explicit solution to the singular discrete time stationary linear filtering problem a closed form solution to the stationary discrete time linear filtering problem is obtained explicitly in terms of the system state space matrices in the limiting singular case where the measurement noise tends to zero simple expressions in closed form are obtained for the kalman gain matrix both for uniform and nonuniform rank systems and the explicit eigenstructure of the kalman filter closed loop matrix is derived the minimum error covariance matrices of the a priori and a posteriori filtered estimates are obtained using this special eigenstructure and a remarkably different behavior of the solution in the minimum and nonminimum phase cases is found

pinning control of complex dynamical networks with general topology abstract recently the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes e g symmetric coupling uniform coupling and linear coupling however most real networks often consist of local units which interact with each other via asymmetric and heterogeneous connections in this paper pinning control of a continuous time complex dynamical network with general coupling topologies is studied some generic stability criteria based on master stability function msf are derived for such a general controlled network which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes then these results are extended to discrete time case previous results about symmetric uniform or linear coupled networks in this area are included as special cases of the present work numerical simulations of directed networks with weighted coupling pinned by specifically selective pinning scheme are given for illustration and verification

reciprocity of networks with degree correlations and arbitrary degree sequences although most of the real networks contain a mixture of directed and bidirectional reciprocal connections the reciprocity r has received little attention as a subject of theoretical understanding we study the expected reciprocity of networks with arbitrary input and output degree sequences and given 2 node degree correlations by means of statistical ensemble approach we demonstrate that degree correlations are crucial to understand the reciprocity in real networks and a hierarchy of correlation contributions to r is revealed numerical experiments using network randomization methods show very good agreement to our analytical estimations

loop transfer recovery techniques for discrete time optimal regulators using prediction estimators for discrete time lqg optimal regulators using current estimators it has been shown that perfect recoveries of the loop transfer matrices at the input or at the output are possible for square minimum phase systems however current estimators cannot be used when the processing time of the controller is significant in this note the loop transfer recoveries using prediction estimators for square minimum phase systems are considered it is shown that although the perfect recoveries are impossible the feedback properties obtained by the recovery techniques are those that can be recovered best in the presence of the delay in the controller

an explicit expression for the minimum phase image of transfer function matrices a simple expression is obtained for the transfer function matrix of the minimum phase image of a left invertible continuous time invariant system with zeros in the right half plane that may be of multiplicities greater than one this expression is obtained by multiplying the system transfer function matrix from the right by a special inner matrix and it is explicitly given in terms of the input zero directions that correspond to the zeros of the system in the right half plane the result provides a simple expression for the inner outer factorization of transfer function matrices and it can thus be used in h sub infinity optimal control

a new stable compensator design for exact and approximate loop transfer recovery abstract in this paper a new compensator structure for loop transfer recovery ltr is proposed the proposed compensator a is open loop stable b guarantees closed loop stability and above all c requires much smaller values of gain than the conventional observer based controller for the same degree of loop transfer recovery the fact that the new compensator requires much smaller values of gain than the conventional controller results in several practical advantages the most important among them being the reduction in controller band width and freedom from the woes of saturation the trade off between the value of gain and the degree of loop transfer recovery as well as the bounds on singular values of sensitivity and complementary sensitivity functions is shown clearly both full and reduced order compensators for ltr when the design specifications are reflected either at the input or at the output point of the given plant are considered numerical examples illustrate the advantages of the new compensator structure the new compensator structure is inspired by a careful and clear understanding of how loop transfer recovery occurs when conventional observer based controllers are used to motivate and deduce our new compensator structure a unified treatment of observer theory for ltr is presented in the context of such a unification some new results are also given

