Coloring random graphs

We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring, whereas graphs with high connectivity are uncolorable. Depending on q, we find the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a clustering phase c in [c(d),c(q)] in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms.     

A complex networks approach for data clustering

This work proposes a method for data clustering based on complex networks theory. A data set is represented as a network by considering different metrics to establish the connection between each pair of objects. The clusters are obtained by taking into account five community detection algorithms. The network-based clustering approach is applied in two real-world databases and two sets of artificially generated data. The obtained results suggest that the exponential of the Minkowski distance is the most suitable metric to quantify the similarities between pairs of objects. In addition, the community identification method based on the greedy optimization provides the best cluster solution. We compare the network-based clustering approach with some traditional clustering algorithms and verify that it provides the lowest classification error rate.     

Dense mode clustering in brain maps

A mode-based clustering method is developed for identifying spatially dense clusters in brain maps. This type of clustering focuses on identifying clusters in brain maps independent of their shape or overall variance. This can be useful for both localization in terms of interpretation and for subsequent graphical analysis that might require more coherent or dense regions of interest as starting points. The method automatically does signal/noise sharpening through density mode seeking. We also discuss the problem of parameter selection with this method and propose a new method involving 2-parameter control surface, in which we show that the same cluster solution results from tradeoff of these 2 parameters (the local density k and the radius r of the spherical kernel). We benchmark the new dense mode clustering by using several artificially created data sets and brain imaging data sets from an event perception task by perturbing the data set with noise and measuring three kinds of deviation from the original cluster solution. We present benchmark results that demonstrate that the mode clustering method consistently outperforms the commonly used single-linkage clustering, k means method (centroid method) and Ward's method (variance method).     

Traveling Salesman Problem with Clustering

In the original traveling salesman problem, the traveling salesman has the task to find the shortest closed tour through a proposed set of nodes, touching each node exactly once and returning to the initial node at the end. For the sake of the tour length to be minimized, nodes close to each other might not be visited one after the other but separated in the tour. However, for some practical applications, it is useful to group nodes to clusters, such that all nodes of a cluster are visited contiguously. Here we present an approach which leads to an automatic clustering with a clustering parameter governing the sizes of the clusters.     

Speech utterance clustering based on the maximization of within-cluster homogeneity of speaker voice characteristics

This paper investigates the problem of how to partition unknown speech utterances into a set of clusters, such that each cluster consists of utterances from only one speaker, and the number of clusters reflects the unknown speaker population size. The proposed method begins by specifying a certain number of clusters, corresponding to one of the possible speaker population sizes, and then maximizes the level of overall within-cluster homogeneity of the speakers' voice characteristics. The within-cluster homogeneity is characterized by the likelihood probability that a cluster model, trained using all the utterances within a cluster, matches each of the within-cluster utterances. To attain the maximal sum of likelihood probabilities for all utterances, the proposed method applies a genetic algorithm to determine the cluster in which each utterance should be located. For greater computational efficiency, also proposed is a clustering criterion that approximates the likelihood probability with a divergence-based model similarity between a cluster and each of the within-cluster utterances. The clustering method then examines various legitimate numbers of clusters by adapting the Bayesian information criterion to determine the most likely speaker population size. The experimental results show the superiority of the proposed method over conventional methods based on hierarchical clustering.     

Personalized PageRank Clustering: A graph clustering algorithm based on random walks

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.     

Cluster model approach for electronic structure of Si and Ge(111) and GaAs(110) surfaces

For the purpose of exploring how realistic a cluster model can be for semiconductor surfaces, extended Huckel theory calculations are performed on clusters modeling Si and Ge(111) and GaAs(110) surfaces as prototypes. Boundary conditions of the clusters are devised to be reduced. The ideal, relaxed, and reconstructed Si and Ge(111) surfaces are dealt with. Hydrogen chemisorbed (111) clusters of Si and Ge are also investigated as prototypes of chemisorption systems. Some comparison of the results with finite slab calculations and experiments is presented. The cluster-size dependence of the calculated energy levels, local densities of states, and charge distributions is examined for Si and Ge(111) clusters. It is found that a 45-atom cluster which has seven layers along the [111] direction is large enough to identify basic surface states and study the hydrogen chemisorption on Si and Ge(111) surfaces. Also, it is presented that surface states on the clean Si and Ge(111) clusters exist independent of relaxation. Further, the calculation for the relaxed GaAs(110) cluster gives the empty and filled dangling-orbital surface states comparable to experimental data and results of finite slab calculations. The cluster approach is concluded to be a highly useful and economical one for semiconductor surface problems.     

