many clusters that have well defined biological functions

benchmarks for testing community detection algorithms on directed and weighted graphs with overlapping communities many complex networks display a mesoscopic structure with groups of nodes sharing many links with the other nodes in their group and comparatively few with nodes of different groups this feature is known as community structure and encodes precious information about the organization and the function of the nodes many algorithms have been proposed but it is not yet clear how they should be tested recently we have proposed a general class of undirected and unweighted benchmark graphs with heterogeneous distributions of node degree and community size an increasing attention has been recently devoted to develop algorithms able to consider the direction and the weight of the links which require suitable benchmark graphs for testing in this paper we extend the basic ideas behind our previous benchmark to generate directed and weighted networks with built in community structure we also consider the possibility that nodes belong to more communities a feature occurring in real systems such as social networks as a practical application we show how modularity optimization performs on our benchmark

detect overlapping and hierarchical community structure in networks abstract clustering and community structure is crucial for many network systems and the related dynamic processes it has been shown that communities are usually overlapping and hierarchical however previous methods investigate these two properties of community structure separately this paper proposes an algorithm eagle to detect both the overlapping and hierarchical properties of complex community structure together this algorithm deals with the set of maximal cliques and adopts an agglomerative framework the quality function of modularity is extended to evaluate the goodness of a cover the examples of application to real world networks give excellent results

an efficient community detection algorithm using greedy surprise maximization community detection is an important and crucial problem in complex network analysis although classical modularity function optimization approaches are widely used for identifying communities the modularity function q suffers from its resolution limit recently the surprise function s was experimentally proved to be better than the q function however up until now there has been no algorithm available to perform searches to directly determine the maximal surprise values in this paper considering the superiority of the s function over the q function we propose an efficient community detection algorithm called agso algorithm based on greedy surprise optimization and its improved version fagso fast agso which are based on greedy surprise optimization and do not suffer from the resolution limit in addition f agso does not need the number of communities k to be specified in advance tests on experimental networks show that f agso is able to detect optimal partitions in both simple and even more complex networks moreover algorithms based on surprise maximization perform better than those algorithms based on modularity maximization including blondel guillaume lambiotte lefebvre bgll clauset newman moore cnm and the other state of the art algorithms such as infomap order statistics local optimization method oslom and label propagation algorithm lpa

asymptotic normality of maximum likelihood and its variational approximation for stochastic blockmodels variational methods for parameter estimation are an active research area potentially offering computationally tractable heuristics with theoretical performance bounds we build on recent work that applies such methods to network data and establish asymptotic normality rates for parameter estimates of stochastic blockmodel data by either maximum likelihood or variational estimation the result also applies to various sub models of the stochastic blockmodel found in the literature

a note on gauss hermite quadrature summary for gauss hermite quadrature we consider a systematic method for transforming the variable of integration so that the integrand is sampled in an appropriate region the effectiveness of the quadrature then depends on the ratio of the integrand to some gaussian density being a smooth function well approximated by a low order polynomial it is pointed out that in this approach order one gauss hermite quadrature becomes the laplace approximation thus the quadrature as implemented here can be thought of as a higher order laplace approximation

finding communities in directed networks by pagerank random walk induced network embedding abstract community structure has been found to exist ubiquitously in many different kinds of real world complex networks most of the previous literature ignores edge directions and applies methods designed for community finding in undirected networks to find communities here we address the problem of finding communities in directed networks our proposed method uses pagerank random walk induced network embedding to transform a directed network into an undirected one where the information on edge directions is effectively incorporated into the edge weights starting from this new undirected weighted network previously developed methods for undirected network community finding can be used without any modification moreover our method improves on recent work in terms of community definition and meaning we provide two simulated examples a real social network and different sets of power law benchmark networks to illustrate how our method can correctly detect communities in directed networks

community detection by signaling on complex networks based on a signaling process of complex networks a method for identification of community structure is proposed for a network with n nodes every node is assumed to be a system which can send receive and record signals each node is taken as the initial signal source to excite the whole network one time then the source node is associated with an n dimensional vector which records the effects of the signaling process by this process the topological relationship of nodes on the network could be transferred into a geometrical structure of vectors in n dimensional euclidean space then the best partition of groups is determined by f statistics and the final community structure is given by the k means clustering method this method can detect community structure both in unweighted and weighted networks it has been applied to ad hoc networks and some real networks such as the zachary karate club network and football team network the results indicate that the algorithm based on the signaling process works well

