Fuzzy clustering algorithms based on resolution and their application in image compression

This paper presents an idea of clustering resolution. On the basis of the idea, fuzzy clustering algorithms based on resolution are deduced, which naturally comprise a set of clustering algorithms. Thus, c-means algorithm and fuzzy c-means algorithms are actually special examples in the set. As an application for codebook design in image compression based on vector quantization, fuzzy clustering algorithms based on multiresolution are developed, which are almost prior to conventional algorithms in all aspects.     

Algorithms of fuzzy clustering with partial supervision

The paper is concerned with methods of fuzzy clustering based minimization of a scalar performance index with the aid of some labelled patterns. Some modifications of the performance index that take into account the results of partial supervision are proposed. The results of the algorithms introduced are exemplified by the use of numerical examples (Gustafson's cross and EKG data set).     

一种使用启发式搜索优化的模糊规则分类方法

文章提出了一种基于模糊规则的分类方法。该方法首先介绍了基于模糊C均值聚类的模糊规则提取,然后利用所建立的模糊规则库设计了一种分类算法,并且利用启发式搜索来精简分类规则。使用IRIS数据对该文的方法进行了性能测试,结果表明该方法在训练样本较少的情况下,能得到很好的分类效果,并且通过规则精简,所使用的规则数目大大下降,而分类性能更加优良。     

Fast agglomerative clustering using information of k-nearest neighbors

In this paper, we develop a method to lower the computational complexity of pairwise nearest neighbor (PNN) algorithm. Our approach determines a set of candidate clusters being updated after each cluster merge. If the updating process is required for some of these clusters, k-nearest neighbors are found for them. The number of distance calculations for our method is O(N²), where N is the number of data points. To further reduce the computational complexity of the proposed algorithm, some available fast search approaches are used. Compared to available approaches, our proposed algorithm can reduce the computing time and number of distance calculations significantly. Compared to FPNN, our method can reduce the computing time by a factor of about 26.8 for the data set from a real image. Compared with PMLFPNN, our approach can reduce the computing time by a factor of about 3.8 for the same data set.     

An agglomerative clustering algorithm using a dynamic k-nearest-neighbor list

In this paper, a new algorithm is developed to reduce the computational complexity of Ward’s method. The proposed approach uses a dynamic k-nearest-neighbor list to avoid the determination of a cluster’s nearest neighbor at some steps of the cluster merge. Double linked algorithm (DLA) can significantly reduce the computing time of the fast pairwise nearest neighbor (FPNN) algorithm by obtaining an approximate solution of hierarchical agglomerative clustering. In this paper, we propose a method to resolve the problem of a non-optimal solution for DLA while keeping the corresponding advantage of low computational complexity. The computational complexity of the proposed method DKNNA + FS (dynamic k-nearest-neighbor algorithm with a fast search) in terms of the number of distance calculations is O(N²), where N is the number of data points. Compared to FPNN with a fast search (FPNN + FS), the proposed method using the same fast search algorithm (DKNNA + FS) can reduce the computing time by a factor of 1.90-2.18 for the data set from a real image. In comparison with FPNN + FS, DKNNA + FS can reduce the computing time by a factor of 1.92-2.02 using the data set generated from three images. Compared to DLA with a fast search (DLA + FS), DKNNA + FS can decrease the average mean square error by 1.26% for the same data set.     

基于模糊聚类的图书目录查询方法研究

在此提出一种基于模糊聚类的目录查询新方法,该方法基于模糊C均值聚类算法,并结合了编辑距离算法。针对传统的模糊C均值聚类算法的聚类结果不稳定性问题,引入了高权样本点集;并且在处理聚类过程中的边界值归属不足问题,引入编辑距离算法。     

A powerful hybrid clustering method based on modified stem cells and Fuzzy C-means algorithms

One of the simple techniques for Data Clustering is based on Fuzzy C-means (FCM) clustering which describes the belongingness of each data to a cluster by a fuzzy membership function instead of a crisp value. However, the results of fuzzy clustering depend highly on the initial state selection and there is also a high risk for getting the best results when the datasets are large. In this paper, we present a hybrid algorithm based on FCM and modified stem cells algorithms, we called it SC-FCM algorithm, for optimum clustering of a dataset into K clusters. The experimental results obtained by using the new algorithm on different well-known datasets compared with those obtained by K-means algorithm, FCM, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Ant Colony Optimization (ACO), Artificial Bee Colony (ABC) Algorithm demonstrate the better performance of the new algorithm.     

