An new initialization method for fuzzy c-means algorithm

In this paper an initialization method for fuzzy c-means (FCM) algorithm is proposed in order to solve the two problems of clustering performance affected by initial cluster centers and lower computation speed for FCM. Grid and density are needed to extract approximate clustering center from sample space. Then, an initialization method for fuzzy c-means algorithm is proposed by using amount of approximate clustering centers to initialize classification number, and using approximate clustering centers to initialize initial clustering centers. Experiment shows that this method can improve clustering result and shorten clustering time validly.     

基于改进粒子群算法的模糊聚类-概率神经网络模型的企业财务危机预警模型研究

为了充分发挥概率神经网络在企业财务危机预警中的作用,克服概率神经网络平滑参数难以确定和空间复杂度高的不足,本文提出一类新的参数动态调整的粒子群算法优化概率神经网络的平滑参数,进而采用改进粒子群算法优化初始隶属度矩阵的模糊聚类方法实现对样本的选择,解决了概率神经网络平滑参数的确定及空间结构复杂的问题。提出了基于改进粒子群算法的模糊聚类-概率神经网络企业财务危机预警模型,并以我国上市公司作为研究对象进行了实证研究。结果表明,经过模糊聚类和改进粒子群算法优化的概率神经网络具有更优的预测性能,并在企业财务危机长期预警方面具有一定效用。     

硬聚类和模糊聚类的结合——双层FCM快速算法

模糊c均值(FCM)聚类算法在模式识别领域中得到了广泛的应用,但FCM算法在大数据集的情况下需要大量的CPU时间,令用户感到十分不便,提高算法的速度是一个急待解决的问题。本文提出的双层FCM聚类算法是一种快速算法,它体现了硬聚类和模糊聚类的结合,以硬聚类的结果对模糊聚类的初始值进行指导,从而明显地缩短了迭代过程。双层FCM算法所用的CPU时间仅为FCM算法的十三分之一,因而具有很强的实用价值。     

An Evolutionary Approach to Spatial Fuzzy c-Means Clustering

Fuzzy c-means clustering algorithm (FCM) can provide a non-parametric and unsupervised approach to the cluster analysis of data. Several efforts of fuzzy clustering have been undertaken by Bezdek and other researchers. Earlier studies in this field have reported problems due to the setting of optimum initial condition, cluster validity measure, and high computational load. More recently, the fuzzy clustering has benefited of a synergistic approach with Genetic Algorithms (GA) that play the role of an useful optimization technique that helps to better tolerate some classical drawbacks, such as sensitivity to initialization, noise and outliers, and susceptibility to local minima. We propose a genetic-level clustering methodology able to cluster objects represented by R ^p spaces. The unsupervised cluster algorithm, called SFCM (Spatial Fuzzy c-Means), is based on a fuzzy clustering c-means method that searches the best fuzzy partition of the universe assuming that the evaluation of each object with respect to some features is unknown, but knowing that it belongs to circular regions of R ² space. Next we present a Java implementation of the algorithm, which provides a complete and efficient visual interaction for the setting of the parameters involved into the system. To demonstrate the applications of SFCM, we discuss a case study where it is shown the generality of our model by treating a simple 3-way data fuzzy clustering as example of a multicriteria optimization problem.     

基于混合细菌趋药性的聚类分割算法

为解决模糊C均值算法对初始值敏感、容易陷入局部极值的问题,提出基于混合细菌趋药性的聚类分割算法,在简单细菌趋药性算法的基础上,将粒子群算法引入.新算法使用粒子群算法、细菌趋药性算法两步优化得到的结果作为模糊C均值算法的初始值,同时新算法中引入精英保持策略,进一步提高算法效率.实验结果表明,新算法具有较快的收敛速度,.同时能够获得较好的图像分割效果和质量.     