ranking the spreading ability of nodes in complex networks based on local structure abstract ranking nodes by their spreading ability in complex networks is a fundamental problem which relates to wide applications local metric like degree centrality is simple but less effective global metrics such as betweenness and closeness centrality perform well in ranking nodes but are of high computational complexity recently to rank nodes effectively and efficiently a semi local centrality measure has been proposed as a tradeoff between local and global metrics however in semi local centrality only the number of the nearest and the next nearest neighbors of a node is taken into account while the topological connections among the neighbors are neglected in this paper we propose a local structural centrality measure which considers both the number and the topological connections of the neighbors of a node to evaluate the performance of our method we use the susceptible infected recovered sir model to simulate the epidemic spreading process on both artificial and real networks by measuring the rank correlation between the ranked list generated by simulation results and the ones generated by centrality measures we show that our method can rank the spreading ability of nodes more accurately than centrality measures such as degree k shell betweenness closeness and local centrality further we show that our method can better distinguish the spreading ability of nodes

asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications in this paper we extend our previous work on the stochastic block model a commonly used generative model for social and biological networks and the problem of inferring functional groups or communities from the topology of the network we use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram we describe in detail properties of the detectability undetectability phase transition and the easy hard phase transition for the community detection problem our analysis translates naturally into a belief propagation algorithm for inferring the group memberships of the nodes in an optimal way i e that maximizes the overlap with the underlying group memberships and learning the underlying parameters of the block model finally we apply the algorithm to two examples of real world networks and discuss its performance

scalable detection of statistically significant communities and hierarchies using message passing for modularity modularity is a popular measure of community structure however maximizing the modularity can lead to many competing partitions with almost the same modularity that are poorly correlated with each other it can also produce illusory communities in random graphs where none exist we address this problem by using the modularity as a hamiltonian at finite temperature and using an efficient belief propagation algorithm to obtain the consensus of many partitions with high modularity rather than looking for a single partition that maximizes it we show analytically and numerically that the proposed algorithm works all of the way down to the detectability transition in networks generated by the stochastic block model it also performs well on real world networks revealing large communities in some networks where previous work has claimed no communities exist finally we show that by applying our algorithm recursively subdividing communities until no statistically significant subcommunities can be found we can detect hierarchical structure in real world networks more efficiently than previous methods

inferring overlapping community structure with degree corrected block model abstract recent research has shown great interest in statistical inference methods for community detection not only in models and algorithms but also in the detectability in this paper we propose a fast community detection algorithm based on the degree corrected block model by introducing a parameter to select the candidate solutions our algorithm is able to detect overlapping communities experiments on a range of networks have achieved state of the art results moreover we show that the algorithm based on the degree corrected block model also suffers the detectability limitation which is in accord with the most recent research on the detectability threshold

dynamical behaviour of the planar non linear mechanical system part ii experiment the experimental work has been undertaken on the washing complex dynamics to verify the theoretical approach from part i the measured time histories were analyzed by using spectral and phase space analyses the correlation dimension and the largest lyapunov exponent were estimated on a reconstructed phase space through an embedding procedure by using different measured time histories the largest positive lyapunov exponent and the non integer value of the correlation dimension of the attractor confirm the chaotic nature of the washing complex dynamics the visualization procedure was also implemented in three dimensional space differences were found in the values of the correlation dimension and largest lyapunov exponent when estimating them from different measured signals at the same time those estimated values show the same nature of motion power spectra and bicoherences have been used to analyze the washing complex dynamical behaviour it has been found that the dominant mode is the spin dry frequency while the higher modes have significantly lower power the quadratic phase coupling between the second and fifth harmonic is present thus confirming that the process is non linear it is also shown that the bicoherence estimate is sensitive to division by a small number which can increase its number of peaks in this case the magnitude bispectrum has been used to provide a more realistic picture of quadratic phase coupling the model described in part i is able to simulate the amplitude and the frequency of the predominant harmonic of the washing complex in the steady state but is unable to simulate all the richness of the motion of the washing complex

a parameter free community detection method based on centrality and dispersion of nodes in complex networks abstract k means is a simple and efficient clustering algorithm to detect communities in networks however it may suffer from a bad choice of initial seeds also called centers that seriously affect the clustering accuracy and the convergence rate additionally in k means the number of communities should be specified in advance till now it is still an open problem on how to select initial seeds and how to determine the number of communities in this study a new parameter free community detection method named k rank d was proposed first based on the fact that good initial seeds usually have high importance and are dispersedly located in a network we proposed a modified pagerank centrality to evaluate the importance of a node and drew a decision graph to depict the importance and the dispersion of nodes then the initial seeds and the number of communities were selected from the decision graph actively and intuitively as the start parameter of k means experimental results on synthetic and real world networks demonstrate the superior performance of our approach over competing methods for community detection

