Fuzzy C-Means Algorithm Based on Density Canopy and Manifold Learning

Fuzzy C-Means(FCM)is an effective and widely used clustering algorithm,but there are still some problems.considering the number of clusters must be determined manually,the local optimal solutions is easily influenced by the random selection of initial cluster centers,and the performance of Euclid distance in complex high-dimensional data is poor.To solve the above problems,the improved FCM clustering algorithm based on density Canopy and Manifold learning(DM-FCM)is proposed.First,a density Canopy algorithm based on improved local density is proposed to automatically deter-mine the number of clusters and initial cluster centers,which improves the self-adaptability and stability of the algorithm.Then,considering that high-dimensional data often present a nonlinear structure,the manifold learning method is applied to construct a manifold spatial structure,which preserves the global geometric properties of complex high-dimensional data and improves the clustering effect of the algorithm on complex high-dimensional datasets.Fowlkes-Mallows Index(FMI),the weighted average of homogeneity and completeness(V-measure),Adjusted Mutual Information(AMI),and Adjusted Rand Index(ARI)are used as performance measures of clustering algorithms.The experimental results show that the manifold learning method is the superior distance measure,and the algorithm improves the clustering accuracy and performs superiorly in the clustering of low-dimensional and complex high-dimensional data.

Fuzzy c-means text clustering based on topic concept sub-space

To improve the accuracy of text clustering, fuzzy c-means clustering based on topic concept sub-space （TCS2FCM） is introduced for classifying texts. Five evaluation functions are combined to extract key phrases. Concept phrases, as well as the descriptions of final clusters, are presented using WordNet origin from key phrases. Initial centers and membership matrix are the most important factors affecting clustering performance. Orthogonal concept topic sub-spaces are built with the topic concept phrases representing topics of the texts and the initialization of centers and the membership matrix depend on the concept vectors in sub-spaces. The results show that, different from random initialization of traditional fuzzy c-means clustering, the initialization related to text content contributions can improve clustering precision.

A New Method of Wind Turbine Bearing Fault Diagnosis Based on Multi-Masking Empirical Mode Decomposition and Fuzzy C-Means Clustering

Based on Multi-Masking Empirical Mode Decomposition (MMEMD) and fuzzy c-means (FCM) clustering, a new method of wind turbine bearing fault diagnosis FCM-MMEMD is proposed, which can determine the fault accurately and timely. First, FCM clustering is employed to classify the data into different clusters, which helps to estimate whether there is a fault and how many fault types there are. If fault signals exist, the fault vibration signals are then demodulated and decomposed into different frequency bands by MMEMD in order to be analyzed further. In order to overcome the mode mixing defect of empirical mode decomposition (EMD), a novel method called MMEMD is proposed. It is an improvement to masking empirical mode decomposition (MEMD). By adding multi-masking signals to the signals to be decomposed in different levels, it can restrain low-frequency components from mixing in highfrequency components effectively in the sifting process and then suppress the mode mixing. It has the advantages of easy implementation and strong ability of suppressing modal mixing. The fault type is determined by Hilbert envelope finally. The results of simulation signal decomposition showed the high performance of MMEMD. Experiments of bearing fault diagnosis in wind turbine bearing fault diagnosis proved the validity and high accuracy of the new method.

Knowledge-Driven Possibilistic Clustering with Automatic Cluster Elimination

Traditional Fuzzy C-Means(FCM)and Possibilistic C-Means(PCM)clustering algorithms are data-driven,and their objective function minimization process is based on the available numeric data.Recently,knowledge hints have been introduced to formknowledge-driven clustering algorithms,which reveal a data structure that considers not only the relationships between data but also the compatibility with knowledge hints.However,these algorithms cannot produce the optimal number of clusters by the clustering algorithm itself;they require the assistance of evaluation indices.Moreover,knowledge hints are usually used as part of the data structure(directly replacing some clustering centers),which severely limits the flexibility of the algorithm and can lead to knowledgemisguidance.To solve this problem,this study designs a newknowledge-driven clustering algorithmcalled the PCM clusteringwith High-density Points(HP-PCM),in which domain knowledge is represented in the form of so-called high-density points.First,a newdatadensitycalculation function is proposed.The Density Knowledge Points Extraction(DKPE)method is established to filter out high-density points from the dataset to form knowledge hints.Then,these hints are incorporated into the PCM objective function so that the clustering algorithm is guided by high-density points to discover the natural data structure.Finally,the initial number of clusters is set to be greater than the true one based on the number of knowledge hints.Then,the HP-PCM algorithm automatically determines the final number of clusters during the clustering process by considering the cluster elimination mechanism.Through experimental studies,including some comparative analyses,the results highlight the effectiveness of the proposed algorithm,such as the increased success rate in clustering,the ability to determine the optimal cluster number,and the faster convergence speed.

