Constructing a yield model for integrated circuits based on a novel fuzzy variable of clustered defect pattern

As the wafer size increases, the clustering phenomenon of defects becomes significant. In addition to clustered defects, various clustering patterns also influence the wafer yield. In fact, the recognition of clustering pattern usually exists fuzziness. However, the wafer yield models in previous studies did not consider the fuzziness of clustering pattern belonging to which shape in recognition. Therefore, the objective of this study is to develop a new fuzzy variable of clustering pattern (FVCP) by using fuzzy logic control, and predict the wafer yield by using back-propagation neural network (BPNN) incorporating ant colony optimization (ACO). The proposed method utilizes defect counts, cluster index (CI), and FVCP as inputs for ACO-BPNN. A simulated study is utilized to demonstrate the effectiveness of the proposed model.     

A FCM-based deterministic forecasting model for fuzzy time series

The study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling uncertainty and vagueness inherent in the data collected. A variety of forecasting models including high-order models have been devoted to improving forecasting accuracy. However, the high-order forecasting approach is accompanied by the crucial problem of determining an appropriate order number. Consequently, such a deficiency was recently solved by Li and Cheng [S.-T. Li, Y.-C. Cheng, Deterministic Fuzzy time series model for forecasting enrollments, Computers and Mathematics with Applications 53 (2007) 1904–1920] using a deterministic forecasting method. In this paper, we propose a novel forecasting model to enhance forecasting functionality and allow processing of two-factor forecasting problems. In addition, this model applies fuzzy c-means (FCM) clustering to deal with interval partitioning, which takes the nature of data points into account and produces unequal-sized intervals. Furthermore, in order to cope with the randomness of initially assigned membership degrees of FCM clustering, Monte Carlo simulations are used to justify the reliability of the proposed model. The superior accuracy of the proposed model is demonstrated by experiments comparing it to other existing models using real-world empirical data.     

Parameter identification of PWARX models using fuzzy distance weighted least squares method

PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input–output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method.     

Unsupervised possibilistic clustering

In fuzzy clustering, the fuzzy c-means (FCM) clustering algorithm is the best known and used method. Since the FCM memberships do not always explain the degrees of belonging for the data well, Krishnapuram and Keller proposed a possibilistic approach to clustering to correct this weakness of FCM. However, the performance of Krishnapuram and Keller's approach depends heavily on the parameters. In this paper, we propose another possibilistic clustering algorithm (PCA) which is based on the FCM objective function, the partition coefficient (PC) and partition entropy (PE) validity indexes. The resulting membership becomes the exponential function, so that it is robust to noise and outliers. The parameters in PCA can be easily handled. Also, the PCA objective function can be considered as a potential function, or a mountain function, so that the prototypes of PCA can be correspondent to the peaks of the estimated function. To validate the clustering results obtained through a PCA, we generalized the validity indexes of FCM. This generalization makes each validity index workable in both fuzzy and possibilistic clustering models. By combining these generalized validity indexes, an unsupervised possibilistic clustering is proposed. Some numerical examples and real data implementation on the basis of the proposed PCA and generalized validity indexes show their effectiveness and accuracy.     

减法聚类-ANFIS在网络故障诊断的应用研究

提出了一种基于减法聚类-自适应模糊神经网络（ANFIS）的网络故障诊断建模方法。减法聚类算法生成初始模糊推理系统,ANFIS建立网络故障诊断原始模型,应用混合算法对模糊规则的参数进行训练并建立最终的模型。仿真实验表明基于减法聚类-ANFIS的建模方法是有效的;通过仿真结果比较,减法聚类-ANFIS的网络故障诊断能力及收敛速度均优于BP神经网络,更适合作为网络故障诊断模型。     

Mountain c-regressions method

Since Quandt [The estimation of the parameters of a linear regression system obeying two separate regimes, Journal of the American Statistical Association 53 (1958) 873-880] initiated the research on 2-regressions analysis, switching regression had been widely studied and applied in psychology, economics, social science and music perception. In fuzzy clustering, the fuzzy c-means (FCM) is the most commonly used algorithm. Hathaway and Bezdek [Switching regression models and fuzzy clustering, IEEE Transactions on Fuzzy Systems 1 (1993) 195-204] embedded FCM into switching regression where it was called fuzzy c-regressions (FCR). However, the FCR always depends heavily on initial values. In this paper, we propose a mountain c-regressions (MCR) method for solving the initial-value problem. First, we perform data transformation for the switching regression data set, and then implement the modified mountain clustering on the transformed data to extract c cluster centers. These extracted c cluster centers in the transformed space will correspond to c regression models in the original data set. The proposed MCR method can form well-estimated c regression models for switching regression data sets. According to the properties of transformation, the proposed MCR is also robust to noise and outliers. Several examples show the effectiveness and superiority of our proposed method.     