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

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

biased percolation on scale free networks biased degree dependent percolation was recently shown to provide strategies for turning robust networks fragile and vice versa here we present more detailed results for biased edge percolation on scale free net works we assume a network in which the probability for an edge between nodes i and j to be retained is proportional to kikjwith ki and kj the degrees of the nodes we discuss two methods of network recon struction sequential and simultaneous and investigate their properties by analytical and numerical means the system is examined away from the percolation transition where the size of the giant cluster is obtained and close to the transition where nonuniversal critical exponents are extracted using the generating functions method the theory is found to agree quite well with simulations by presenting an extension of the fortuin kasteleyn construction we find that biased percolation is well described by the q 1 limit of the q state potts model with inhomogeneous couplings

effect of degree correlations on networked traffic dynamics abstract in order to enhance the transport capacity of scale free networks we study the relation between the degree correlation and the transport capacity of the network we calculate the degree degree correlation coefficient the maximal betweenness and the critical value of the generating rate r c traffic congestion occurs for r r c numerical experiments indicate that both assortative mixing and disassortative mixing can enhance the transport capacity we also reveal how the network structure affects the transport capacity assortative disassortative mixing changes distributions of nodes betweennesses and as a result the traffic decreases through nodes with the highest degree while it increases through the initially idle nodes

automatic clustering using genetic algorithms abstract in face of the clustering problem many clustering methods usually require the designer to provide the number of clusters as input unfortunately the designer has no idea in general about this information beforehand in this article we develop a genetic algorithm based clustering method called automatic genetic clustering for unknown k agcuk in the agcuk algorithm noising selection and division absorption mutation are designed to keep a balance between selection pressure and population diversity in addition the davies bouldin index is employed to measure the validity of clusters experimental results on artificial and real life data sets are given to illustrate the effectiveness of the agcuk algorithm in automatically evolving the number of clusters and providing the clustering partition

robustness of zero shifting via generalized sampled data hold functions in this paper we study robustness and sensitivity properties of a sampled data feedback system with a generalized sampled data hold function gshf we argue that shifting non minimum phase zeros using gshf control can lead to difficulties unless the zero is outside the closed loop bandwidth

performance limitations in the robust servomechanism problem for discrete time lti systems fundamental limitations for error tracking regulation are obtained for the robust servomechanism problem rsp for a sampled system in studying this problem the cheap control problem for a multi input multi output discrete time system is considered and explicit expressions are obtained for the limiting steady state solution of its associated algebraic riccati equation are as the weight on the control energy tends to zero application of these results is then made to obtain explicit expressions for the limiting performance costs associated with error tracking regulation in the rsp these limitations can be characterized by the system order the dimension of the outputs the number of the system s transmission zeros and the location of the system s nonminimum phase transmission zeros

asymptotic recovery for discrete time systems an asymptotic recovery design procedure is proposed for square discrete time linear time invariant multivariable systems which allows a state feedback design to be approximately recovered by a dynamic output feedback scheme both the case of negligible processing time compared to the sampling interval and of significant processing time are discussed in the former case it is possible to obtain perfect recovery if the plant is minimum phase and has the smallest possible number of zeros at infinity in other cases good recovery is frequently possible new conditions are found which ensure that the return ratio being recovered exhibits good robustness properties

a tabu search based algorithm for the fuzzy clustering problem the fuzzy clustering problem fcp is a mathematical program which is difficult to solve since it is nonconvex which implies possession of many local minima the fuzzy c means heuristic is the widely known approach to this problem but it is guaranteed only to yield local minima in this paper we propose a new approach to this problem which is based on tabu search technique and aims at finding a global solution of fcp we compare the performance of the algorithm with the fuzzy c means algorithm

