基于广义反向学习的磷虾群算法及其在数据聚类中的应用

针对磷虾群（KH）算法在寻优过程中因种群多样性降低而过早收敛的问题，提出基于广义反向学习的磷虾群算法GOBL-KH。首先，通过余弦递减策略确定步长因子平衡算法的探索与开发能力；然后，加入广义反向学习策略对每个磷虾进行广义反向搜索，增强磷虾探索其周围邻域空间的能力。将改进的算法在15个经典测试函数上进行测试并与KH算法、步长线性递减的磷虾群（KHLD）算法和余弦递减步长的磷虾群（KHCD）算法比较，实验结果表明:GOBL-KH算法可有效避免早熟且具有较高的求解精度。为体现算法有效性，将GOBL-KH算法与K均值算法结合提出HK-KH算法用于解决数据聚类问题，即在每次迭代后用最优个体或经过K均值迭代一次后的新个体替换最差个体，使用UCI五个真实数据集进行测试并与K均值、遗传算法（GA）、粒子群优化（PSO）算法、蚁群算法（ACO）、KH算法、磷虾群聚类算法（KHCA）、改进磷虾群（IKH）算法进行比较，结果表明:HK-KH算法适用于解决数据聚类问题且具有较强的全局收敛性和较高的稳定性。     

创意FCM算法

针对现有模糊聚类方法仅仅是对已有数据点的聚类的不足,提出了在已有数据集的基础上找到新的一类集群的聚类方法 CFCM。该算法在FCM算法的基础上,通过引入观测点P作为聚类的先验知识,来大致确定未知集群的聚类中心,定义了权重系数λ来限定观测点对新的一类聚类中心形成的影响程度。人造数据集和UCI真实数据集的实验结果表明,该算法不仅对已知数据点有较好的聚类效果,并且可以在观测点P的作用下在特定区域创造出新的一类无已知数据点的集群中心点的大致位置,因而在实际中有潜在应用价值。     

Study on multi-center fuzzy C-means algorithm based on transitive closure and spectral clustering

Fuzzy C-means (FCM) clustering has been widely used successfully in many real-world applications. However, the FCM algorithm is sensitive to the initial prototypes, and it cannot handle non-traditional curved clusters. In this paper, a multi-center fuzzy C-means algorithm based on transitive closure and spectral clustering (MFCM-TCSC) is provided. In this algorithm, the initial guesses of the locations of the cluster centers or the membership values are not necessary. Multi-centers are adopted to represent the non-spherical shape of clusters. Thus, the clustering algorithm with multi-center clusters can handle non-traditional curved clusters. The novel algorithm contains three phases. First, the dataset is partitioned into some subclusters by FCM algorithm with multi-centers. Then, the subclusters are merged by spectral clustering. Finally, based on these two clustering results, the final results are obtained. When merging subclusters, we adopt the lattice similarity method as the distance between two subclusters, which has explicit form when we use the fuzzy membership values of subclusters as the features. Experimental results on two artificial datasets, UCI dataset and real image segmentation show that the proposed method outperforms traditional FCM algorithm and spectral clustering obviously in efficiency and robustness.     

Hybridization of Chaos and Flower Pollination Algorithm over K-Means for data clustering

