[Show abstract][Hide abstract] ABSTRACT: We used buffer superposition, Delaunay triangulation skeleton line, and other methods to achieve the aggregation and amalgamation of the vector data, adopted the method of combining mathematical morphology and cellular automata to achieve the patch generalization of the raster data, and selected the two evaluation elements (namely, semantic consistency and semantic completeness) from the semantic perspective to conduct the contrast evaluation study on the generalization results from the two levels, respectively, namely, land type and map. The study results show that: (1) before and after the generalization, it is easier for the vector data to guarantee the area balance of the patch; the raster data’s aggregation of the small patch is more obvious. (2) Analyzing from the scale of the land type, most of the land use types of the two kinds of generalization result’s semantic consistency is above 0.6; the semantic completeness of all types of land use in raster data is relatively low. (3) Analyzing from the scale of map, the semantic consistency of the generalization results for the two kinds of data is close to 1, while, in the aspect of semantic completeness, the land type deletion situation of the raster data generalization result is more serious.
Full-text · Article · Jun 2014 · Abstract and Applied Analysis
[Show abstract][Hide abstract] ABSTRACT: Clustering data has a wide range of applications and has attracted considerable attention in data mining and artificial intelligence. However it is difficult to find a set of clusters that best fits natural partitions without any class information. In this paper, a method for detecting the optimal cluster number is proposed. The optimal cluster number can be obtained by the proposal, while partitioning the data into clusters by FCM (Fuzzy c-means) algorithm. It overcomes the drawback of FCM algorithm which needs to define the cluster number
in advance. The method works by converting the fuzzy cluster result into a weighted bipartite network and then the optimal cluster number can be detected by the improved bipartite modularity. The experimental results on artificial and real data sets show the validity of the proposed method.
No preview · Article · Feb 2014 · Mathematical Problems in Engineering
[Show abstract][Hide abstract] ABSTRACT: This paper considers the impact of the distance from cluster heads (CHs) to the sink, and uses evolution game-theoretic model to analyze the communication energy optimization. We present the area division scheme of sensors so as to achieve a desirable communication energy optimization. By analyzing the evolution stable strategy (ESS) of territory game model, we propose a clustering algorithm based on territory game (TGC algorithm) to define the area limits. TGC algorithm mitigates the unbalanced energy consumption caused by the asymmetrical distance from CHs to the sink. By analyzing the ESS of the war of attrition game, we propose a clustering algorithm based on the war of energy attrition (WEAC algorithm). WEAC algorithm selects CHs from low energy sensors only considering individual remaining energy rather than the distance from their CHs to the sink. Simulations are given to validate the proposed TGC and WEAC algorithms. The results show the proposed algorithms achieve desirable network performances.
No preview · Article · Aug 2013 · Computers & Electrical Engineering
[Show abstract][Hide abstract] ABSTRACT: This paper presents an efficient algorithm, called dynamic fuzzy cluster (DFC), for dynamically
clustering time series by introducing the definition of key point and improving FCM algorithm. The proposed algorithm works by determining those time series whose class labels are vague and further partitions them into different clusters over time. The main advantage of this approach compared with other existing algorithms is that the property of some time series belonging to different clusters over time can be partially revealed. Results from simulation-based experiments on geographical data demonstrate the excellent performance and the desired results have been obtained. The proposed algorithm can be applied to solve other clustering problems in data mining.
No preview · Article · Apr 2013 · Abstract and Applied Analysis
[Show abstract][Hide abstract] ABSTRACT: Based on a simple transformation, and with the aid of symbolic computation, a Bäcklund transformation relating the Jimbo–Miwa equation and a system of linear partial differential equations is obtained, which enables us to construct exact solutions of the Jimbo–Miwa equation through the Wronskian determinants of independent solutions of the linear system. Particularly, explicit Wronskian form NN-soliton solutions for the Jimbo–Miwa equation are presented. Moreover, the introduced transformation also helps to construct bi-soliton-like solutions of the Jimbo–Miwa equation. Due to the arbitrary functions they contain, the bi-soliton-like solutions can represent various waves such as classical cross-line bi-solitons, curved bi-solitons and bi-soliton-like breathers.
