Enhanced neural gas network for prototype-based clustering

In practical cluster analysis tasks, an efficient clustering algorithm should be less sensitive to parameter configurations and tolerate the existence of outliers. Based on the neural gas (NG) network framework, we propose an efficient prototype-based clustering (PBC) algorithm called enhanced neural gas (ENG) network. Several problems associated with the traditional PBC algorithms and original NG algorithm such as sensitivity to initialization, sensitivity to input sequence ordering and the adverse influence from outliers can be effectively tackled in our new scheme. In addition, our new algorithm can establish the topology relationships among the prototypes and all topology-wise badly located prototypes can be relocated to represent more meaningful regions. Experimental results¹on synthetic and UCI datasets show that our algorithm possesses superior performance in comparison to several PBC algorithms and their improved variants, such as hard c-means, fuzzy c-means, NG, fuzzy possibilistic c-means, credibilistic fuzzy c-means, hard/fuzzy robust clustering and alternative hard/fuzzy c-means, in static data clustering tasks with a fixed number of prototypes.     

A hybrid genetic algorithm–fuzzy c-means approach for incomplete data clustering based on nearest-neighbor intervals

Incomplete data are often encountered in data sets used in clustering problems, and inappropriate treatment of incomplete data can significantly degrade the clustering performance. In view of the uncertainty of missing attributes, we put forward an interval representation of missing attributes based on nearest-neighbor information, named nearest-neighbor interval, and a hybrid approach utilizing genetic algorithm and fuzzy c-means is presented for incomplete data clustering. The overall algorithm is within the genetic algorithm framework, which searches for appropriate imputations of missing attributes in corresponding nearest-neighbor intervals to recover the incomplete data set, and hybridizes fuzzy c-means to perform clustering analysis and provide fitness metric for genetic optimization simultaneously. Several experimental results on a set of real-life data sets are presented to demonstrate the better clustering performance of our hybrid approach over the compared methods.     

基于PSO_KFCM的医学图像分割

在核模糊聚类算法(KFCM)的基础上,提出了一种新的PSO KFCM聚类算法.新算法利用高斯核函数,把输入空间的样本映射到高维特征空间,利用微粒群算法的全局搜索、快速收敛的特点,代替KFCM算法逐次迭代的过程,在特征空间中进行聚类,克服了KFCM对初始值和噪声数据敏感、易陷入局部最优的缺点.通过对医学图像进行分割,仿真实验结果表明,新算法在性能上比KFCM聚类算法有较大改进,具有更好的聚类效果,且算法能够很快地收敛.     

Fuzzy wavelet neural network based on fuzzy clustering and gradient techniques for time series prediction

This paper presents the development of fuzzy wavelet neural network system for time series prediction that combines the advantages of fuzzy systems and wavelet neural network. The structure of fuzzy wavelet neural network (FWNN) is proposed, and its learning algorithm is derived. The proposed network is constructed on the base of a set of TSK fuzzy rules that includes a wavelet function in the consequent part of each rule. A fuzzy c-means clustering algorithm is implemented to generate the rules, that is the structure of FWNN prediction model, automatically, and the gradient-learning algorithm is used for parameter identification. The use of fuzzy c-means clustering algorithm with the gradient algorithm allows to improve convergence of learning algorithm. FWNN is used for modeling and prediction of complex time series and prediction of foreign-exchange rates. Exchange rates are dynamic process that changes every day and have high-order nonlinearity. The statistical data for the last 2 years are used for the development of FWNN prediction model. Effectiveness of the proposed system is evaluated with the results obtained from the simulation of FWNN-based systems and with the comparative simulation results of previous related models.     

Fuzzy C-means based clustering for linearly and nonlinearly separable data

In this paper we present a new distance metric that incorporates the distance variation in a cluster to regularize the distance between a data point and the cluster centroid. It is then applied to the conventional fuzzy C-means (FCM) clustering in data space and the kernel fuzzy C-means (KFCM) clustering in a high-dimensional feature space. Experiments on two-dimensional artificial data sets, real data sets from public data libraries and color image segmentation have shown that the proposed FCM and KFCM with the new distance metric generally have better performance on non-spherically distributed data with uneven density for linear and nonlinear separation.     

多核模糊聚类

针对单核聚类的性能局限性问题,提出将高斯核、Sigmoid核以及多项式核等多种核组成一种新的多核函数,并利用于模糊核进行聚类。高斯核在聚类中有广泛应用,同时Sigmoid核在神经网络中被证明具有很好的全局分类性能。将不同的核函数组合起来的多核函数将结合各种核函数的优点,其聚类性能优于利用单核的模糊核聚类（KFCM）,实验结果表明了该方法的有效性。     

基于小波变换和KFCM的彩色图像分割

提出一种将小波变换和核模糊C均值聚类算法相结合的快速彩色图像分割算法。利用小波变换的多分辨率特性,在分辨率最大尺度上的LL子带进行均值漂移聚类,快速获得初始粗分割结果,在其基础上进行模糊核聚类分割,将上一层的结果用于下一层的初始化,重复至最低分辨率后用最小分类器对原始图像进行最终分割。实验结果证明,该算法分割速度快,对自然彩色图像的分割结果优于模糊C均值算法和均值漂移算法。     