Classical clustering algorithms like K-means often converge to local optima and have slow convergence rates for larger datasets. To overcome such situations in clustering, swarm based algorithms have been proposed. Swarm based approaches attempt to achieve the optimal solution for such problems in reasonable time. Many swarm based algorithms such as Flower Pollination Algorithm (FPA), Cuckoo Search Algorithm (CSA), Black Hole Algorithm (BHA), Bat Algorithm (BA) Particle Swarm Optimization (PSO), Firefly Algorithm (FFA), Artificial Bee Colony (ABC) etc have been successfully applied to many non-linear optimization problems. In this paper, an algorithm is proposed which hybridizes Chaos Optimization and Flower Pollination over K-means to improve the efficiency of minimizing the cluster integrity. The proposed algorithm referred as Chaotic FPA (CFPA) is compared with FPA, CSA, BHA, BA, FFA, and PSO over K-Means for data clustering problem. Experiments are conducted on sixteen benchmark datasets. Algorithms are compared on four different performance parameters — cluster integrity, execution time, number of iterations to converge (NIC) and stability. Results obtained are analyzed statistically using Non-parametric Friedman test. If Friedman test rejects the Null hypothesis then pair wise comparison is done using Nemenyi test. Experimental Result demonstrates the following: (a) CFPA and BHA have better performance on the basis of cluster integrity as compared to other algorithms; (b) Prove the superiority of CFPA and CSA over others on the basis of execution time; (c) CFPA and FPA converges earlier than other algorithms to evaluate optimal cluster integrity; (d) CFPA and BHA produce more stable results than other algorithms.     

基于粒子群优化和遗传算法的协同聚类算法

为充分发挥粒子群优化算法和遗传算法各自的优势,提出一种新的基于粒子群和遗传算法的协同进化算法,并将其应用于聚类分析。通过构建2个相互竞争的种群,采用相对适应度度量方法,在一个纯自举的过程中产生最优竞争个体。在现实世界数据集上的仿真实验表明,该算法在收敛精度方面优于基于遗传算法的聚类方法和基本粒子群优化聚类算法。     

基于多链量子蜂群算法的模糊聚类图像分割

针对传统模糊C-均值聚类算法对初始值和噪声敏感的缺点,提出了一种基于多链量子蜂群算法的模糊C-均值聚类算法。首先,将多链拓展编码方案应用到量子蜂群算法中,提出了多链量子蜂群算法;其次,利用多链量子蜂群算法来优化模糊C-均值聚类的初始聚类中心;最后,设计一种新的利用多链量子蜂群算法优化模糊C-均值聚类中心的图像分割算法。实验结果表明,所提出的基于多链量子蜂群算法的模糊C-均值聚类图像分割算法是有效的,相对于传统模糊C-均值聚类算法及基于模糊的人工蜂群算法,所提算法在分割正确率、分割速度及鲁棒性上均更有效。     

A new clustering method based on the bio-inspired cuttlefish optimization algorithm

Most of the well-known clustering methods based on distance measures, distance metrics and similarity functions have the main problem of getting stuck in the local optima and their performance strongly depends on the initial values of the cluster centers. This paper presents a new approach to enhance the clustering problems with the bio-inspired Cuttlefish Algorithm (CFA) by searching the best cluster centers that can minimize the clustering metrics. Various UCI Machine Learning Repository datasets are used to test and evaluate the performance of the proposed method. For the sake of comparison, we have also analysed several algorithms such as K-means, Genetic Algorithm and the Particle Swarm Optimization (PSO) Algorithm. The simulations and obtained results demonstrate that the performance of the proposed CFA-Clustering method is superior to the other counterpart algorithms in most cases. Therefore, the CFA can be considered as an alternative stochastic method to solve clustering problems.     

结合头脑风暴优化的混合蚁群优化算法

特征选择能够有效提升数据分类的性能。为了进一步提升蚁群优化（ACO）在特征选择上的求解能力,提出一种结合头脑风暴优化的混合蚁群优化（ABO）算法。该算法利用信息交流档案维护历史较好解,并通过基于松弛因子的时间最久优先方法动态更新档案。当ACO的全局最优解多次未更新时,采用基于Fuch混沌映射方法的路径-想法转换算子将档案中的路径解转换为想法解,并将其作为初始种群,通过头脑风暴优化（BSO）在更广阔的空间中搜索较好解。对所提算法在6组典型的二分类数据集上进行实验,分析了其参数敏感性,并与混合萤火虫粒子群优化（HFPSO）算法、粒子群优化与引力搜索算法（PSOGSA）以及遗传算法（GA） 这三种典型的演化算法进行对比。实验结果表明,相较于对比算法,所提算法在分类正确率上至少可提高2.88%~5.35%,在F1指标上至少可提高0.02~0.05,验证了所提算法的有效性和优越性。     