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

mean field level analysis of epidemics in directed networks the susceptible infected removed spreading model in a directed graph is studied the mean field level rate equations are built with the degree degree connectivity correlation element and the in out degree distribution and the outbreak threshold is obtained analytically it is determined by the combination of connectivity probability and the degree distribution furthermore the methods of calculating the degree degree correlations in directed networks are presented the numerical results of the discrete epidemic processes in networks verify our analyses

paper sensitivity integrals for multivariable discrete time systems the purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete time systems we present extensions to both the classical poisson integral and bode s sensitivity integral formulae the main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete time systems due to such system characteristics as open loop unstable poles and nonminimum phase zeros and to such design requirements as stability and bandwidth constraints these formulae are similar to those for multivariable continuous time systems obtained elsewhere and they reveal that feedback design limitations depend on directionality properties of the sensitivity function and on those of unstable poles and nonminimum phase zeros in the open loop transfer function

universal emergence of pagerank the pagerank algorithm enables us to rank the nodes of a network through a specific eigenvector of the google matrix using a damping parameter 0 1 using extensive numerical simulations of large web networks with a special accent on british university networks we determine numerically and analytically the universal features of the pagerank vector at its emergence when 1 the whole network can be divided into a core part and a group of invariant subspaces for 1 pagerank converges to a universal power law distribution on the invariant subspaces whose size distribution also follows a universal power law the convergence of pagerank at 1 is controlled by eigenvalues of the core part of the google matrix which are extremely close to unity leading to large relaxation times as for example in spin glasses

percolation in directed scale free networks many complex networks in nature have directed links a property that affects the network s navigability and large scale topology here we study the percolation properties of such directed scale free networks with correlated in and out degree distributions we derive a phase diagram that indicates the existence of three regimes determined by the values of the degree exponents in the first regime we regain the known directed percolation mean field exponents in contrast the second and third regimes are characterized by anomalous exponents which we calculate analytically in the third regime the network is resilient to random dilution i e the percolation threshold is pc 1

integrated rough fuzzy clustering for categorical data analysis abstract in recent times advanced data mining research has been mostly focusing on clustering of categorical data where a natural ordering in attribute values is missing to address this fact the rough fuzzy k modes clustering technique has been recently developed in order to handle imperfect information i e indiscernibility coarseness and vagueness within the dataset however it has been observed that the said technique suffers from the problem of local optima due to the random choice of initial cluster modes hence in this paper we have proposed an integrated clustering technique using multi phase learning in this regard first simulated annealing based rough fuzzy k modes and genetic algorithm based rough fuzzy k modes are proposed in order to perform the clustering better by considering clustering as an underlying optimization problem these clustering methods individually produce clusters having set of central and peripheral points thereafter for each case final improved clustering results are obtained by assigning peripheral points to a particular crisp cluster using random forest where central points are used as training set second the varying cardinality of the training and testing sets produced by each clustering method further motivated us to propose a generalized technique called integrated rough fuzzy clustering using random forest where results of three aforementioned clustering techniques are used to compute the roughness measure based on this measure three different sets namely best central points semi best central points and pure peripheral points are determined thereafter using multi phase learning best central points are used to classify the semi best central points and then using both of them pure peripheral points are classified by random forest experimental results are reported quantitatively and visually to demonstrate the effectiveness of the proposed methods in comparison with well known state of the art methods for six synthetic and five real life datasets finally statistical significance tests are conducted to establish the superiority of the results produced by the proposed methods

multiple phase transitions in long range first passage percolation on square lattices we consider a model of long range first passage percolation on the d dimensional square lattice in which any two distinct vertices are connected by an edge having exponentially distributed passage time with mean where 0 is a fixed parameter and is the l1 norm on we analyze the asymptotic growth rate of the set t which consists of all such that the first passage time between the origin 0 and x is at most t as t we show that depending on the values of there are four growth regimes i instantaneous growth for 2d 1 like the nearest neighbor first passage percolation model corresponding to 2015 wiley periodicals inc

discrete time lqg ltr technique for systems with time delays loop transfer recovery ltr is applied for lqg controllers with prediction estimators for a class of square minimum phase discrete time linear systems with time delays we consider the class of plants described by the triple a b c whose time delay structure is characterized by the following hypothesis on the plant impulse response cb cab cad 2b 0 det cad 1b 0 when the estimator gain is fixed by recovery technique it is shown that the loop transfer matrix at the plant input is equal to the transfer matrix obtained with the optimal digital regulator having d sample controller delays described in 6 the dual result corresponding to the situation where the feedback gain is fixed by recovery technique is also analysed