基于非均匀分簇的无线传感器网络路由协议

在无线传感器网络中,分簇技术是一种有效延长网络生命周期的方法。但是这种多跳的网络模型,如果节点均匀分布并且簇的大小相等,则靠近基站的簇头由于要中继更多的数据,则会导致能量空洞现象。因此提出一种非均匀分簇方法来缓解能量空洞问题。首先,通过节点的剩余能量、到基站的距离以及邻居节点数量来选择簇头。簇一旦形成之后,通过单跳和多跳的混合机制将数据发送到基站。实验结果表明,此协议能有效的延长网络的生命周期,均衡网络能耗,有效延缓能量空洞的形成速度。     

Stimulus-evoked activity in clustered networks of stochastic rate-based neurons

Understanding the effect of network connectivity patterns on the relation between the spontaneous and the stimulus-evoked network activity has become one of the outstanding issues in neuroscience. We address this problem by considering a clustered network of stochastic rate-based neurons influenced by external and intrinsic noise. The bifurcation analysis of an effective model of network dynamics, comprised of coupled mean-field models representing each of the clusters, is used to gain insight into the structure of metastable states characterizing the spontaneous and the induced dynamics. We show that the induced dynamics strongly depends on whether the excitation is aimed at a certain cluster or the same fraction of randomly selected units, whereby the targeted stimulation reduces macroscopic variability by biasing the network toward a particular collective state. The immediate effect of clustering on the induced dynamics is established by comparing the excitation rates of a clustered and a homogeneous random network.     

Late-stage coarsening of adlayers by dynamic cluster coalescence

We consider the late stages of adlayer coarsening when this process is dominated by cluster diffusion and coalescence. The growth rate of the average cluster size can be directly related to the cluster diffusion coefficient of individual clusters. The distribution of cluster sizes and the spatial correlations between clusters are examined as a function of coverage and cluster diffusion rate using Monte Carlo simulations. We also show how the Smoluchowski equation can give an approximate closed-form solution for the cluster size distribution during coarsening by coalescence. The coarsening of adlayers by cluster coalescence in a model that includes local inter-cluster interactions is also examined.     

Phase clustering in globally coupled photochemical oscillators

We experimentally investigate the formation of clusters in a population of globally coupled photochemical oscillators. The system consists of catalytic micro-particles in Belousov-Zhabotinsky solution and the coupling exploits the excitatory properties of light; an increase in the light intensity leads to excitation (“firing") of an oscillator. As the coupling strength is increased, a transition occurs from incoherence to clustering, whereby the oscillators split into synchronised groups, to complete synchronisation. Multistability is observed between a one-phase cluster (fully synchronised group) and two-phase clusters (two groups with the same frequency but different phases). The results are reproduced in simulations and we demonstrate that the heterogeneity of the population as well as the relaxational nature of the oscillators is important in the observation of clusters. We also examine the exploitation of the phase model for the prediction of clusters in experiments.     

A New Validity Index Based on Fuzzy Energy and Fuzzy Entropy Measures in Fuzzy Clustering Problems

Two well-known drawbacks in fuzzy clustering are the requirement of assigning in advance the number of clusters and random initialization of cluster centers. The quality of the final fuzzy clusters depends heavily on the initial choice of the number of clusters and the initialization of the clusters, then, it is necessary to apply a validity index to measure the compactness and the separability of the final clusters and run the clustering algorithm several times. We propose a new fuzzy C-means algorithm in which a validity index based on the concepts of maximum fuzzy energy and minimum fuzzy entropy is applied to initialize the cluster centers and to find the optimal number of clusters and initial cluster centers in order to obtain a good clustering quality, without increasing time consumption. We test our algorithm on UCI (University of California at Irvine) machine learning classification datasets comparing the results with the ones obtained by using well-known validity indices and variations of fuzzy C-means by using optimization algorithms in the initialization phase. The comparison results show that our algorithm represents an optimal trade-off between the quality of clustering and the time consumption.     

Transport through quantum dots: a combined DMRG and embedded-cluster approximation study

The numerical analysis of strongly interacting nanostructures requires powerful techniques. Recently developed methods, such as the time-dependent density matrix renormalization group (tDMRG) approach or the embedded-cluster approximation (ECA), rely on the numerical solution of clusters of finite size. For the interpretation of numerical results, it is therefore crucial to understand finite-size effects in detail. In this work, we present a careful finite-size analysis for the examples of one quantum dot, as well as three serially connected quantum dots. Depending on “odd-even” effects, physically quite different results may emerge from clusters that do not differ much in their size. We provide a solution to a recent controversy over results obtained with ECA for three quantum dots. In particular, using the optimum clusters discussed in this paper, the parameter range in which ECA can reliably be applied is increased, as we show for the case of three quantum dots. As a practical procedure, we propose that a comparison of results for static quantities against those of quasi-exact methods, such as the ground-state density matrix renormalization group (DMRG) method or exact diagonalization, serves to identify the optimum cluster type. In the examples studied here, we find that to observe signatures of the Kondo effect in finite systems, the best clusters involving dots and leads must have a total z-component of the spin equal to zero.     