基于混合单纯形算法的模糊均值图像分割

针对模糊C均值算法用于图像分割时对初始值敏感、容易陷入局部极值的问题,提出基于混合单纯形算法的模糊均值图像分割算法.算法利用Nelder-Mead单纯形算法计算量小、搜索速度快和粒子群算法自适应能力强、具有较好的全局搜索能力的特点,将混合单纯形算法的结果作为模糊C均值算法的输入,并将其用于图像分割.实验结果表明:基于混合单纯形算法的模糊均值图像分割算法在改善图像分割质量的同时,提高了算法的运行速度.     

A fuzzy multi-objective particle swarm optimization for effective data clustering

Data clustering, also called unsupervised learning, is a fundamental issue in data mining that is used to understand and mine the structure of an untagged assemblage of data into separate groups based on their similarity. Recent studies have shown that clustering techniques that optimize a single objective may not provide satisfactory result because no single validity measure works well on different kinds of data sets. Moreover, the performance of clustering algorithms degrades with more and more overlaps among clusters in a data set. These facts have motivated us to develop a fuzzy multi-objective particle swarm optimization framework in an innovative fashion for data clustering, termed as FMOPSO, which is able to deliver more effective results than state-of-the-art clustering algorithms. The key challenge in designing FMOPSO framework for data clustering is how to resolve cluster assignments confusion with such points in the data set which have significant belongingness to more than one cluster. The proposed framework addresses this problem by identification of points having significant membership to multiple classes, excluding them, and re-classifying them into single class assignments. To ascertain the superiority of the proposed algorithm, statistical tests have been performed on a variety of numerical and categorical real life data sets. Our empirical study shows that the performance of the proposed framework (in both terms of efficiency and effectiveness) significantly outperforms the state-of-the-art data clustering algorithms.     

On the use of divergence distance in fuzzy clustering

Clustering algorithms divide up a dataset into a set of classes/clusters, where similar data objects are assigned to the same cluster. When the boundary between clusters is ill defined, which yields situations where the same data object belongs to more than one class, the notion of fuzzy clustering becomes relevant. In this course, each datum belongs to a given class with some membership grade, between 0 and 1. The most prominent fuzzy clustering algorithm is the fuzzy c-means introduced by Bezdek (Pattern recognition with fuzzy objective function algorithms, 1981), a fuzzification of the k-means or ISODATA algorithm. On the other hand, several research issues have been raised regarding both the objective function to be minimized and the optimization constraints, which help to identify proper cluster shape (Jain et al., ACM Computing Survey 31(3):264–323, 1999). This paper addresses the issue of clustering by evaluating the distance of fuzzy sets in a feature space. Especially, the fuzzy clustering optimization problem is reformulated when the distance is rather given in terms of divergence distance, which builds a bridge to the notion of probabilistic distance. This leads to a modified fuzzy clustering, which implicitly involves the variance–covariance of input terms. The solution of the underlying optimization problem in terms of optimal solution is determined while the existence and uniqueness of the solution are demonstrated. The performances of the algorithm are assessed through two numerical applications. The former involves clustering of Gaussian membership functions and the latter tackles the well-known Iris dataset. Comparisons with standard fuzzy c-means (FCM) are evaluated and discussed.     

土壤分类的模糊集成算法与应用

土壤是一个多性状的连续体,其分类的首选方法是模糊聚类分析.但是模糊聚类分析中现有的基于模糊等价关系的动态聚类法和模糊c-均值法各有利弊,采用其中一种方法聚类肯定存在不足.为此集成两种聚类方法的优点,避其缺点,提出了用基于模糊等价关系的动态聚类方法和方差分析方法确定聚类数目和初始聚类中心,再用模糊c-均值法决定最终分类结果的集成算法,并将其应用到松花江流域土壤分类中,得到了较为切合实际的分类结果.     