a time efficient pattern reduction algorithm for k means clustering this paper presents an efficient algorithm called pattern reduction pr for reducing the computation time of k means and k means based clustering algorithms the proposed algorithm works by compressing and removing at each iteration patterns that are unlikely to change their membership thereafter not only is the proposed algorithm simple and easy to implement but it can also be applied to many other iterative clustering algorithms such as kernel based and population based clustering algorithms our experiments from 2 to 1000 dimensions and 150 to 10 000 000 patterns indicate that with a small loss of quality the proposed algorithm can significantly reduce the computation time of all state of the art clustering algorithms evaluated in this paper especially for large and high dimensional data sets

strong correlations between text quality and complex networks features abstract concepts of complex networks have been used to obtain metrics that were correlated to text quality established by scores assigned by human judges texts produced by high school students in portuguese were represented as scale free networks word adjacency model from which typical network features such as the in outdegree clustering coefficient and shortest path were obtained another metric was derived from the dynamics of the network growth based on the variation of the number of connected components the scores assigned by the human judges according to three text quality criteria coherence and cohesion adherence to standard writing conventions and theme adequacy development were correlated with the network measurements text quality for all three criteria was found to decrease with increasing average values of outdegrees clustering coefficient and deviation from the dynamics of network growth among the criteria employed cohesion and coherence showed the strongest correlation which probably indicates that the network measurements are able to capture how the text is developed in terms of the concepts represented by the nodes in the networks though based on a particular set of texts and specific language the results presented here point to potential applications in other instances of text analysis

robustness of onionlike correlated networks against targeted attacks recently it was found by schneider et al proc natl acad sci usa 108 3838 2011 using simulations that scale free networks with onion structure are very robust against targeted high degree attacks the onion structure is a network where nodes with almost the same degree are connected motivated by this work we propose and analyze based on analytical considerations an onionlike candidate for a nearly optimal structure against simultaneous random and targeted high degree node attacks the nearly optimal structure can be viewed as a set of hierarchically interconnected random regular graphs the degrees and populations of whose nodes are specified by the degree distribution this network structure exhibits an extremely assortative degree degree correlation and has a close relationship to the onion structure after deriving a set of exact expressions that enable us to calculate the critical percolation threshold and the giant component of a correlated network for an arbitrary type of node removal we apply the theory to the cases of random scale free networks that are highly vulnerable against targeted high degree node removal our results show that this vulnerability can be significantly reduced by implementing this onionlike type of degree degree correlation without much undermining the almost complete robustness against random node removal we also investigate in detail the robustness enhancement due to assortative degree degree correlation by introducing a joint degree degree probability matrix that interpolates between an uncorrelated network structure and the onionlike structure proposed here by tuning a single control parameter the optimal values of the control parameter that maximize the robustness against simultaneous random and targeted attacks are also determined our analytical calculations are supported by numerical simulations

heterogeneous bond percolation on multitype networks with an application to epidemic dynamics considerable attention has been paid in recent years to the use of networks in modeling complex real world systems among the many dynamical processes involving networks propagation processes in which the final state can be obtained by studying the underlying network percolation properties have raised formidable interest in this paper we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability as previously demonstrated the multitype approach allows many nontrivial mixing patterns such as assortativity and clustering between nodes we derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion we also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism we further show that the multitype approach by naturally allowing heterogeneity in the bond occupation probability overcomes some of the correlation issues encountered by previous models we illustrate this point in the context of contact network epidemiology

fuzzy c means optimality of solutions and effective termination of the algorithm abstract in this paper the solutions produced by the fuzzy c means algorithm for a general class of problems are examined and a method to test for the local optimality of such solutions is established an equivalent mathematical program is defined for the c means problem utilizing a generalized norm then the properties of the resulting optimization problem are investigated it is shown that the gradient of the resulting objective function at the solution produced by the c means algorithm in this case takes a special structure which can be used in terminating the algorithm moreover the local optimality of the solution obtained is checked utilizing the hessian of the criterion function the solution is a local minimum point if the hessian matrix at this point is positive semidefinite simple rules are proposed to help in checking the definiteness of the matrix