local resolution limit free potts model for community detection we report on an exceptionally accurate spin glass type potts model for community detection with a simple algorithm we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise it is also competitive with the best currently available algorithms in terms of speed and size of solvable systems we find that the computational demand often exhibits superlinear scaling o l 1 3 where l is the number of edges in the system and we have applied the algorithm to synthetic systems as large as 40 ifmmode times else texttimes fi 10 6 nodes and over 1 ifmmode times else texttimes fi 10 9 edges a previous stumbling block encountered by popular community detection methods is the so called resolution limit being a local measure of community structure our potts model is free from this resolution limit effect and it further remains a local measure on weighted and directed graphs we also address the mitigation of resolution limit effects for two other popular potts models

personalized pagerank clustering a graph clustering algorithm based on random walks abstract graph clustering has been an essential part in many methods and thus its accuracy has a significant effect on many applications in addition exponential growth of real world graphs such as social networks biological networks and electrical circuits demands clustering algorithms with nearly linear time and space complexity in this paper we propose personalized pagerank clustering ppc that employs the inherent cluster exploratory property of random walks to reveal the clusters of a given graph we combine random walks and modularity to precisely and efficiently reveal the clusters of a graph ppc is a top down algorithm so it can reveal inherent clusters of a graph more accurately than other nearly linear approaches that are mainly bottom up it also gives a hierarchy of clusters that is useful in many applications ppc has a linear time and space complexity and has been superior to most of the available clustering algorithms on many datasets furthermore its top down approach makes it a flexible solution for clustering problems with different requirements

i o efficient calculation of h group closeness centrality over disk resident graphs we introduce h group closeness centrality in this work h group closeness centrality of a group of nodes measures how close this node group is to other nodes in a graph and can be used in numerous applications such as measuring the importance and influence of a group of users in a social network when a large graph contains billions of edges that cannot reside entirely in a computers main memory computing and maximizing h group closeness centrality both become challenging in this work we present a systematic solution for efficiently computing and maximizing h group closeness centrality in large disk resident graphs only using a common pc our solution leverages a probabilistic counting method to efficiently estimate h group closeness with high accuracy rather than exhaustively computing it in an exact fashion furthermore we design an i o efficient greedy algorithm to find a node group that approximately maximizes h group closeness centrality in a graph our algorithm exploits several appealing properties of the defined h group closeness measure to reduce the computational cost of handling a disk resident graph extensive evaluation on large real world and synthetic graphs demonstrates the efficiency of our proposed method for example our proposed i o efficient greedy algorithm is about 300 times faster than a simple multi pass method on the twitter graph with 1 4 billion edges this reduces the running time of identifying one group member from nearly an hour to less than 20s on average

detecting network communities by propagating labels under constraints we investigate the recently proposed label propagation algorithm lpa for identifying network communities we reformulate the lpa as an equivalent optimization problem giving an objective function whose maxima correspond to community solutions by considering properties of the objective function we identify conceptual and practical drawbacks of the label propagation approach most importantly the disparity between increasing the value of the objective function and improving the quality of communities found to address the drawbacks we modify the objective function in the optimization problem producing a variety of algorithms that propagate labels subject to constraints of particular interest is a variant that maximizes the modularity measure of community quality performance properties and implementation details of the proposed algorithms are discussed bipartite as well as unipartite networks are considered

asymptotic normality and valid inference for gaussian variational approximation we derive the precise asymptotic distributional behavior of gaussian variational approximate estimators of the parameters in a single predictor poisson mixed model these results are the deepest yet obtained concerning the statistical properties of a variational approximation method moreover they give rise to asymptotically valid statistical inference a simulation study demonstrates that gaussian variational approximate confidence intervals possess good to excellent coverage properties and have a similar precision to their exact likelihood counterparts 1 introduction variational approximation methods are enjoying an increasing amount of development and use in statistical problems this raises questions regarding their statistical properties such as consistency of point estimators and validity of statistical inference we make significant inroads into answering such questions via thorough theoretical treatment of one of the simplest nontrivial settings for which variational approximation is beneficial the poisson mixed model with a single predictor variable and random intercept we call this the simple poisson mixed model the model treated here is also treated in 7 but there attention is confined to bounds and rates of convergence we improve upon their results by obtaining the asymptotic distributions of the estimators the results reveal that the estimators are asymptotically normal have negligible bias and that their variances decay at least as fast as m 1 w herem is the number of groups for the slope parameter the faster mn 1 rate is obtained where n is the number of repeated measures an important practical ramification of our theory is asymptotically valid statistical inference for the model parameters in particular a form of studentization leads to theoretically justifiable confidence intervals for all model parameters unlike those based on the exact likelihood all gaussian variational approximate point estimates and confidence intervals can be computed without the need for numer

modularity density of network community divisions the problem of dividing a network into communities is extremely complex and grows very rapidly with the number of nodes and edges that are involved in order to develop good algorithms to identify optimal community divisions it is extremely beneficial to identify properties that are similar for most networks we introduce the concept of modularity density the distribution of modularity values as a function of the number of communities and find strong indications that the general features of this modularity density are quite similar for different networks the region of high modularity generally has very low probability density and occurs where the number of communities is small the properties and shape of the modularity density may give valuable information and aid in the search for efficient algorithms to find community divisions with high modularities