一种基于数据相关性的半监督模糊聚类集成方法

现有的半监督聚类集成方法能利用先验信息,使集成的准确性、鲁棒性和稳定性得到提高,但在集成阶段加入成对约束信息时,只考虑了给定的约束信息而忽视了约束点与被约束点的邻域点之间的关系.针对此问题,提出了一种基于数据相关性的半监督模糊聚类集成方法.该方法首先利用半监督模糊聚类算法建立集成信息矩阵,并将其转换为相似性矩阵;然后,利用已知的约束信息及约束点与被约束点的邻域点之间的关系来修改相似性矩阵;最后,利用图划分算法得到最终的聚类结果.真实数据上的实验结果表明,提出的方法可以有效提高聚类质量.     

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.     

基于不完全树结构小波变换及模糊聚类神经网络的纹理分割

提出了一种新的不完全树结构小波变换用于纹理特征提取,给出了一种一人类视觉过程相一致的多分辨率多通道纹理分析方法,它由：1）特征提取：使用不完全树结构小波变换抽取纹理特征;2）基于模糊神经 网络的特征粗分类：①基于样本分布密度的模糊Kohonen聚类网络权植初始化,②使用缩减的特征向量对网络进行训练,得到粗分割结果;3）细化粗分割结果等几部分构成。实验结果证明了其有效性。     

Adaptive Fuzzy-GARCH model applied to forecasting the volatility of stock markets using particle swarm optimization

Fluctuations in the stock market follow the principle of volatility clustering in which changes are cataloged by similarity; as such, large changes tend to follow large changes, and small changes tend to follow small changes. This clustering is one of the major reasons why many generalized autoregression conditional heteroscedasticity (GARCH) models do not forecast the stock market well. In this paper, an adaptive Fuzzy-GARCH model with particle swarm optimization (PSO) is proposed to solve this problem.The adaptive Fuzzy-GARCH model refers to both GARCH models and the parameters of membership functions, which are determined by the characteristics of market itself. Here, we present an iterative algorithm based on PSO to estimate the parameters of the membership functions. The PSO method aims to achieve a global optimal solution with a rapid convergence rate. The three stock markets of Taiwan, Japan, and Germany were analyzed to illustrate the performance of the proposed method.     

一种协同的FCPM模糊聚类算法

比重隶属度模糊聚类(FCPM)算法可从不同角度解决聚类问题,取得较好效果。协同聚类算法利用不同特征子集之间的协同关系,并与其它聚类算法相结合,可提高原有的聚类性能。文中在FCPM聚类算法的基础上进行改进,将其与协同聚类算法相结合,提出一种协同的FCPM聚类算法。该算法在原有FCPM聚类算法的基础上,提高对数据集的聚类效果。在对数据集Wine和Iris进行测试的结果表明,该方法优于FCPM算法,说明该方法的有效性。     

Single point iterative weighted fuzzy C-means clustering algorithm for remote sensing image segmentation

In this paper, a remote sensing image segmentation procedure that utilizes a single point iterative weighted fuzzy C-means clustering algorithm is proposed based upon the prior information. This method can solve the fuzzy C-means algorithm's problem that the clustering quality is greatly affected by the data distributing and the stochastic initializing the centrals of clustering. After the probability statistics of original data, the weights of data attribute are designed to adjust original samples to the uniform distribution, and added in the process of cyclic iteration, which could be suitable for the character of fuzzy C-means algorithm so as to improve the precision. Furthermore, appropriate initial clustering centers adjacent to the actual final clustering centers can be found by the proposed single point adjustment method, which could promote the convergence speed of the overall iterative process and drastically reduce the calculation time. Otherwise, the modified algorithm is updated from multidimensional data analysis to color images clustering. Moreover, with the comparison experiments of the UCI data sets, public Berkeley segmentation dataset and the actual remote sensing data, the real validity of proposed algorithm is proved.     

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.     

Soft clustering of multidimensional data: a semi-fuzzy approach

This paper discusses new approaches to unsupervised fuzzy classification of multidimensional data. In the developed clustering models, patterns are considered to belong to some but not necessarily all clusters. Accordingly, such algorithms are called ‘semi-fuzzy’ or ‘soft’ clustering techniques. Several models to achieve this goal are investigated and corresponding implementation algorithms are developed. Experimental results are reported.     

