基于改进的直觉模糊核聚类的图像分割方法

针对噪声图像模糊性的本质，提出了基于改进的直觉模糊核聚类的图像分割方法。采用直觉模糊集描述噪声图像包含的不确定性信息，将图像的灰度信息转换到直觉模糊域进行处理；将模糊核聚类拓展为直觉模糊核聚类，在图像的直觉模糊域进行聚类；通过高斯核函数和欧氏距离分别对像素8-邻域的灰度和空间信息进行建模，综合平衡灰度和空间信息对聚类的作用，并将其作为惩罚项加入到直觉模糊核聚类的目标函数中；通过梯度下降法，推导了迭代求解算法；通过典型的合成图像和自然图像分割实例，验证了所提算法的有效性和鲁棒性。     

A Possibilistic Fuzzy c-Means Clustering Algorithm

In 1997, we proposed the fuzzy-possibilistic c-means (FPCM) model and algorithm that generated both membership and typicality values when clustering unlabeled data. FPCM constrains the typicality values so that the sum over all data points of typicalities to a cluster is one. The row sum constraint produces unrealistic typicality values for large data sets. In this paper, we propose a new model called possibilistic-fuzzy c-means (PFCM) model. PFCM produces memberships and possibilities simultaneously, along with the usual point prototypes or cluster centers for each cluster. PFCM is a hybridization of possibilistic c-means (PCM) and fuzzy c-means (FCM) that often avoids various problems of PCM, FCM and FPCM. PFCM solves the noise sensitivity defect of FCM, overcomes the coincident clusters problem of PCM and eliminates the row sum constraints of FPCM. We derive the first-order necessary conditions for extrema of the PFCM objective function, and use them as the basis for a standard alternating optimization approach to finding local minima of the PFCM objective functional. Several numerical examples are given that compare FCM and PCM to PFCM. Our examples show that PFCM compares favorably to both of the previous models. Since PFCM prototypes are less sensitive to outliers and can avoid coincident clusters, PFCM is a strong candidate for fuzzy rule-based system identification.     

Cluster Validity for the Fuzzy c-Means Clustering Algorithrm

The uniform data function is a function which assigns to the output of the fuzzy c-means (Fc-M) or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm. For the preselected number of cluster c, the Fc-M algorithm produces c vectors in the space in which the data lie, called cluster centers, which represent points about which the data are concentrated. It also produces for each data point c-membership values, numbers between zero and one which measure the similarity of the data points to each of the cluster centers. It is these membership values which indicate how the point is classified. They also indicate how well the point has been classified, in that values close to one indicate that the point is close to a particular center, but uniformly low memberships indicate that the point has not been classified clearly. The uniform data functional (UDF) combines the memberships in such a way as to indicate how well the data have been classified and is computed as follows. For each data point compute the ratio of its smallest membership to its largest and then compute the probability that one could obtain a smaller ratio (indicating better classification) from a clustering of a standard data set in which there is no cluster structure. These probabilities are then averaged over the data set to obtain the values of the UDF.     

区间型数据的模糊c均值聚类算法

提取区间型数据的特征值,给出适用于区间型数据模糊聚类的FCM算法族(IFCM)。该算法适用于不同特征样本数据的模糊聚类运算,并可对聚类结果进行优化。聚类效果的仿真比较表明,IFCM聚类的平均失真度比基于欧氏距离的FCM聚类算法低6.81%。由于距离定义的合理性,IFCM可以根据区间型数据的不同特点调整特征值的聚类权重,并推广至多维类型数据的模糊聚类。     