基于核模糊C均值的眼底视网膜血管分割算法

针对眼底视网膜图像对比度差、背景不一致的问题,提出了一种基于核模糊C均值的眼底视网膜血管分割算法。首先采用二维高斯匹配滤波预处理以增强血管,然后采用核模糊C均值算法对增强眼底图像进行分割,并根据血管与各类隶属度的关系自动合并聚类图像得到最终的血管图像。实验结果表明,该算法分割结果令人满意。     

Recognition of control chart patterns using fuzzy SVM with a hybrid kernel function

Accurate control chart patterns recognition (CCPR) plays an essential role in the implementation of control charts. However, it is a challenging problem since nonrandom control chart patterns (CCPs) are normally distorted by “common process variations”. In this paper, a novel method of CCPR by integrating fuzzy support vector machine (SVM) with hybrid kernel function and genetic algorithm (GA) is proposed. Firstly, two shape features and two statistical features that do not depend on the distribution parameters and number of samples are presented to explicitly describe the characteristics of CCPs. Then, a novel multiclass method based on fuzzy SVM with a hybrid kernel function is proposed. In this method, the influence of outliers on classification accuracy of SVM-based classifiers is weakened by assigning a degree of membership for every training sample. Meanwhile, a hybrid kernel function combining Gaussian kernel and polynomial kernel is adopted to further enhance the generalization ability of the classifiers. To solve the issue of features selection and parameters optimization, GA is used to simultaneously optimize the input features subsets and parameters of fuzzy SVM-based classifier. Finally, several simulation experiments and a real example are addressed to validate the feasibility and effectiveness of the proposed methodology. And the results of simulation experiments demonstrate that it can achieve excellent performance for CCPR and outperforms other approaches, such as learning vector quantization network, multi-layer perceptron network, probability neural network, fuzzy clustering and SVM, in term of recognition accuracy. The results of the practical cases manifest that the proposed method has application potential for solving the problem of control chart interpretation in real-world.     

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。     

Further reduced form of wavelet feature for text independent speaker recognition

A text independent speaker recognition system based on wavelet transform derived from fuzzy c-means clustering is proposed. The fuzzy c-means clustering is applied to the speaker data compression in spectrum domain. A set of experiments are conducted, which gives a 95% recognition rate for 100 Mandarin speakers.     

基于小波包和改进的FCM的医学图像分割

提出应用最优小波包变换对磁共振颅脑图像做分解,以各子带小波包系数的能量形成纹理特征集;并运用基于核函数的模糊C均值聚类算法（Kernel-Based Fuzzy C-means Algorithm,KFCM）对所提取到的特征集进行聚类分析,从而实现了对磁共振颅脑图像的有效分割。实验证明应用KFCM算法做分割的收敛速度和抗噪性明显优于FCM算法。     

Detecting patterns in process data with fractal dimension

In quality control discipline, pattern classification is focused on the detection of unnatural patterns in process data. In this paper, fractal dimension is proposed as a new classifier for pattern classification. Fractal dimension is an index for measuring the complexity of an object. Its applications were found in such diverse fields as manufacturing, material science, medical, and image processing. A method for detecting patterns in process data using the fractal dimension is proposed in this paper. A Monte Carlo study was carried out to study the fractal dimension (D) and the Y-intercept (Y_int) values of process data with patterns of interest. The patterns included in the study are natural pattern, upward linear trend, downward linear trend, cycle, systematic variable, stratification, mixture, upward sudden shift, and downward sudden shift. Based on the results, the approach is effective in detecting such non-periodic patterns as the natural patterns, linear trends (at slope ≥0.2), systematic variable, stratification, mixture, and sudden shifts. For the cyclical pattern, although the D and Y_int-values are not stable, the approach can provide useful information when the period of the cycle is greater than 2 and is less than or equal to half the window size (2N/2). The minor drawbacks of this approach are that it is not sensitive for detecting linear trends with small slope and the slope of the original data is needed to detect the difference between upward and downward linear trends and the difference between upward and downward sudden shifts.     

Robust fuzzy relational classifier incorporating the soft class labels

Fuzzy relational classifier (FRC) is a recently proposed two-step nonlinear classifier. At first, the unsupervised fuzzy c-means (FCM) clustering is performed to explore the underlying groups of the given dataset. Then, a fuzzy relation matrix indicating the relationship between the formed groups and the given classes is constructed for subsequent classification. It has been shown that FRC has two advantages: interpretable classification results and avoidance of overtraining. However, FRC not only lacks the robustness which is very important for a classifier, but also fails on the dataset with non-spherical distributions. Moreover, the classification mechanism of FRC is sensitive to the improper class labels of the training samples, thus leading to considerable decline in classification performance. The purpose of this paper is to develop a Robust FRC (RFRC) algorithm aiming at overcoming or mitigating all of the above disadvantages of FRC and maintaining its original advantages. In the proposed RFRC algorithm, we employ our previously proposed robust kernelized FCM (KFCM) to replace FCM to enhance its robustness against outliers and its suitability for the non-spherical data structures. In addition, we incorporate the soft class labels into the classification mechanism to improve its performance, especially for the datasets containing the improper class labels. The experimental results on 2 artificial and 11 real-life benchmark datasets demonstrate that RFRC algorithm can consistently outperform FRC in classification performance.     