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

local convergence of the fuzzy c means algorithms abstract much understanding has recently been gained concerning global convergence properties of the fuzzy c means fcm family of clustering algorithms these global convergence properties which hold for all iteration sequences guarantee that every fcm iteration sequence converges at least along a subsequence to a stationary point of an fcm objective function in this paper we prove a local convergence property that is a property pertaining to iteration sequences started near a solution specifically a simple result is proved which shows that whenever an fcm algorithm is started sufficiently near a minimizer of the corresponding objective function then the iteration sequence must converge to that particular minimizer the result guarantees that once captured by the local neighborhood of a minimizer the succeeding iterate sequence will not escape thus infinite oscillation of such a sequence cannot occur the rate of convergence of the sequence to such a point is also discussed

the lqg ltr procedure for multivariable feedback control design this paper provides a tutorial overview of the lqg ltr design procedure for linear multivariable feedback systems lqg ltr is interpreted as the solution of a specific weighted h2 tradeoff between transfer functions in the frequency domain properties of this solution are examined for both minimum phase and nonminimum phase systems this leads to a formal weight augmentation procedure for the minimum phase case which permits essentially arbitrary specification of system sensitivity functions in terms of the weights while such arbitrary specifications are not possible for nonminimum phase problems a direct relationship between weights and sensitivities is developed for nonminimum phase siso and certain nonminimum phase mimo cases which guides the weight selection process

guaranteed stability margins for the discrete time linear quadratic optimal regulator the stability properties of the linear quadratic deterministic optimal regulator are investigated in the discrete time case guaranteed phase and gain margins are obtained for the regulator in terms of the singular values of the matrices of the regulator state space description these margins are compared to their continuous time counterparts and their implication on the regulator robustness is discussed

giant strongly connected component of directed networks we describe how to calculate the sizes of all giant connected components of a directed graph including the strongly connected one in particular the world wide web is a directed network the results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in and out degree distribution p k i k o we show that if p k i k o does not factorize the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in and out components the calculations of the relative sizes of all the giant components are demonstrated using the simplest examples we explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one

a fuzzy k modes algorithm for clustering categorical data this correspondence describes extensions to the fuzzy k means algorithm for clustering categorical data by using a simple matching dissimilarity measure for categorical objects and modes instead of means for clusters a new approach is developed which allows the use of the k means paradigm to efficiently cluster large categorical data sets a fuzzy k modes algorithm is presented and the effectiveness of the algorithm is demonstrated with experimental results

discrete time loop transfer recovery for systems with nonminimum phase zeros and time delays abstract the purpose of this paper is to study what happens when the discrete time loop transfer recovery ltr procedure is applied to plants with nonminimum phase zeros and with uniform time delay in all channels explicit expressions are given for the asymptotic behavior of the resulting sensitivity function and loop transfer function these results yield a better understanding of the mechanism of the discrete time loop transfer recovery procedure and the design limitations due to nonminimum phase zeros and time delays

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

a tabu search approach for the minimum sum of squares clustering problem in this paper a tabu search based clustering approach called ts clustering is proposed to deal with the minimum sum of squares clustering problem in the ts clustering algorithm five improvement operations and three neighborhood modes are given the improvement operation is used to enhance the clustering solution obtained in the process of iterations and the neighborhood mode is used to create the neighborhood of tabu search the superiority of the proposed method over some known clustering techniques is demonstrated for artificial and real life data sets

an optimization algorithm for clustering using weighted dissimilarity measures one of the main problems in cluster analysis is the weighting of attributes so as to discover structures that may be present by using weighted dissimilarity measures for objects a new approach is developed which allows the use of the k means type paradigm to efficiently cluster large data sets the optimization algorithm is presented and the effectiveness of the algorithm is demonstrated with both synthetic and real data sets