Balanced fuzzy particle swarm optimization

In the present study an extension of particle swarm optimization (PSO) algorithm which is in conformity with actual nature is introduced for solving combinatorial optimization problems. Development of this algorithm is essentially based on balanced fuzzy sets theory. The classical fuzzy sets theory cannot distinguish differences between positive and negative information of membership functions, while in the new method both kinds of information “positive and negative” about membership function are equally important. The balanced fuzzy particle swarm optimization algorithm is used for fundamental optimization problem entitled traveling salesman problem (TSP). For convergence inspecting of new algorithm, method was used for TSP problems. Convergence curves were represented fast convergence in restricted and low iterations for balanced fuzzy particle swarm optimization algorithm (BF-PSO) comparison with fuzzy particle swarm optimization algorithm (F-PSO).     

Two-Stage Image Segmentation Scheme Based on Inexact Alternating Direction Method

Image segmentation is a fundamental problem in both image processing and computer vision with numerous applications. In this paper, we propose a two-stage image segmentation scheme based on inexact alternating direction method. Specifically, we first solve the convex variant of the Mumford-Shah model to get the smooth solution, and the segmentation is then obtained by applying the K-means clustering method to the solution. Some numerical comparisons are arranged to show the effectiveness of our proposed schemes by segmenting many kinds of images such as artificial images, natural images, and brain MRI images.     

The fitness evaluation strategy in particle swarm optimization

The particle swarm optimization (PSO) computational method has recently become popular. However, it has limitations. It may trap into local optima and cause the premature convergence phenomenon, especially for multimodal and high-dimensional problems. In this paper, we focus on investigating the fitness evaluation in terms of a particle’s position. Particularly, we find that the fitness evaluation strategy in the standard PSO has two drawbacks, i.e., “two steps forward and one step back” and “two steps back and one step forward”. In addition, we propose a general fitness evaluation strategy (GFES), by which a particle is evaluated in multiple subspaces and different contexts in order to take diverse paces towards the destination position. As demonstrations of GFES, a series of PSOs with GFES are presented. Experiments are conducted on several benchmark optimization problems. The results show that GFES is effective at handling multimodal and high-dimensional problems.     

基于混沌粒子群算法的Tikhonov正则化参数选取

Tikhonov正则化方法是求解不适定问题最为有效的方法之一,而正则化参数的最优选取是其关键.本文将混沌粒子群优化算法与Tikhonov正则化方法相结合,基于Morozov偏差原理设计粒子群的适应度函数,利用混沌粒子群优化算法的优点,为正则化参数的选取提供了一条有效的途径.数值实验结果表明,本文方法能有效地处理不适定问题,是一种实用有效的方法.     

基于可信性理论的均值-熵-偏度投资组合模型及其算法求解

本文考虑到证券市场的投资者往往面临着随机和模糊两种不确定性的情形,在模糊随机环境下把证券的收益率视作三角模糊变量,在可信性理论基础上建立了带融资约束条件的均值-熵-偏度三目标投资组合决策模型,拓展了基于可信性理论的投资组合决策模型的研究内容,同时通过对约束条件处理方法,外部档案维护方法等关键算子的改良,提出了一种新的约束多目标粒子群算法。本文运用该算法对模型进行求解,把得到的最优解与传统的多目标粒子群算法得到的最优解进行对比,结果表明新算法得到的最优解的质量会显著地优于传统的多目标粒子群算法的最优解,从而验证了算法的有效性和准确性。该算法可以在三维空间中得到一个分布性和逼近性较好的Pareto最优曲面,满足投资者对不同目标的差异需求,为投资者提供合理的投资组合决策方案。     

Mixed fuzzy inter-cluster separation clustering algorithm

Based on inter-cluster separation clustering (ICSC) fuzzy inter-cluster separation clustering (FICSC) deals with all the distances between the cluster centers, maximizes these distances and obtains the better performances of clustering. However, FICSC is sensitive to noises the same as fuzzy c-means (FCM) clustering. Possibilistic type of FICSC is proposed to combine FICSC and possibilistic c-means (PCM) clustering. Mixed fuzzy inter-cluster separation clustering (MFICSC) is presented to extend possibilistic type of FICSC because possibilistic type of FICSC is sensitive to initial cluster centers and always generates coincident clusters. MFICSC can produce both fuzzy membership values and typicality values simultaneously. MFICSC shows good performances in dealing with noisy data and overcoming the problem of coincident clusters. The experimental results with data sets show that our proposed MFICSC holds better clustering accuracy, little clustering time and the exact cluster centers.     