基于划分的模糊聚类算法

在众多聚类算法中，基于划分的模糊聚类算法是模式识剐中最常用的算法类型之一．至今，献中仍不断有关于基于划分的模糊聚类算法的研究成果出现．为了能更为系统和深入地了解这些聚类算法及其性质，本从改变度量方式、改变约束条件、在目标函数中引入熵以及考虑对聚类中心进行约束等几个方面，对在C-均值算法的基础上得到的基于划分的模糊聚类算法作了综述和评价，对各典型算法的优缺点进行了实验比较分析．指出标准FCM算法被广泛应用的原因之一是它对数据的比例变化具有鲁棒性，而其他类似的算法对这种比例变化却很敏感．并以极大熵方法为例进行了比较实验．最后总结了基于划分的模糊聚类算法普遍存在的问题及其发展前景。     

区间数的区间Ⅱ型模糊c均值聚类算法

针对区间数模糊c均值聚类算法存在模糊度指数m无法准确描述数据簇划分情况的问题,对点数据集合的区间Ⅱ型模糊c均值聚类算法进行拓展,将其扩展到区间型不确定数据的聚类中。同时,分析了区间数的区间Ⅱ型模糊c均值聚类算法的收敛性,以确定模糊度指数m1和m2的取值原则。基于合成数据和实测数据的仿真实验结果表明：区间数的区间Ⅱ型模糊c均值聚类算法比区间数的模糊c均值聚类算法的聚类效果好。     

基于模糊c均值聚类的RBFN的混炼胶粘度在线估计

介绍了将基于模糊c均值聚类(FCM)算法的多模型建模方法(简称FMM)与径向基函数神经网络(RBFM)相结合，先用FCM算法将训练集聚类，再用隶属度将子模型的输出结合起来，从而完成软测量模型的建立。这种方法不仅增强了在对象的整个输入空间的预测精度，同时减少了隐层节点数目，加快了学习速度。算法仿真表明，所提出的算法是处理橡胶混炼牯度软测量建模的一种很有效的方法。     

基于加权模糊c均值聚类的快速图像自动分割算法

图像分割是指将一幅图像分解为若干互不交迭的区域的集合，是图像处理和计算机视觉的基本问题之一。为了提高图像分割的效率，提出了一种基于2维直方图加权的塔形模糊c均值（FCM）聚类图像快速分割算法。该方法先通过构造合理的2维直方图对噪声进行抑制；然后通过塔形分解来缩减聚类样本集；最后利用加权FCM聚类算法进行分类。仿真结果表明，该方法的效率明显优于标准的FCM算法。此外，为确定分割的最优类别数c，还引入了一种基于该快速算法的聚类有效性评价函数——修正划分模糊度，实现了最佳图像分割类别数c的自动确定。基于人造图像和实际图像的测试实验结果表明该方法是有效的。     

A Method of Face Recognition Based on Fuzzy c-Means Clustering and Associated Sub-NNs

The face is a complex multidimensional visual model and developing a computational model for face recognition is difficult. In this paper, we present a method for face recognition based on parallel neural networks. Neural networks (NNs) have been widely used in various fields. However, the computing efficiency decreases rapidly if the scale of the NN increases. In this paper, a new method of face recognition based on fuzzy clustering and parallel NNs is proposed. The face patterns are divided into several small-scale neural networks based on fuzzy clustering and they are combined to obtain the recognition result. In particular, the proposed method achieved a 98.75% recognition accuracy for 240 patterns of 20 registrants and a 99.58% rejection rate for 240 patterns of 20 nonregistrants. Experimental results show that the performance of our new face-recognition method is better than those of the backpropagation NN (BPNN) system, the hard c-means (HCM) and parallel NNs system, and the pattern-matching system     

基于遗传算法的模糊聚类分析

模糊C-均值聚类(FCM)应用广泛,但是它容易陷入局部最优,且对初始值很敏感。该文提出了一种基于遗传算法的模糊聚类方法,首先用遗传算法对模糊聚类中聚类中心的个数和聚类中心的选取进行指导,然后利用FCM进行聚类。实验结果表明：该方法可以在一定程度上避免FCM算法对初始值敏感和容易陷入局部最优解的缺陷,使聚类更合理,效果很好。     

A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms

In this paper the convergence of a class of clustering procedures, popularly known as the fuzzy ISODATA algorithms, is established. The theory of Zangwill is used to prove that arbitrary sequences generated by these (Picard iteration) procedures always terminates at a local minimum, or at worst, always contains a subsequence which converges to a local minimum of the generalized least squares objective functional which defines the problem.     