Hierarchical clustering to measure connectivity in fMRI resting-state data

Low frequency oscillations, which are temporally correlated in functionally related brain regions, characterize the mammalian brain, even when no explicit cognitive tasks are performed. Functional connectivity MR imaging is used to map regions of the resting brain showing synchronous, regional and slow fluctuations in cerebral blood flow and oxygenation. In this study, we use a hierarchical clustering method to detect similarities of low-frequency fluctuations. We describe one measure of correlations in the low frequency range for classification of resting-state fMRI data. Furthermore, we investigate the contribution of motion and hardware instabilities to resting-state correlations and provide a method to reduce artifacts. For all cortical regions studied and clusters obtained, we quantify the degree of contamination of functional connectivity maps by the respiratory and cardiac cycle. Results indicate that patterns of functional connectivity can be obtained with hierarchical clustering that resemble known neuronal connections. The corresponding voxel time series do not show significant correlations in the respiratory or cardiac frequency band.     

Analytic extension of the coherent potential approximation to clusters

We put forward the homomorphic cluster coherent potential approximation (HCPA) for substitutionally disordered systems as one possible way of avoiding the breakdown of analyticity in average Green's functions even when effects of clusters are properly taken into account. We assert that a cluster CPA yields an analytic physical solution if a one-particle total Hamiltonian is partitioned into the sum of homomorphic single-cluster Hamiltonians and the CPA condition is applied to one of these homomorphic sub-Hamiltonians.     

Combining clustering and classification for remote-sensing images using unlabeled data

A joint clustering and classification approach is proposed.This approach exploits unlabeled data for efficient clustering,which is applied in the classification with support vector machine(SVM) in the case of small-size training samples.The proposed method requires no prior information on data labels,and yields better cluster structures.Through cluster assumption and the notions of support vectors,the most confident k cluster centers and data points near the cluster boundaries are labeled and used to train a reliable SVM classifier.Our method gains better estimation of data distributions and mitigates the unrepresentative problem of small-size training samples.The data set collected from Landsat Thematic Mapper(Landsat TM-5) validates the effectiveness of the proposed approach.     

Multiparticle rapidity clustering in 200 GeV/cπ−p interactions

A study of multiparticle rapidity clustering is made using a generalized rapidity-gap method. The data for events with ?6 charged particles are compared to what would be expected from uncorrelated particle production. We find clear evidence for cluster production. The data are consistent with ～ 20% of all charged particles being produced in clusters of two charged particles; clusters of higher multiplicity are not required.     

A Penalized Matrix Normal Mixture Model for Clustering Matrix Data

Along with advances in technology, matrix data, such as medical/industrial images, have emerged in many practical fields. These data usually have high dimensions and are not easy to cluster due to their intrinsic correlated structure among rows and columns. Most approaches convert matrix data to multi dimensional vectors and apply conventional clustering methods to them, and thus, suffer from an extreme high-dimensionality problem as well as a lack of interpretability of the correlated structure among row/column variables. Recently, a regularized model was proposed for clustering matrix-valued data by imposing a sparsity structure for the mean signal of each cluster. We extend their approach by regularizing further on the covariance to cope better with the curse of dimensionality for large size images. A penalized matrix normal mixture model with lasso-type penalty terms in both mean and covariance matrices is proposed, and then an expectation maximization algorithm is developed to estimate the parameters. The proposed method has the competence of both parsimonious modeling and reflecting the proper conditional correlation structure. The estimators are consistent, and their limiting distributions are derived. We applied the proposed method to simulated data as well as real datasets and measured its clustering performance with the clustering accuracy (ACC) and the adjusted rand index (ARI). The experiment results show that the proposed method performed better with higher ACC and ARI than those of conventional methods.     

Clustering of Periodic Orbits and Ensembles of Truncated Unitary Matrices

In present article we consider a combinatorial problem of counting and classification of periodic orbits in dynamical systems on an example of the baker’s map. Periodic orbits of a chaotic system can be organized into a set of clusters, where orbits from a given cluster traverse approximately the same points of the phase space but in a different time-order. We show that counting of cluster sizes in the baker’s map can be turned into a spectral problem for matrices from truncated unitary ensemble (TrUE). We formulate a conjecture of universality of the spectral edge in the eigenvalues distribution of TrUE and utilize it to derive asymptotics of the second moment of cluster distribution in the regime when both the orbit lengths and the parameter controlling closeness of the orbit actions tend to infinity. The result obtained allows to estimate the size of average cluster for various numbers of encounters in periodic orbit.     

Magnetic moments and adiabatic magnetization of free cobalt clusters

Magnetizations and magnetic moments of free cobalt clusters Co(N) (12 < N < 200) in a cryogenic (25 K < or = T < or = 100 K) molecular beam were determined from Stern-Gerlach deflections. All clusters preferentially deflect in the direction of the increasing field and the average magnetization resembles the Langevin function for all cluster sizes even at low temperatures. We demonstrate in the avoided crossing model that the average magnetization may result from adiabatic processes of rotating and vibrating clusters in the magnetic field and that spin relaxation is not involved. This resolves a long-standing problem in the interpretation of cluster beam deflection experiments with implications for nanomagnetic systems in general.