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。     

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。     

基于模糊划分测度的聚类有效性指标

聚类有效性指标用于评价聚类结果的有效性。根据聚类的基本特性,提出了一个新的用于发现最优模糊划分的聚类有效性指标,该有效性指标采用模糊划分测度和信息熵两个重要因子来评价模糊聚类的有效性。其中,模糊划分测度用于评价聚类的类内紧致性与类间分离性,而信息熵则反映了模糊聚类划分结果的不确定性程度。实验结果表明,该聚类有效性指标能对模糊聚类结果的有效性进行正确的评价,特别是对于空间数据的聚类有效性评价,同其他有效性指标相比,它不仅能得到最优的模糊划分,而且对权重系数也是不敏感的。     

新模糊聚类有效性指标

模糊聚类是模式识别、机器学习和图像处理等领域的重要研究内容。模糊C-均值聚类算法是最常用的模糊聚类实现算法,该算法需要预先给定聚类数才能对数据集进行聚类。提出了一种新的聚类有效性指标,对聚类结果进行有效性验证。该指标从划分熵、隶属度、几何结构角度,定义了紧凑度、分离度、重叠度三个重要特征测量。在此基础上,提出了一种最佳聚类数确定方法。将新聚类有效性指标和传统有效性指标在6个人工数据集和3个真实数据集进行实验验证。实验结果表明,所提出的指标和方法能够有效地对聚类结果进行评估,适合确定样本的最佳聚类数。     

一个改进的模糊聚类有效性指标

聚类有效性指标既可用来评价聚类结果的有效性,也可以用来确定最佳聚类数。根据模糊聚类的基本特性,提出了一种新的模糊聚类有效性指标。该指标结合了数据集的分布特征和数据隶属度两个重要因素来评价聚类结果,提高了判别的准确性。实验证明,该指标能对模糊聚类结果进行正确的评价,并自动获得最佳聚类数,特别是对类间有交叠的情况能够做出准确判定。     

紧邻类与小类数据集下的模糊聚类有效性指标

模糊聚类有效性指标主要是为了解决模糊C-均值算法需要事先给定最佳聚类数的缺陷,但是现有的大多数模糊聚类有效性指标一般过于依赖聚类质心,使得这类指标在含有紧邻类与大小、密度差异大的数据集上无法准确地判断最佳聚类数。为了缓解这个问题,提出了新聚类有效性指标WS。WS指标在一定程度上考虑了最大最小隶属度法则与模糊集偏差,从而全面展示了数据集的整体信息。在人工与真实数据集上,评估WS指标与现有一些指标的有效性,新指标展现出了较高的准确性。在不同的模糊度下,WS有效性指标表现出了较好的鲁棒性。     

核模糊C均值算法的聚类有效性研究

针对核模糊C均值聚类（Kemelized Fuzzy C-Means,KFCM）算法的有效性评价,以核非线性映射为工具,将原空间中的六个著名有效性指标推广到高维特征空间,得到其对应的核化形式,并通过数值比较实验考察这些核化指标的性能及其对高斯核宽度β和模糊指数m的敏感特性。结果表明,在所考察的指标中,著名的Xie-Beni指标VXB及其改进指标VK的核化版本具有最好的性能和可靠性,可优先作为KFCM聚类算法的有效性准则。     

一种新的聚类有效性函数:模糊划分的模糊熵

模糊聚类分析结果是否合理的问题属于模糊聚类有效性判定课题,其核心是模糊聚类有效性函数的构造。文中基于序关系定义了模糊划分模糊熵来描述模糊划分的模糊程度。考虑到现有的一类有效的模糊聚类有效性函数就是基于数据集的模糊划分的,因此文中也用模糊划分的模糊熵作为聚类有效性函数。实验表明,模糊划分的模糊熵作为模糊聚类的有效性函数是合理的、可行的。     

模糊聚类有效性的研究进展

聚类有效性评价对聚类分析具有重要意义,是聚类分析的瓶颈之一。本文从基于数据集模糊划分的方法和基于数据集几何结构的方法两方面,归纳综述了常用的模糊聚类有效性评价函数,并讨论了模糊聚类最佳类别数的自动确定问题。     

一种新的聚类有效性函数

聚类有效性函数是用于评价聚类结果优劣的指标,准确地给出初始聚类类别数将使得聚类结果趋于合理化。根据模糊不确定性理论及聚类问题的基本特性,引入了新的紧密度度量指标D_i（U;c）,在此基础上提出了一个旨在寻求最优聚类类别数的有效性函数。该函数基于数据集的紧密度与分离度特征,综合考虑了数据成员的隶属度及数据集的几何结构。实验结果表明该有效性函数能够发现最优的聚类类别数,对于分类结构较为明确的数据集表现出良好的性能,并且对于权重系数具有良好的鲁棒性。     

A cluster validity index for fuzzy clustering

A new cluster validity index is proposed for the validation of partitions of object data produced by the fuzzy c-means algorithm. The proposed validity index uses a variation measure and a separation measure between two fuzzy clusters. A good fuzzy partition is expected to have a low degree of variation and a large separation distance. Testing of the proposed index and nine previously formulated indices on well-known data sets shows the superior effectiveness and reliability of the proposed index in comparison to other indices and the robustness of the proposed index in noisy environments.     