Non-dominated sorting genetic algorithm using fuzzy membership chromosome for categorical data clustering

In this research, a data clustering algorithm named as non-dominated sorting genetic algorithm-fuzzy membership chromosome (NSGA-FMC) based on K-modes method which combines fuzzy genetic algorithm and multi-objective optimization was proposed to improve the clustering quality on categorical data. The proposed method uses fuzzy membership value as chromosome. In addition, due to this innovative chromosome setting, a more efficient solution selection technique which selects a solution from non-dominated Pareto front based on the largest fuzzy membership is integrated in the proposed algorithm. The multiple objective functions: fuzzy compactness within a cluster (π) and separation among clusters (sep) are used to optimize the clustering quality. A series of experiments by using three UCI categorical datasets were conducted to compare the clustering results of the proposed NSGA-FMC with two existing methods: genetic algorithm fuzzy K-modes (GA-FKM) and multi-objective genetic algorithm-based fuzzy clustering of categorical attributes (MOGA (π, sep)). Adjusted Rand index (ARI), π, sep, and computation time were used as performance indexes for comparison. The experimental result showed that the proposed method can obtain better clustering quality in terms of ARI, π, and sep simultaneously with shorter computation time.     

Spatial dependence-based fuzzy regression clustering

Fuzzy clustering based regression analysis is a novel hybrid approach to capture the linear structure while considering the classification structure of the measurement. Using the concept that weights provided via the fuzzy degree of clustering, some regression models have been proposed in literature. In these models, membership values derived from clustering or some weights obtained from geometrical functions are employed as the weights of regression system. This paper addresses a weighted fuzzy regression analysis based on spatial dependence measure of the memberships. By the methodology presented in this paper, the relative weights are used in fuzzy regression models instead of direct membership values or their geometrical transforms. The experimental studies indicate that the spatial dependence based analyses yield more reliable results to show the correlation of the independent variables into the dependent variable. In addition, it has been observed that spatial dependence based models have high estimation and generalization capacities.     

Partition-and-merge based fuzzy genetic clustering algorithm for categorical data

Categorical data clustering is a difficult and challenging task due to the special characteristic of categorical attributes: no natural order. Thus, this study aims to propose a two-stage method named partition-and-merge based fuzzy genetic clustering algorithm (PM-FGCA) for categorical data. The proposed PM-FGCA uses a fuzzy genetic clustering algorithm to partition the dataset into a maximum number of clusters in the first stage. Then, the merge stage is designed to select two clusters among the clusters that generated in the first stage based on its inter-cluster distances and merge two selected clusters to one cluster. This procedure is repeated until the number of clusters equals to the predetermined number of clusters. Thereafter, some particular instances in each cluster are considered to be re-assigned to other clusters based on the intra-cluster distances. The proposed PM-FGCA is implemented on ten categorical datasets from UCI machine learning repository. In order to evaluate the clustering performance, the proposed PM-FGCA is compared with some existing methods such as k-modes algorithm, fuzzy k-modes algorithm, genetic fuzzy k-modes algorithm, and non-dominated sorting genetic algorithm using fuzzy membership chromosomes. Adjusted Ranked Index (ARI), Normalized Mutual Information (NMI), and Davies–Bouldin (DB) index are selected as three clustering validation indices which are represented to both external index (i.e., ARI and NMI) and internal index (i.e., DB). Consequently, the experimental result shows that the proposed PM-FGCA outperforms the benchmark methods in terms of the tested indices.     

一种扩展的条件模糊C-均值聚类算法

在综合分析标准的模糊C-均值聚类算法和条件模糊C-均值聚类算法基础上,对模糊划分空间进行修改,进一步弱化模糊划分矩阵的约束,给出一种扩展的条件模糊C-均值聚类算法。算法的划分矩阵和原型不依赖于背景约束及模糊划分矩阵的隶属度总和。实验结果表明：该算法可以得到不同的聚类原型,并具有很好的聚类效果。     

A wavelet-based autoregressive fuzzy model for forecasting algal blooms

This paper proposes fuzzy models for forecasting the complex behavior of algal blooms. The models are developed through the integration of autoregressive models, the Takagi-Sugeno fuzzy model, and discrete wavelet transform algorithms. The premise parts of the proposed models are determined using the subtractive clustering technique and the consequent parts are optimized using weighted least squares. To train and validate the proposed fuzzy models, a large number of data sets were collected from Daecheong reservoir in Geum River in the Republic of Korea. The data include both water quality and hydrological variables. Total nitrogen, total phosphorous, dissolved oxygen, chemical oxygen demand, biochemical oxygen demand, pH, air temperature, water temperature and outflow water were evaluated as input signals while chlorophyll-a was used as an output. It is demonstrated from the simulation that the proposed fuzzy models are effective in forecasting algal blooms.