No preview · Article · Feb 2013 · Computers & Mathematics with Applications
[Show abstract][Hide abstract] ABSTRACT: A novel cluster validity index whose implementation is based on the membership degrees and improved bipartite modularity of bipartite network is proposed for the validation of partitions produced by the fuzzy c-means (FCM) algorithm. FCM algorithm is employed to group the dataset in order to obtain the membership degree of samples. Then, a weighted bipartite network is constructed by samples and centroids of each cluster. This allows the introduction of a new measurement for optimizing the numbers of clusters for fuzzy partitions. The proposed index utilizes the optimum membership as its global property and the modularity of bipartite network as its local independent property. The proposed index is compared with a number of popular validation indices on fifteen datasets. The experimental results show that the effectiveness and reliability of the proposal is superior to other indices.
No preview · Article · Jan 2013 · Fuzzy Sets and Systems
[Show abstract][Hide abstract] ABSTRACT: The aim of this paper is to detect communities in complex networks. A density set algorithm (DSA) is proposed by introducing the concept of density set. The key idea of the algorithm is to constantly construct density sets in a network and decide whether the density set constructed later can lead to generate a new community or amalgamate it with an old one. Step by step, the networks with apparent community structure can be partitioned well by the proposed method. The running time of DSA is approximately O(n+m) for a general network and O(n) for a sparse network, where n is the number of nodes and m the number of edges in a network. Tests on three typical real-world networks and a benchmark reveal that DSA produces the desired results. So the proposal is reasonable and has the potential for wide applications in physics and computer science.
No preview · Article · Jul 2011 · Dianzi Keji Daxue Xuebao/Journal of the University of Electronic Science and Technology of China
[Show abstract][Hide abstract] ABSTRACT: A snowball algorithm is proposed to find community structures in complex networks by introducing the definition of community core and some quantitative conditions. A community core is first constructed, and then its neighbors, satisfying the quantitative conditions, will be tied to this core until no node can be added. Subsequently, one by one, all communities in the network are obtained by repeating this process. The use of the local information in the proposed algorithm directly leads to the reduction of complexity. The algorithm runs in O(n+m) time for a general network and O(n) for a sparse network, where n is the number of vertices and m is the number of edges in a network. The algorithm fast produces the desired results when applied to search for communities in a benchmark and five classical real-world networks, which are widely used to test algorithms of community detection in the complex network. Furthermore, unlike existing methods, neither global modularity nor local modularity is utilized in the proposal. By converting the considered problem into a graph, the proposed algorithm can also be applied to solve other cluster problems in data mining.
No preview · Article · Nov 2010 · Physica A: Statistical Mechanics and its Applications
[Show abstract][Hide abstract] ABSTRACT: A generalized KP equation with variable coefficients, including the KP equation and the cylindrical KP equation as its special cases is investigated using a constructive algorithm and symbolic computation. Explicit bi-soliton-like solutions of the equation are obtained under certain constraints on the coefficient functions. For different coefficient functions, the solutions can model different types of bi-soliton-like waves. Some interesting bi-soliton-like waves are graphically revealed.
Preview · Article · Nov 2010 · Mathematical and Computer Modelling
[Show abstract][Hide abstract] ABSTRACT: This paper presents a fuzzy support vector classifier by integrating modified fuzzy c-means clustering based on Mahalanobis distance into fuzzy support vector data description. The proposed algorithm can be
used to deal with the outlier sensitivity problem in traditional multi-class classification problems. The modified fuzzy c-means clustering algorithm based on Mahalanobis distance takes into the samples’ correlation account, and is improved to
generate different weight values for main training data points and outliers according to their relative importance in the
training data. Experimental results show that the proposed method can reduce the effect of outliers and give high classification
KeywordsSupport vector data description-Fuzzy c-means algorithm-Mahalanobis distance-Support vector machine
No preview · Article · Oct 2010 · Journal of Intelligent Information Systems
[Show abstract][Hide abstract] ABSTRACT: In this paper, the first integral method is employed for constructing the new exact travelling wave solutions of nonlinear partial differential equations. The power of this manageable method is confirmed by applying it for two selected nonlinear partial equations. This approach can also be applied to other systems of nonlinear differential equations.