A tabu search-based algorithm for the fuzzy clustering problem

The Fuzzy Clustering Problem (FCP) is a mathematical program which is difficult to solve since it is nonconvex, which implies possession of many local minima. The fuzzy C-means heuristic is the widely known approach to this problem, but it is guaranteed only to yield local minima. In this paper, we propose a new approach to this problem which is based on tabu search technique, and aims at finding a global solution of FCP. We compare the performance of the algorithm with the fuzzy C-means algorithm.     

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。     

Fuzzy clustering with partial supervision

Presented here is a problem of fuzzy clustering with partial supervision, i.e., unsupervised learning completed in the presence of some labeled patterns. The classification information is incorporated additively as a part of an objective function utilized in the standard FUZZY ISODATA. The algorithms proposed in the paper embrace two specific learning scenarios of complete and incomplete class assignment of the labeled patterns. Numerical examples including both synthetic and real-world data arising in the realm of software engineering are also provided.     

Fuzzy relational clustering based on comparing two proximity matrices with utilization of particle swarm optimization

The first stage of knowledge acquisition and reduction of complexity concerning a group of entities is to partition or divide the entities into groups or clusters based on their attributes or characteristics. Clustering algorithms normally require both a method of measuring proximity between patterns and prototypes and a method for aggregating patterns. However sometimes feature vectors or patterns may not be available for objects and only the proximities between the objects are known. Even if feature vectors are available some of the features may not be numeric and it may not be possible to find a satisfactory method of aggregating patterns for the purpose of determining prototypes. Clustering of objects however can be performed on the basis of data describing the objects in terms of feature vectors or on the basis of relational data. The relational data is in terms of proximities between objects. Clustering of objects on the basis of relational data rather than individual object data is called relational clustering. The premise of this paper is that the proximities between the membership vectors, which are obtained as the objective of clustering, should be proportional to the proximities between the objects. The values of the components of the membership vector corresponding to an object are the membership degrees of the object in the various clusters. The membership vector is just a type of feature vector. Based on this premise, this paper describes another fuzzy relational clustering method for finding a fuzzy membership matrix. The method involves solving a rather challenging optimization problem, since the objective function has many local minima. This makes the use of a global optimization method such as particle swarm optimization (PSO) attractive for determining the membership matrix for the clustering. To minimize computational effort, a Bayesian stopping criterion is used in combination with a multi-start strategy for the PSO. Other relational clustering methods generally find local optimum of their objective function.     

An accelerated K-means clustering algorithm using selection and erasure rules

The K-means method is a well-known clustering algorithm with an extensive range of applications,such as biological classification,disease analysis,data mining,and image compression.However,the plain K-means method is not fast when the number of clusters or the number of data points becomes large.A modified K-means algorithm was presented by Fahim et al.(2006).The modified algorithm produced clusters whose mean square error was very similar to that of the plain K-means,but the execution time was shorter.In this study,we try to further increase its speed.There are two rules in our method:a selection rule,used to acquire a good candidate as the initial center to be checked,and an erasure rule,used to delete one or many unqualified centers each time a specified condition is satisfied.Our clustering results are identical to those of Fahim et al.(2006).However,our method further cuts computation time when the number of clusters increases.The mathematical reasoning used in our design is included.     

一种基于粒子群优化的可能性C均值聚类改进方法

提出了一种基于拉子群优化的可能性c均值(Possibilistic Gmeans, PCM)聚类改进方法。该方法首先通过改进PCM算法的目标函数来计算数据模式的隶属度矩阵和聚类中心完成粒子编码,从而降低算法对初始中心的敏感,提高聚类的精度;其次,通过粒子群优化(Particle Swarm Optimization, PSO)算法对编码进行优化,以有效地克服PCM聚类算法容易导致聚类一致性和陷入局部最优解的缺点,减少算法的迭代次数。通过人造数据集和UCI数据集上的实验,表明该算法在计算复杂度、聚类精度和全局寻优能力方面表现得较为突出。     