隶属度修正类模糊C-均值聚类算法的对比分析

为了更深入的对模糊C-均值聚类算法进行研究,从提高算法的收敛速度角度着手,总结归纳了以RCFCM、S-FCM、PIM和FCMα等算法为代表的隶属度修正类模糊C-均值聚类算法,跟踪阐述了其研究进展.为了展现算法的全貌,从不同参数和不同模糊指数等角度实验分析了各算法的性质和特点.根据实验分析结果,为其后续研究指明了方向.上述工作将为FCM算法的进一步研究提供有益的参考.     

RSA密码系统有效实现算法

大整数模幂乘运算一直是制约RSA广泛应用的瓶颈,在对传统算法剖析的基础上,提出了一种新的快速模乘算法,借鉴生成Wallace tree的思想,结合查找表和并行乘法运算进行RSA模幂运算。理论分析和试验证明新算法时间复杂度降低到O(logn)。     

RSA密码系统有效实现算法

本文提出了实现RSA算法的一种快速、适合于硬件实现的方案，在该方案中，我们作用加法链将求幂运算转化为求平方和乘法运算并大大降低了运算的次数，使用Montgomery算法将模N乘法转化为模R（基数）的算法，模R乘积的转化，以及使用一种新的数母加法器作为运算部件的基础。     

模糊C-均值聚类新算法在说话人辨认中的应用

该文提出了一种将模糊C-均值聚类法的各种改进算法与矢量量化法相结合的说话人辨认的新方法。首先从语音信号中提取MFCC特征矢量,其次利用矢量量化来设计码书,最后用改进算法对待识语音进行辨认。新算法的辨认率达到95%以上,抗噪性能也优于矢量量化法。     

基于模糊C-均值聚类的TSP演化算法

提出了一种基于FCM聚类的TSP演化算法。该算法以聚类中心为新的结点组成一个简单的TSP问题,用演化算法寻求其最短路径。在最短路径中,对于每一聚类,可寻求其距前面的聚类和后面的聚类最近的两结点之间的最短距离,若其中的结点较多,则再次演化得到其最短路径,若结点较少,则可用Warshall算法可得到最短路径。通过三个阶段的演化可得到较好的结果。     

A New Convergence Proof of Fuzzy c-Means

In this letter, we give a new, more direct derivation of the convergence properties of the fuzzy c-means (FCM) algorithm, using the equivalence between the original and reduced FCM criterion. From the point of view of the reduced criterion, the FCM algorithm is simply a steepest descent algorithm with variable steplength. We prove that steplength adjustment follows from the majorization principle for steplength. By applying the majorization principle we give a straightforward proof of global convergence. Further convergence properties follow immediately using known results of optimization theory     

一种基于遗传算法的分布式的模糊聚类算法

模糊聚类是一种非监督的聚类算法,但不能保证找到全局最小值,因为是从一个给定的点开始通过迭代的方法找到一个目标函数的最小值。为了克服这个缺点,在模糊聚类算法中结合遗传算法从一个多点的概念去产生多个数据空间。直接将遗传算法应用到模糊聚类中是不合适的,因为数据集通常是巨大的,在这种情况下,染色体的长度会很长。鉴于此,提出了一种基于遗传算法的分布式的模糊聚类算法,将大的进化环境分成若干个小的进化环境。通过理论证明是可行的,且该算法能极大地提高聚类的速度。     

一种模糊聚类系统的设计与实现

介绍一种基于模糊逻辑的数据聚类技术,讨论了模糊C均值聚类方法。模糊C均值算法就是利用模糊逻辑理论和聚类思想,将n样本划分到c个类别中的一个,使得被划分到同一簇的对象之间相似度最大,而不同簇之间的相似度最小。