Application of fuzzy ARTMAP and fuzzy <Emphasis Type="Italic">c</Emphasis>-means clustering to pattern classification with incomplete data

In this paper, a hybrid neural network that is capable of incremental learning and classification of patterns with incomplete data is proposed. Fuzzy ARTMAP (FAM) is employed as the constituting network for pattern classification while fuzzy c-means (FCM) clustering is used as the underlying algorithm for processing training as well as test samples with missing features. To handle an incomplete training set, FAM is first trained using complete samples only. Missing features of the training samples are estimated and replaced using two FCM-based strategies. Then, network training is conducted using all the complete and estimated samples. To handle an incomplete test set, a non-substitution FCM-based strategy is employed so that a predicted output can be produced rapidly. The performance of the proposed hybrid network is evaluated using a benchmark problem, and its practical applicability is demonstrated using a medical diagnosis task. The results are compared, analysed and quantified statistically with the bootstrap method. Implications of the proposed network for pattern classification tasks with incomplete data are discussed.     

A HYBRID INTELLIGENT MODEL BASED ON EVOLUTIONARY FUZZY CLUSTERING AND SYNDICATE NEURAL NETWORKS

In this article, a new hybrid intelligent model comprising a cluster allocation and adaptation component is developed for solving classification and pattern recognition problems. Its computation ability has been verified through various benchmark problems and biometric applications. The proposed model consists of two components: cluster distribution and adaptation. In the first module, mean patterns are distributed into the number of clusters based on the evolutionary fuzzy clustering, which is the basis for network structure selection in next module. In the second module, training and subsequent generalization is performed by the syndicate neural networks (SNN). The number of SNNs required in the second module will be same as the number of clusters. Whereas each network contains as many output neurons as the maximum number of members assigned to each cluster. The proposed novel fusion of evolutionary fuzzy clustering with a neural network yields superior performance in classification and pattern recognition problems. Performance evaluation has been carried out over a wide spectrum of benchmark problems and real-life biometric recognition problems with noise and occlusion. Experimental results demonstrate the efficacy of the methodology over existing ones.     

基于改进磷虾群优化的中心极大化KFCM算法在IDS的应用*

由于核模糊C-均值算法(Kernel Fuzzy C-means,KFCM)随机选择初始聚类中心,易导致算法陷入局部最优,且算法在聚类中心较近或重合时,易产生一致性聚类结果。为解决以上问题,提出一种改进算法。改进算法对原目标函数进行重新定义,通过在目标函数中增加一项聚类中心约束项来调控簇间分离度,从而避免算法出现一致性聚类结果。利用改进磷虾群算法对基于新目标函数的KFCM算法进行优化,使算法不再依赖初始聚类中心,提高算法的稳定性。基于距离最大最小原则产生多组较优的聚类中心作为初始磷虾群体并在算法迭代过程中融合一种新的精英保留策略,从而确保算法收敛到全局极值。通过对个体随机扩散活动进行分段式logistic混沌搜索,提高算法全局寻优能力。使用KDD CUP 99入侵检测数据进行仿真实验表明,改进算法具有更好的检测性能,解决了传统的聚类算法在入侵检测中稳定性差,检测准确率低的问题。     

An adaptive spatially constrained fuzzy c-means algorithm for multispectral remotely sensed imagery clustering

This paper presents a novel adaptive spatially constrained fuzzy c-means (ASCFCM) algorithm for multispectral remotely sensed imagery clustering by incorporating accurate local spatial and grey-level information. In this algorithm, a novel weighted factor is introduced considering spatial distance and membership differences between the centred pixel and its neighbours simultaneously. This factor can adaptively estimate the accurate spatial constrains from neighbouring pixels. To further enhance its robustness to noise and outliers, a novel prior probability function is developed by integrating the mutual dependency information in the neighbourhood to obtain accurate spatial contextual information. The proposed algorithm is free of any experimentally adjusted parameters and totally adaptive to the local image content. Not only the neighbourhood but also the centred pixel terms of the objective function are all accurately estimated. Thus, the ASCFCM enhances the conventional fuzzy c-means (FCM) algorithm by producing homogeneous regions and reducing the edge blurring artefact simultaneously. Experimental results using a series of synthetic and real-world images show that the proposed ASCFCM outperforms the competing methodologies, and hence provides an effective unsupervised method for multispectral remotely sensed imagery clustering.