基于核的可能性聚类算法

针对模糊C-均值算法聚类分析时的缺陷,采用能够较好地处理噪音和孤立点的可能性聚类算法,并将核学习方法的思想应用于可能性聚类算法中,提出一种基于核的可能性聚类算法。该方法利用Mercer核将观察空间的待分类样本点经过一个非线性映射后,映射到一个高维的核空间,突出不同类别样本之间的特征差异,使得原来线性不可分的样本点在核空间中变得更加线性可分,从而更好地聚类。经仿真实验表明,基于核的可能性聚类算法比模糊C-均值以及可能性聚类算法具有更好的聚类效果,且算法能够很快地收敛。     

Fuzzy J-Means: a new heuristic for fuzzy clustering

A fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called Fuzzy J-Means, where the neighbourhood is defined by all possible centroid-to-pattern relocations. The “integer” solution is then moved to a continuous one by an alternate step, i.e., by finding centroids and membership degrees for all patterns and clusters. To alleviate the difficulty of being stuck in local minima of poor value, this local search is then embedded into the Variable Neighbourhood Search metaheuristic. Results on five standard test problems from the literature are reported and compared with those obtained with the well-known Fuzzy C-Means heuristic. It appears that solutions of substantially better quality are obtained with the proposed methods than with this former one.     

Fuzzy spectral clustering with robust spatial information for image segmentation

In recent years, spectral clustering has become one of the most popular clustering algorithms in areas of pattern analysis and recognition. This algorithm uses the eigenvalues and eigenvectors of a normalized similarity matrix to partition the data, and is simple to implement. However, when the image is corrupted by noise, spectral clustering cannot obtain satisfying segmentation performance. In order to overcome the noise sensitivity of the standard spectral clustering algorithm, a novel fuzzy spectral clustering algorithm with robust spatial information for image segmentation (FSC_RS) is proposed in this paper. Firstly, a non-local-weighted sum image of the original image is generated by utilizing the pixels with a similar configuration of each pixel. Then a robust gray-based fuzzy similarity measure is defined by using the fuzzy membership values among gray values in the new generated image. Thus, the similarity matrix obtained by this measure is only dependent on the number of the gray-levels and can be easily stored. Finally, the spectral graph partitioning method can be applied to this similarity matrix to group the gray values of the new generated image and then the corresponding pixels in the image are reclassified to obtain the final segmentation result. Some segmentation experiments on synthetic and real images show that the proposed method outperforms traditional spectral clustering methods and spatial fuzzy clustering in efficiency and robustness.     

模糊聚类方法在医学病理图像分类中的应用

图象分割和对象提取是从图象处理到图象分析的关键步骤。本文将经典的模糊C-均值聚类算法和模糊测度和模糊积分结合起来,并将这两种算法应用于医学病理图象的分割。经典的模糊C-均值聚类算法采用欧式距离计算像素之间的相似度,本文中采用模糊测度和模糊积分计算像素之间的相似度,基于模糊测度和模糊积分的特点,这种计算方法可以提高计算的准确度。最后对两种算法的处理结果进行了比较,结果表明改进的模糊C-均值算法对医学病理图像的分割效果比原算法有所改进。     

利用多进制小波变换和模糊c-均值聚类进行纹理分割

提出了一种基于多进制小波变换的多纹理特征提取方法,通过对小波系数的标准差作为纹理测度以生成特征向量,利用模糊c-均值聚类算法进行纹理分割,获得了较好的实验结果。     

基于临近像素空间距离的模糊C均值聚类算法

针对传统图像分割算法对不同类型噪声敏感性缺陷的问题,基于临近像素空间距离的模糊C均值聚类算法即SFCM (fuzzy C means clustering algorithm based on the space distance of the nearest pixels)算法,采用核化的空间距离公式,将点到点之间的距离转化为点到空间的距离,很好的平衡了考察像素点临近像素点的灰度信息与位置信息间的关系,进一步克服了临近像素的位置差异对考察像素影响不同的缺点.通过在合成图像和自然图像上的大量实验并与几个传统算法进行对比,不仅表现出了很强的抗干扰能力,提高了聚类精度,并且很好的保留了原图像边缘等细节信息,体现出了较强的鲁棒性.