A KNN-based two-step fuzzy clustering weighted algorithm for WLAN indoor positioning

Although k-nearest neighbors （KNN） is a popular fingerprint match algorithm for its simplicity and accuracy, because it is sensitive to the circumstances, a fuzzy c-means （FCM） clustering algorithm is applied to improve it. Thus, a KNN-based two-step FCM weighted （KTFW） algorithm for indoor positioning in wireless local area networks （WLAN） is presented in this paper. In KTFW algorithm, k reference points （RPs） chosen by KNN are clustered through FCM based on received signal strength （RSS） and location coordinates. The right clusters are chosen according to rules, so three sets of RPs are formed including the set of k RPs chosen by KNN and are given different weights. RPs supposed to have better contribution to positioning accuracy are given larger weights to improve the positioning accuracy. Simulation results indicate that KTFW generally outperforms KNN and its complexity is greatly reduced through providing initial clustering centers for FCM.

Research and Implementation of the Enterprise Evaluation Based on a Fusion Clustering Model of AHP-FCM

Traditional clustering method is easy to slow convergence speed because of high data dimension and setting random initial clustering center. To improve these problems, a novel method combining subtractive clustering with fuzzy C-means( FCM)clustering will be advanced. In the method, the initial cluster number and cluster center can be obtained using subtractive clustering. On this basis,clustering result will be further optimized with FCM. In addition,the data dimension will be reduced through the analytic hierarchy process( AHP) before clustering calculating.In order to verify the effectiveness of fusion algorithm,an example about enterprise credit evaluation will be carried out. The results show that the fusion clustering algorithm is suitable for classifying high-dimension data,and the algorithm also does well in running up processing speed and improving visibility of result. So the method is suitable to promote the use.

Fault Pattern Recognition based on Kernel Method and Fuzzy C-means

A method about fault identification is proposed to solve the relationship among fault features of large rotating machinery, which is extremely complicated and nonlinear. This paper studies the rotor test-rig and the clustering of data sets and fault pattern recognitions. The present method firstly maps the data from their original space to a high dimensional Kernel space which makes the highly nonlinear data in low-dimensional space become linearly separable in Kernel space. It highlights the differences among the features of the data set. Then fuzzy C-means （FCM） is conducted in the Kernel space. Each data is assigned to the nearest class by computing the distance to the clustering center. Finally, test set is used to judge the results. The convergence rate and clustering accuracy are better than traditional FCM. The study shows that the method is effective for the accuracy of pattern recognition on rotating machinery.

Adaptive Image Digital Watermarking with DCT and FCM

A novel adaptive digital image watermark algorithm is proposed. Fuzzy c-means clustering （FCM） is used to classify the original image blocks into two classes based on several characteristic parameters of human visual system （HVS）. One is suited for embedding a digital watermark, the other is not. So the appropriate blocks in an image are selected to embed the watermark. The wetermark is embedded in the middle-frequency part of the host image in conjunction with HVS and discrete cosine transform （DCT）. The maximal watermark strength is fixed according to the frequency masking. In the same time, for the good performance, the watermark is modulated into a fractal modulation array. The simulation results show that we can remarkably extract the hiding watermark and the algorithm can achieve good robustness with common signal distortion or geometric distortion and the quality of the watermarked image is guaranteed.

A NEW UNSUPERVISED CLASSIFICATION ALGORITHM FOR POLARIMETRIC SAR IMAGES BASED ON FUZZY SET THEORY

In this letter, a new method is proposed for unsupervised classification of terrain types and man-made objects using POLarimetric Synthetic Aperture Radar (POLSAR) data. This technique is a combi-nation of the usage of polarimetric information of SAR images and the unsupervised classification method based on fuzzy set theory. Image quantization and image enhancement are used to preprocess the POLSAR data. Then the polarimetric information and Fuzzy C-Means (FCM) clustering algorithm are used to classify the preprocessed images. The advantages of this algorithm are the automated classification, its high classifica-tion accuracy, fast convergence and high stability. The effectiveness of this algorithm is demonstrated by ex-periments using SIR-C/X-SAR (Spaceborne Imaging Radar-C/X-band Synthetic Aperture Radar) data.