discriminative metric learning for multi view graph partitioning we propose discriminative metric learning for multi view graph partitioning we envision the multi view graph as an adaptive dynamic system the intra view connections and the inter view couplings are interplayed extensive experiments have been conducted to show the effectiveness in recent years multi view graph partitioning has attracted more and more attention but most efforts have been made to develop graph partitioning approaches directly in the original topological structure in many real world applications graph may contain noisy links and the distance metric may not be so discriminative for revealing cluster structure this paper addresses the problem of discriminative metric learning for multi view graph partitioning in particular we propose a novel method called multi view dml abbr of multi view discriminative metric learning to transform the metric space in the original graph into a more discriminative metric space in which better graph partitioning results will be obtained we envision the multi view graph as an adaptive dynamic system where both the intra view connections and the inter view couplings are interplayed to gradually update the relation metric among nodes on the one hand the inter view coupling will be influenced by the intra view connection between two nodes on the other hand the inter view coupling will also affect the intra view connection such interplay eventually makes the whole graph reach a steady state which has a stronger cluster structure than the original graph extensive experiments are conducted on both synthetic and real world graphs to confirm that the proposed method is able to learn more discriminative metric

variational approximations for categorical causal modeling with latent variables latent class models in the social and behavioral sciences have remained structurally simple one reason for this is that inference in statistical models can be computationally difficult methods for approximate inference known as variational approximations which have been developed in the machine learning graphical modeling and statistical physics literatures can be used to alleviate the computational difficulties of inference for latent variable models the aim of the present article is to set these methods alongside some social and behavioral science literature to which they are relevant and in particular to consider their potential for categorical causal modeling using latent class analysis we have collated a number of popular categorical data models with latent variables and causal structure typically incorporating a markovian structure the efficacy of the approximation methods has been demonstrated through simulations related to an important behavioral science model

community detection as an inference problem we express community detection as an inference problem of determining the most likely arrangement of communities we then apply belief propagation and mean field theory to this problem and show that this leads to fast accurate algorithms for community detection

a modified evidential methodology of identifying influential nodes in weighted networks abstract how to identify influential nodes in complex networks is still an open hot issue in the existing evidential centrality evc node degree distribution in complex networks is not taken into consideration in addition the global structure information has also been neglected in this paper a new evidential semi local centrality esc is proposed by modifying evc in two aspects firstly the basic probability assignment bpa of degree generated by evc is modified according to the actual degree distribution rather than just following uniform distribution bpa is the generation of probability in order to model uncertainty secondly semi local centrality combined with modified evc is extended to be applied in weighted networks numerical examples are used to illustrate the efficiency of the proposed method

locally optimal heuristic for modularity maximization of networks community detection in networks based on modularity maximization is currently done with hierarchical divisive or agglomerative as well as partitioning heuristics hybrids and in a few papers exact algorithms we consider here the case of hierarchical networks in which communities should be detected and propose a divisive heuristic which is locally optimal in the sense that each of the successive bipartitions is done in a provably optimal way this heuristic is compared with the spectral based hierarchical divisive heuristic of newman proc natl acad sci usa 103 8577 2006 and with the hierarchical agglomerative heuristic of clauset newman and moore phys rev e 70 066111 2004 computational results are given for a series of problems of the literature with up to 4941 vertices and 6594 edges they show that the proposed divisive heuristic gives better results than the divisive heuristic of newman and than the agglomerative heuristic of clauset et al

replica inference approach to unsupervised multiscale image segmentation we apply a replica inference based potts model method to unsupervised image segmentation on multiple scales this approach was inspired by the statistical mechanics problem of community detection and its phase diagram specifically the problem is cast as identifying tightly bound clusters communities or solutes against a background or solvent within our multiresolution approach we compute information theory based correlations among multiple solutions replicas of the same graph over a range of resolutions significant multiresolution structures are identified by replica correlations manifest by information theory overlaps we further employ such information theory measures such as normalized mutual information and variation of information thermodynamic quantities such as the system entropy and energy and dynamic measures monitoring the convergence time to viable solutions as metrics for transitions between various solvable and unsolvable phases within the solvable phase transitions between contending solutions such as those corresponding to segmentations on different scales may also appear with the aid of these correlations as well as thermodynamic measures the phase diagram of the corresponding potts model is analyzed at both zero and finite temperatures optimal parameters corresponding to a sensible unsupervised segmentations appear within the easy phase of the potts model our algorithm is fast and shown to be at least as accurate as the best algorithms to date and to be especially suited to the detection of camouflaged images