interfaces and the edge percolation map of random directed networks the traditional node percolation map of directed networks is reanalyzed in terms of edges in the percolated phase edges can mainly organize into five distinct giant connected components interfaces bridging the communication of nodes in the strongly connected component and those in the in and out components formal equations for the relative sizes in the number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two point correlations the uncorrelated null model is fully solved analytically and compared against simulations finding an excellent agreement interfaces and their particular conformations giving place from hairy ball percolation landscapes to bottleneck straits could bring new light to the discussion of how a structure is interwoven with functionality in flow networks

ltr design of discrete time proportional integral observers applies the proportional integral pi observer in connection with loop transfer recovery ltr design for discrete time systems both the prediction and the filtering versions of the pi observer are considered we show that a pi observer makes it possible to obtain time recovery i e exact recovery for t spl rarr spl infin under mild conditions two systematic ltr design methods one based on an extension of the linear quadratic gaussian loop transfer recovery lqg ltr and the other based on linear matrix inequality lmi are derived for the discrete time pi observer case explicit expressions for the recovery error when exact recovery is not achievable for all frequencies are also given

sandpile model on an optimized scale free network on euclidean space deterministic sandpile models are studied on a cost optimized barabasi albert ba scale free network whose nodes are the sites of a square lattice for the optimized ba network the sandpile model has the same critical behaviour as the btw sandpile whereas for the un optimized ba network the critical behaviour is mean field like

incremental learning based multiobjective fuzzy clustering for categorical data the problem of clustering categorical data where attribute values cannot be naturally ordered as numerical values has gained more importance in recent time due to the special properties of categorical attributes the clustering of categorical data seems to be more complicated than that of numerical data although a few clustering algorithms that optimize single clustering objective have been proposed it has found that such single measure may not be appropriate for all kind of datasets hence in this article an incremental learning based multiobjective fuzzy clustering for categorical data is proposed for this purpose a multiobjective modified differential evolution based fuzzy clustering algorithm is developed thereafter it integrates with the well known supervised classifier called random forest using incremental learning to propose the aforementioned technique here the multiobjective algorithm produces a set of optimal clustering solutions known as pareto optimal solutions by optimizing two conflicting objectives simultaneously subsequently through incremental learning using random forest classifier final solution is evolved from the ensemble pareto optimal solutions the results of the proposed method are demonstrated quantitatively and visually in comparison with widely used state of the art methods for six synthetic and four real life datasets finally statistical test is conducted to show the superiority of the results produced by the proposed method

second look at the spread of epidemics on networks in an important paper newman phys rev e66 016128 2002 claimed that a general network based stochastic susceptible infectious removed sir epidemic model is isomorphic to a bond percolation model where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor in this paper we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the sir epidemic model in any finite population in the limit of a large population i the distribution of self limited outbreak sizes is identical to the size distribution of small out components ii the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears iii the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in component and iv the relative final size of an epidemic is equal to the proportion of the network contained in the giant out component for the sir model considered by newman we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold the same epidemic threshold and the same final size of an epidemic as the bond percolation model however the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution we confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations in the appendix we show that an isomorphism to an epidemic percolation network can be defined for any time homogeneous stochastic sir model

clustering categorical data sets using tabu search techniques clustering methods partition a set of objects into clusters such that objects in the same cluster are more similar to each other than objects in different clusters according to some defined criteria the fuzzy k means type algorithm is best suited for implementing this clustering operation because of its effectiveness in clustering data sets however working only on numeric values limits its use because data sets often contain categorical values in this paper we present a tabu search based clustering algorithm to extend the k means paradigm to categorical domains and domains with both numeric and categorical values using tabu search based techniques our algorithm can explore the solution space beyond local optimality in order to aim at finding a global solution of the fuzzy clustering problem it is found that the clustering results produced by the proposed algorithm are very high in accuracy