融合粒子群和混合蛙跳的模糊C-均值算法

针对模糊聚类算法中存在的对初始值敏感、易陷入局部最优等问题,提出了一种融合粒子群算法和混合蛙跳算法的模糊C-均值聚算法。通过设计了一种新颖的搜索粒度系数,充分利用粒子群算法收敛速度快、局部搜索能力强的优点与混合蛙跳算法全局寻优能力强、跳出局部最优能力好的特点,同时对SFLA中更新算法进行了改进。实验结果表明,该算法提高了模糊聚类算法的搜索能力和聚类效果,在全局寻优能力、跳出局部最优能力、收敛速度等方面具有优势。     

基于微粒群优化的模糊C-均值聚类彩色图像分割

模糊C-均值聚类算法广泛用于图像分割,但存在聚类性能受类中心初始化影响,且计算量大等问题。为此,提出了一种基于微粒群的模糊C-均值聚类图像分割算法,该方法利用微粒群较强的搜索能力搜索聚类中心。由于搜索聚类中心是按密度进行,计算量小,故可以大幅提高模糊C-均值算法的计算速度。实验表明,这种方法可以使模糊聚类的速度得到明显提高,实现图像的快速分割。     

Immunodomaince based Clonal Selection Clustering Algorithm

Based on clonal selection principle and the immunodominance theory, a new immune clustering algorithm, Immunodomaince based Clonal Selection Clustering Algorithm (ICSCA) is proposed in this paper. Firstly, by introducing a new immunodomaince operator to Clonal Selection Algorithm (CSA), the gene of elites in antibody population can be extracted and generalized to ordinary antibodies so as to gain on-line priori knowledge and share information among individuals. Then, one iteration of Fuzzy C-means clustering algorithm (FCM) and adaptive updating mechanism of antibody population are utilized to improve the diversity of antibody population in order to speed up the convergence speed. The proposed method has been extensively compared with FCM, GA-clustering algorithm (GACA) and Clonal Selection Algorithm based FCM (CSAFCM) over a test suit of several real life data sets and synthetic data sets. Experimental results indicate the superiority of the ICSCA over FCM, GAFCM and CSAFCM on clustering accuracy and robustness.     

一种基于改进混合蛙跳的KFCM算法

针对核模糊C-均值（KFCM）聚类算法存在易陷入局部极小值,对初始值敏感的缺点。将混合蛙跳算法（shuffled frog leaping algorithm,SFLA）用于KFCM中,但在聚类数较大和维数较高时,聚类效果不理想,为此提出将自适应惯性权重引入混合蛙跳算法的更新策略中,再用改进后的混合蛙跳算法求得最优解作为KFCM算法的初始聚类中心,利用KFCM算法优化初始聚类中心,求得全局最优解,从而有效克服了KFCM算法的缺点。人造数据和经典数据集的实验结果表明,新算法与KFCM和FCM聚类算法相比,寻优能力更强,迭代次数更少,聚类效果更好。     

求解旅行商问题的多尺度量子自由粒子优化算法

针对目前元启发式算法在求解组合优化问题中的旅行商问题(TSP)时求解缓慢的问题,受量子理论中波函数的启发提出一种多尺度自适应的量子自由粒子优化算法。首先,在可行域中随机初始化表示城市序列的粒子,作为初始的搜索中心;然后,以每个粒子为中心进行当前尺度下的均匀分布函数的采样,并交换采样位置上的城市编号产生新解;最后,根据新解相较上一次迭代中最优解的优劣进行搜索尺度的自适应调整,并在不同的尺度下进行迭代搜索直到满足算法结束条件。将该算法和混合粒子群优化(HPSO)算法、模拟退火(SA)算法、遗传算法(GA)和蚁群优化算法应用在TSP上进行性能测试,实验结果表明自由粒子模型算法适合求解组合优化问题,在TSP数据集上相比目前较优算法在求解速度上平均提升50%以上。     