FCM算法的改进及仿真实验研究

模糊C均值(FCM)聚类算法可以用来建立样本对类别的不确定性描述。文章提出一种基于拉普拉斯系数优化目标函数的FCM聚类算法。在目标函数中引入拉普拉斯系数,给对象之间的结构信息赋予权重,从而提高算法的质量和效率。通过紧凑性来优化聚类的有效性,并利用最大有效性的方法来提高改进算法的抗噪性能。仿真实验表明,改进的FCM算法与标准算法相比具有更准确的聚类效果,且受噪声影响小,鲁棒性强。

Automated measurement of three-dimensional cerebral cortical thickness in Alzheimer’s patients using localized gradient vector trajectory in fuzzy membership maps

Our purpose in this study was to develop an automated method for measuring three-dimensional (3D) cerebral cortical thicknesses in patients with Alzheimer’s disease (AD) using magnetic resonance (MR) images. Our proposed method consists of mainly three steps. First, a brain parenchymal region was segmented based on brain model matching. Second, a 3D fuzzy membership map for a cerebral cortical region was created by applying a fuzzy c-means (FCM) clustering algorithm to T1-weighted MR images. Third, cerebral cortical thickness was three- dimensionally measured on each cortical surface voxel by using a localized gradient vector trajectory in a fuzzy membership map. Spherical models with 3 mm artificial cortical regions, which were produced using three noise levels of 2%, 5%, and 10%, were employed to evaluate the proposed method. We also applied the proposed method to T1-weighted images obtained from 20 cases, i.e., 10 clinically diagnosed AD cases and 10 clinically normal (CN) subjects. The thicknesses of the 3 mm artificial cortical regions for spherical models with noise levels of 2%, 5%, and 10% were measured by the proposed method as 2.953 ± 0.342, 2.953 ± 0.342 and 2.952 ± 0.343 mm, respectively. Thus the mean thicknesses for the entire cerebral lobar region were 3.1 ± 0.4 mm for AD patients and 3.3 ± 0.4 mm for CN subjects, respectively (p < 0.05). The proposed method could be feasible for measuring the 3D cerebral cortical thickness on individual cortical surface voxels as an atrophy feature in AD.

Fuzzy Clustering with Novel Separable Criterion

Fuzzy clustering has been used widely in pattern recognition, image processing, and data analysis An improved fuzzy clustering algorithm was developed based on the conventional fuzzy c-means （FCM） to obtain better quality clustering results. The update equations for the membership and the cluster center are derived from the alternating optimization algorithm. Two fuzzy scattering matrices in the objective function assure the compactness between data points and cluster centers, and also strengthen the separation between cluster centers in terms of a novel separable criterion. The clustering algorithm properties are shown to be an improvement over the FCM method＇s properties. Numerical simulations show that the clustering algorithm gives more accurate clustering results than the FCM method.

Research of Improved Fuzzy c-means Algorithm Based on a New Metric Norm

For the question that fuzzy c-means(FCM)clustering algorithm has the disadvantages of being too sensitive to the initial cluster centers and easily trapped in local optima,this paper introduces a new metric norm in FCM and particle swarm optimization(PSO)clustering algorithm,and proposes a parallel optimization algorithm using an improved fuzzy c-means method combined with particle swarm optimization(AF-APSO).The experiment shows that the AF-APSO can avoid local optima,and get the best fitness and clustering performance significantly.

Advanced Fuzzy C-Means Algorithm Based on Local Density and Distance

This paper presents an advanced fuzzy C-means(FCM) clustering algorithm to overcome the weakness of the traditional FCM algorithm, including the instability of random selecting of initial center and the limitation of the data separation or the size of clusters. The advanced FCM algorithm combines the distance with density and improves the objective function so that the performance of the algorithm can be improved. The experimental results show that the proposed FCM algorithm requires fewer iterations yet provides higher accuracy than the traditional FCM algorithm. The advanced algorithm is applied to the influence of stars' box-office data, and the classification accuracy of the first class stars achieves 92.625%.