不确定同时取送货车辆路径问题及粒子群算法研究

研究了不确定同时取送货车辆路径问题(VRPSPD),考虑运行环境的不确定性,顾客时间窗口要求和对顾客同时进行取货和送货服务的情况,以运作成本最低和顾客满意度最高为决策目标,构建不确定VRPSPD数学模型。模型中,引入模糊随机理论来描述决策环境中的双重不确定性,假定顾客需求量(送货量)和取货量是模糊随机变量。随后,提出基于模糊随机算子的改进粒子群算法对模型进行求解。为了适应模型特点和提高算法效率,设计合理的编码和解码过程,制定多个适应度函数方案处理多目标问题,并应用更加科学的更新策略。最后在应用案例中,通过参数测试获取合理的算法参数取值,采用计算结果分析和求解算法测评验证模型和算法的有效性。     

改进的遗传模糊聚类算法

对基于遗传算法的FCM(模糊c^-均值法)聚类算法进行了改进,能更好地把遗传算法的全局搜索能力和FCM的局部搜索能力结合起来。实验结果表明，这种改进的算法在分类正确率和稳定性上优于[1]和[3]中的方法；收敛速度和对初值的敏感性都明显优于FCM。     

A new multiobjective procedure for solving nonconvex environmental/economic power dispatch

In this article, an improved multiobjective chaotic interactive honey bee mating optimization (CIHBMO) is proposed to find the feasible optimal solution of the environmental/economic power dispatch problem with considering operational constraints of the generators. The three conflicting and noncommensurable: fuel cost, pollutant emissions, and system loss, should be minimized simultaneously while satisfying certain system constraints. To achieve a good design with different solutions in a multiobjective optimization problem, Pareto dominance concept is used to generate and sort the dominated and nondominated solutions. Also, fuzzy set theory is used to extract the best compromise solution. The propose method has been individually examined and applied to the standard Institute of Electrical and Electronics Engineers (IEEE) 30‐bus six generator, IEEE 180‐bus 14 generator and 40 generating unit (with valve point effect) test systems. The computational results reveal that the multiobjective CIHBMO algorithm has excellent convergence characteristics and is superior to other multiobjective optimization algorithms. Also, the result shows its great potential in handling the multiobjective problems in power systems. © 2014 Wiley Periodicals, Inc. Complexity 20: 47–62, 2014     

非局部加权模糊C均值聚类图像分割

去除噪声与保持图像细节特征是含噪声图像分割中面临的一对矛盾。为此,提出一种改进的模糊C均值算法,通过引入非局部加权距离以抑制噪声影响。其中,权值通过局部图像块距离的指数形式计算,并利用半局部统计特性自适应调整其光滑参数。实验结果表明,新方法具有较强的抗噪声能力,同时能够保持较多地细节特征。     

Soft clustering – Fuzzy and rough approaches and their extensions and derivatives

Clustering is one of the most widely used approaches in data mining with real life applications in virtually any domain. The huge interest in clustering has led to a possibly three-digit number of algorithms with the k-means family probably the most widely used group of methods. Besides classic bivalent approaches, clustering algorithms belonging to the domain of soft computing have been proposed and successfully applied in the past four decades. Bezdek’s fuzzy c-means is a prominent example for such soft computing cluster algorithms with many effective real life applications. More recently, Lingras and West enriched this area by introducing rough k-means. In this article we compare k-means to fuzzy c-means and rough k-means as important representatives of soft clustering. On the basis of this comparison, we then survey important extensions and derivatives of these algorithms; our particular interest here is on hybrid clustering, merging fuzzy and rough concepts. We also give some examples where k-means, rough k-means, and fuzzy c-means have been used in studies.