新的模糊聚类有效性指标

在经典的模糊C均值（FCM）算法中,聚类数需要预先给出,否则算法无法工作,这在一定程度上限制了FCM算法的应用范围。针对FCM算法中聚类数需要预先设定问题,提出了一种新的模糊聚类有效性指标。首先,通过运行FCM算法得到隶属度矩阵;然后,通过隶属度矩阵计算类内紧密性和类间重叠性;最后,利用类内的紧密性和类间的重叠性定义了一个新的聚类有效性指标。该指标克服了FCM算法中类数需要预先设定的缺点,利用该指标可以发现最符合数据自然分布的类的数目。通过对人工数据集和实际数据集的测试表明,对于模糊因子取1.8,2.0和2.2三个不同的常用值,均能发现最优聚类数。     

A validity measure for fuzzy clustering

The authors present a fuzzy validity criterion based on a validity function which identifies compact and separate fuzzy c-partitions without assumptions as to the number of substructures inherent in the data. This function depends on the data set, geometric distance measure, distance between cluster centroids and more importantly on the fuzzy partition generated by any fuzzy algorithm used. The function is mathematically justified via its relationship to a well-defined hard clustering validity function, the separation index for which the condition of uniqueness has already been established. The performance of this validity function compares favorably to that of several others. The application of this validity function to color image segmentation in a computer color vision system for recognition of IC wafer defects which are otherwise impossible to detect using gray-scale image processing is discussed     

A stability based validity method for fuzzy clustering

An important goal in cluster analysis is the internal validation of results using an objective criterion. Of particular relevance in this respect is the estimation of the optimum number of clusters capturing the intrinsic structure of your data. This paper proposes a method to determine this optimum number based on the evaluation of fuzzy partition stability under bootstrap resampling. The method is first characterized on synthetic data with respect to hyper-parameters, like the fuzzifier, and spatial clustering parameters, such as feature space dimensionality, clusters degree of overlap, and number of clusters. The method is then validated on experimental datasets. Furthermore, the performance of the proposed method is compared to that obtained using a number of traditional fuzzy validity rules based on the cluster compactness-to-separation criteria. The proposed method provides accurate and reliable results, and offers better generalization capabilities than the classical approaches.     

Cluster validity for fuzzy criterion clustering

In this paper, we define a validity measure for fuzzy criterion clustering which is a novel approach to fuzzy clustering that in addition to being non-distance-based, addresses the cluster validity problem. The model is then recast as a bilevel fuzzy criterion clustering problem. We propose an algorithm for this model that solves both the validity and clustering problems. Our approach is validated via some sample problems.     

Robust validity index for a modified subtractive clustering algorithm

A novel robust validity index is proposed for subtractive clustering (SC) algorithm. Although the SC algorithm is a simple and fast data clustering method with robust properties against outliers and noise; it has two limitations. First, the cluster number generated by the SC algorithm is influenced by a given threshold. Second, the cluster centers obtained by SC are based on data that have the highest potential values but may not be the actual cluster centers. The validity index is a function as a measure of the fitness of a partition for a given data set. To solve the first problem, this study proposes a novel robust validity index that evaluates the fitness of a partition generated by SC algorithm in terms of three properties: compactness, separation and partition index. To solve the second problem, a modified algorithm based on distance relations between data and cluster centers is designed to ascertain the actual centers generated by the SC algorithm. Experiments confirm that the preferences of the proposed index outperform all others.     

一种基于类别融合的模糊最小最大聚类算法

提出了一种新型的基于类别融合的模糊最小最大聚类算法，该算法首先使用初始类别生成子算法对归一化后的数据集进行预处理，从而生成一系列初始模式类别；然后利用类别融合于算法，将类别融合问题转化为求一无向图的连通子图问题，从而得出在同一连通子图中的点融合为同一类，连接子图的数目为最终的聚类数目。仿真结果表明，在处理未知模式类别数目且数据样本任意分布的数据集时，该算法明显优于传统的模糊C均值算法。