基于小波变换和模糊聚类的自适应水印嵌入方法

利用人类视觉系统(HVS)的掩蔽效应和小波多分辨率分析的特点,作者提出了一种通过在图象的小波域的细节部分进行模糊聚类来寻找适合嵌入水印的位置,再用隶属度作为嵌入强度来嵌入水印的新的数字水印嵌入算法.实验表明该方法能在保持图象质量的前提下提高水印的鲁棒性.

Magnetic Tile Surface Defect Detection Based on Texture Feature Clustering

In the field of magnetic tile surface detection, artificial detection efficiency is low, and the traditional image segmentation algorithm cannot show good performance when the gray scale of the magnetic tile itself is small, or the image is affected by uneven illumination. In view of these questions, this paper puts forward a new clustering segmentation algorithm based on texture feature. This algorithm uses Gabor function spectra to represent magnetic tile surface texture and then uses a user-defined local product coefficient to modify Gabor energy spectra to get the center number of fuzzy C-means(FCM) clustering. Moreover, the user-defined Gabor energy spectra image is segmented by clustering algorithm. Finally, it extracts the magnetic tile surface defects according to the changes of regional gray characteristics. Experiments show that the algorithm effectively overcomes the noise interference and makes a good performance on accuracy and robustness, which can effectively detect crack,damage, pit and other defects on the magnetic tile surface.

鲁棒模糊聚类图像分割理论进展

模糊C-均值聚类(fuzzy C-means clustering,FCM)是一种揭示数据内在结构的重要工具之一,其具有良好的扩展性、解释性、准确性和稳定性,已广泛应用于模式分析与机器智能等众多领域。首先,对FCM应用于图像分割研究所取得的进展进行系统梳理和分类;其次,从聚类目标函数构造的距离度量和正则化约束等角度出发,分析和讨论不同类型鲁棒模糊聚类的分割方法,指出其优缺点和应用现状;依据图像分割结构的不适定性,揭示现有的鲁棒模糊聚类分割算法的构造机理和差分演化动力学特性;最后,根据当前深度学习、微分拓扑、代数几何、共形几何代数、信息几何和忆阻神经形态计算等理论展望未来鲁棒模糊聚类分割方法的发展趋势和应用前景。

Analysis of Selecting Gated Community as Opening Its Micro-Inter-Road Network

The opening of gated community to expand the micro-road network in the urban traffic system is a hot topic on the urban congestion. To satisfy the demand of opening early choosing case, this paper proposed a comprehensive selecting framework on qualified communities and its appropriate opening time. Firstly, the static influential factors on internal road structure, boundary road structure and traffic flow are qualitatively analyzed. Then, an evaluation opening state index system based on describing accurately traffic flow state is obtained, which takes the opening factors into account at the boundary road network. In this structure, the modified fuzzy C-means (FCM) method calculates the fuzzy entropy weight and range of each opening states index. Finally, the simulation results show that the proposed method is capable of selecting qualified community and the optimum opening time.

Color Image Segmentation Using Feedforward Neural Networks with FCM

This paper proposes a hybrid technique for color image segmentation. First an input image is converted to the image of CIE L＊a＊b＊ color space. The color features ＂a＂ and ＂b＂ of CIE L^＊a^＊b^＊ are then fed into fuzzy C-means （FCM） clustering which is an unsupervised method. The labels obtained from the clustering method FCM are used as a target of the supervised feed forward neural network. The network is trained by the Levenberg-Marquardt back-propagation algorithm, and evaluates its performance using mean square error and regression analysis. The main issues of clustering methods are determining the number of clusters and cluster validity measures. This paper presents a method namely co-occurrence matrix based algorithm for finding the number of clusters and silhouette index values that are used for cluster validation. The proposed method is tested on various color images obtained from the Berkeley database. The segmentation results from the proposed method are validated and the classification accuracy is evaluated by the parameters sensitivity, specificity, and accuracy.

基于改进的模糊C均值聚类图像分割新算法

模糊C均值(FCM)聚类算法广泛用于图像的自动分割,但是传统的FCM算法没有考虑像素的空间信息,因而对噪声十分敏感。为了克服上述问题,提出了一种新的基于改进的FCM图像分割算法。该方法将空间的信息融入到标准的FCM算法中,通过引入表征邻域像素对中心像素作用的先验概率来重新确定当前像素的模糊隶属度值,该概率在算法执行过程中根据模糊隶属度值自动地予以确定。算法中使用基于统计直方图的快速FCM算法进行初始化,收敛速度大大提高。人造图像和实际图像的实验结果表明该方法的有效性和对噪声具有较强的鲁棒性。