改进的种群分类蚁群算法及其应用

提出了一种改进的种群分类蚁群算法,该算法在种群分类的基础上,引入了蚂蚁的知觉感觉特性等。该算法能明显的防止蚁群算法可能出现早熟的问题,从而解决了传统蚁群算法加速收敛与早熟、停滞现象的矛盾。为了说明该算法的性能,将该算法应用到聚类分析算法中,设计了算法的模型以及算法步骤,并通过仿真实验证明了本算法的可行性和有效性。     

基于模糊C均值聚类及群体智能的WSN分层路由算法

为了提高无线传感器网络（WSN）的能量效率并延长其生命周期,提出了一种基于模糊C均值聚类（FCM）和群体智能的WSN分层路由算法（FCM-SI）。首先采用FCM聚类算法对网络进行分簇,优化普通节点与簇头（CH）间距离;然后采用三参数的人工蜂群（ABC）算法选取每个簇的最优簇头;最后采用蚁群优化（ACO）算法搜索簇头至基站（BS）的多跳路径,路径综合考虑了网络的能耗和负载均衡性能。仿真结果显示,与基于均匀分簇的改进的低功耗自适应分簇（I-LEACH）算法、基于ABC的低功耗自适应分簇（ABC-LEACH）算法和基于ACO的低功耗自适应分簇（ANT-LEACH）算法相比,FCM-SI在100 m×100 m,100个节点的初始网络条件下将网络生命周期分别提高了65.2%、49.6%和29.0%。FCM-SI能够有效地延长网络寿命,提高能量利用效率。     

Note on the relationship between probabilistic and fuzzy clustering

In this short communication, based on Renyi entropy measure, a new Renyi information based clustering algorithm A is presented. Algorithm A and the well-known fuzzy clustering algorithm FCM have the same clustering track. This fact builds the very bridge between probabilistic clustering and fuzzy clustering, and fruitful research results on Renyi entropy measure may help us to further understand the essence of fuzzy clustering.This work was supported in part by the RGC CERG grant under project Hong Kong PolyU 5065/98E.     

Note on the relationship between probabilistic and fuzzy clustering

In this short communication, based on Renyi entropy measure, a new Renyi information based clustering algorithm A is presented. Algorithm A and the well-known fuzzy clustering algorithm FCM have the same clustering track. This fact builds the very bridge between probabilistic clustering and fuzzy clustering, and fruitful research results on Renyi entropy measure may help us to further understand the essence of fuzzy clustering.This work was supported in part by the RGC CERG grant under project HongKong PolyU 5065/98E     

一种基于萤火虫算法的模糊聚类方法

针对模糊C-均值聚类对初始值敏感、容易陷入局部最优的缺陷,提出了一种基于萤火虫算法的模糊聚类方法。该方法结合萤火虫算法良好的全局寻优能力和模糊C-均值算法的较强的局部搜索特性,用萤火虫算法优化搜索FCM的聚类中心,利用FCM进行聚类,有效地克服了模糊C-均值聚类的不足,同时增强了萤火虫算法的局部搜索能力。实验结果表明,该算法具有很好的全局寻优能力和较快的收敛速度,能有效地收敛于全局最优解,具有较好的聚类效果。     

一个新的模糊聚类有效性指标

提出一个新的模糊聚类有效性指标。该指标能确定由模糊C-均值算法(FCM)所得模糊划分的最优划分和最优聚类数,结合了模糊聚类的紧致性和分离性信息,用类内加权平方误差和计算紧致性,用类间相似度计算分离性。在3个人造数据集和3个真实数据集上进行对比实验,结果证明该指标的性能优于其他有效性指标。     

一种新的模糊聚类有效性指标

结合模糊聚类的类内紧致性和类间分离性信息,提出一种新的模糊聚类有效性指标。该指标能够确定由模糊C-均值算法（FCM）所得模糊划分的最优划分和最佳聚类数。在1个人造数据集和4个真实数据集上进行对比实验,结果表明该指标性能的优越性。