No preview · Article · Apr 2010 · Applied Mathematics and Computation
[Show abstract][Hide abstract] ABSTRACT: A method is proposed to construct closed-form solutions of nonlinear differential-difference equations. For the variety of nonlinearities, this method only deals with such equations which
are written in polynomials in function and its derivative. Some closed-form solutions of
Hybrid lattice, Discrete mKdV lattice, and modified Volterra lattice are obtained by using the
proposed method. The travelling wave solutions of nonlinear differential-difference equations
in polynomial in function tanh are included in these solutions. This implies that the proposed
method is more powerful than the one introduced by Baldwin et al. The results obtained in this
paper show the validity of the proposal.
Preview · Article · Sep 2009 · Discrete Dynamics in Nature and Society
[Show abstract][Hide abstract] ABSTRACT: Many networks of interest in the science, including social networks, computer networks and the World Wide Web, are found to be divided naturally into communities or groups. The problem of detecting communities is one of the outstanding issues in the study of network systems. Based on the improved shared nearest neighbor (SNN) similarity matrix, spectral method and fuzzy c-means (FCM) clustering algorithm, this paper proposes a new algorithm for detecting the communities in complex networks. The experiment reveals the validity of the presented method. The results are compared with other ones obtained by the different existing well methods and the conclusion is that the accuracy of the results calculated by this approach is much better than the known ones.
No preview · Article · Aug 2009 · Physica A: Statistical Mechanics and its Applications
[Show abstract][Hide abstract] ABSTRACT: In this paper, to understand the role of nonlinear dispersion in the coupled systems, the nonlinear dispersion Drinfel’d–Sokolov system (called D(m,n) system) is investigated. As a consequence, many types of compacton and solitary pattern solutions are obtained. Moreover, some solitary wave solutions are also deduced for differential parameters m, n. When n=1, the D(m,1) system with linear dispersion is shown to possess also compacton and solitary pattern solutions, which contain the known results. Moreover, some rational solutions of D(m,n) system are also deduced.
No preview · Article · Jan 2009 · Chaos Solitons & Fractals
[Show abstract][Hide abstract] ABSTRACT: In this paper, the (2+1)-dimensional modified Kadomtsev–Petviashvil (KP) equation is investigated with the aid of symbolic computation. We use some fractional transformations to obtain many types of new exact solutions of (2+1)-dimensional modified KP equation. These solutions include rational solutions, periodic wave solutions, solitary wave solutions and doubly periodic wave solutions. These transformations can be also extended to other nonlinear wave equations.
No preview · Article · May 2008 · Chaos Solitons & Fractals
[Show abstract][Hide abstract] ABSTRACT: In this paper, we investigate the three-dimensional KP equation with nonlinear dispersion (simply called 3DKP(m,n) equation) using some transformations. As a result, some compactons and solitary patterns are obtained. In particular, some solitary wave solutions are also given for differential parameters. Moreover, it is shown that the 3DKP(m,1) equation with linear dispersion also has compactons and solitary patterns.
[Show abstract][Hide abstract] ABSTRACT: A new approach is presented which enables one to construct the exact solutions of nonlinear differential difference equations. As its application, the soliton solutions and periodic solutions of Hybrid lattice, discretized mKdV lattice and modified Volterra lattice are conveniently obtained by computing the solutions for a lattice equation introduced by Wadati.
No preview · Article · Feb 2006 · Chaos Solitons & Fractals