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REcENT cONVERGENcE RESULTS FOR THE fuzzy c-means cLUSTERING algorithmS

JOURNAL OF cLASSIFIcATION 1988年第2期5卷 237-247页

作者： HATHAWAY, RJ BEZDEK, Jc BOEING ELECTR INFORMAT PROC LABSEATTLEWA 98124

One of the main techniques embodied in many pattern recognition systems is cluster analysis — the identification of substructure in unlabeled data sets. The fuzzy c-means algorithms (FcM) have often been used to solve certain types of clustering problems. During the last two years several new local results concerning both numerical and stochastic convergence of FcM have been found. Numerical results describe how the algorithms behave when evaluated as optimization algorithms for finding minima of the corresponding family of fuzzy c-means functionals. Stochastic properties refer to the accuracy of minima of FcM functionals as approximations to parameters of statistical populations which are sometimes assumed to be associated with the data. The purpose of this paper is to collect the main global and local, numerical and stochastic, convergence results for FcM in a brief and unified way.

关键词： cluster analysis convergence fuzzy c-means algorithm Optimization Partitioning algorithms Pattern recognition

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Predicting the eddy current loss of a large nuclear power turbo generator using a fuzzy c-means deep Gaussian process regression model

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APPLIED SOFT cOMPUTING 2022年第0期116卷 108328-108328页

作者： Guo, Hai Guo, Hai Song, Yifan Song, Yifan Wang, Likun Wang, Likun Zhao, Jingying Zhao, Jingying Marignetti, Fabrizio Marignetti, Fabrizio Dalian Minzu Univ Coll Comp Sci & Technol Dalian 116600 Peoples R China Dalian Minzu Univ SEAC Key Lab Big Data Appl Technol Dalian 116600 Peoples R China Harbin Univ Sci & Technol Coll Elect & Elect Engn Harbin 150080 Peoples R China Dalian Univ Technol Fac Elect Informat & Elect Engn Dalian 116650 Peoples R China Univ Cassino & South Lazio Dept Elect & Informat Engn I-03043 Cassino Italy

The distribution of the rotor slot wedge eddy current loss in large nuclear power turbo generators is complex and is influenced by many factors. Excessive eddy current loss leads to severe rotor heating, potentially leading to thermal accidents;therefore, the design precision of large generators must be improved. In this paper, a fuzzy c-means Deep Gaussian Process Regression (FcM-DGPR) method is proposed to predict the eddy current loss of a large generator in order to solve the problem of the insufficient accuracy of deep Gaussian process regression (DGPR) with increasing number of the data samples. First, the original dataset is obtained by the finite element method (FEM) and then normalized to construct the samples of the eddy current loss of a large nuclear power generator. Second, the training set is automatically clustered into different subsets by the fuzzy c-means algorithm, and each subset is used to train the DGPR model to obtain different sub models. The membership degree of each data point in the test set is calculated and used to evaluate the sub model of the data. Then, the sub model is used to predict the eddy current loss. Finally, the result is obtained by concatenating the results of each sub model. The results show that the goodness of fit (R-2) is 0.9809, the root mean square error (RMSE) is 0.0271, the prediction error is small, and the model exhibits good prediction performance. Further experimental results show that the FcM-DGPR method is superior to the existing DGPR models and other models and is more suitable for predicting the eddy current loss of large generators. (c) 2021 Published by Elsevier B.V.

关键词： Deep Gaussian process fuzzy c-means algorithm Regression prediction Eddy current Nuclear generator

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A Unified Form of fuzzy c-means and K-means algorithms and its Partitional Implementation

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KNOWLEDGE-BASED SYSTEMS 2021年 214卷 106731-106731页

作者： Borlea, Ioan-Daniel Precup, Radu-Emil Borlea, Alexandra-Bianca Iercan, Daniel Politehn Univ Timisoara Dept Automat & Appl Informat Bd V Parvan 2 RO-300223 Timisoara Romania Edith Cowan Univ Sch Engn 270 Joondalup Dr Joondalup WA 6027 Australia

This paper proposes as an element of novelty the Unified Form (UF) clustering algorithm, which treats fuzzy c-means (FcM) and K-means (KM) algorithms as a single configurable algorithm. UF algorithm was designed to facilitate the FcM and KM algorithms software implementation by offering a solution to implement a single algorithm, which can be configured to work as FcM or KM. The second element of novelty of this paper is the Partitional Implementation of Unified Form (PIUF) algorithm, which is built upon the UF algorithm and designed to solve in an elegant manner the challenges of processing large datasets in a sequential manner and the scalability of the UF algorithm for processing datasets of any size. PIUF algorithm has the advantage of overcoming any possible hardware limitations that can occur if large volumes of data are processed (required to be stored, loaded in memory and processed by a certain specified computational system). PIUF algorithm is designed and formulated to be used on a single machine if the processed dataset is very big and it cannot be entirely loaded in the memory;at the same time it can be scaled to multiple processing nodes for reducing the processing time required to find the optimal solution. UF and PIUF algorithms are implemented and validated in BigTim platform, which is a distributed platform developed by the authors, and offers support for processing various datasets in a parallel manner but they can be implemented in any other data processing platforms. The Iris dataset is considered and next modified to obtain different datasets of different sizes in order to test the algorithms implementations in BigTim platform in different configurations. The analysis of PIUF algorithm and the comparison with FcM, KM and DBScAN clustering algorithms are carried out using two performance indices;three performance indices are employed to evaluate the quality of the obtained clusters. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Distributed platforms fuzzy c-means algorithm K-means algorithm Partitional Implementation Unified form of fuzzy c-means algorithms and K-means algorithms

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New inter-cluster proximity index for fuzzy c-means clustering

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IEIcE TRANSAcTIONS ON INFORMATION AND SYSTEMS 2008年第2期E91D卷 363-366页

作者： Li, Fan Dai, Shijin Liu, Qihe Yang, Guowei Univ Elect Sci & Technol China Sch Engn & Comp Sci Chengdu 610051 Peoples R China Univ Elect Sci & Technol China Sch Commun & Informat Engn Chengdu 610051 Peoples R China

This letter presents a new inter-cluster proximity index for fuzzy partitions obtained from the fuzzy c-means algorithm. It is defined as the average proximity of all possible pairs of clusters. The proximity of each pair of clusters is determined by the overlap and the separation of the two clusters. The former is quantified by using concepts of fuzzy Rough sets theory and the latter by computing the distance between cluster centroids. Experimental results indicate the efficiency of the proposed index.

关键词： fuzzy c-means algorithm fuzzy rough sets inter-cluster proximity cluster validity fuzzy clustering

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Two-stage turnout fault diagnosis based on similarity function and fuzzy c-means

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ADVANcES IN MEcHANIcAL ENGINEERING 2018年第12期10卷

作者： Huang, Shize Yang, Xiaolu Wang, Ling chen, Wei Zhang, Fan Dong, Decun Tongji Univ Minist Educ Key Lab Rd & Traff Engn Coll Transportat Engn Shanghai 201804 Peoples R China

Fault diagnosis for turnouts is crucial to the safety of railways. Existing studies on fault diagnosis depend on human experiences to select reference curves and require fault type information beforehand. Therefore, we proposed a turnout fault diagnosis method, named similarity function and fuzzy c-means based two-stage algorithm to detect faults and identify fault types in real time. First, the reference curve is selected from current curves representing turnout actions by K-means algorithm;then, a similarity function called Frechet distance is used to distinguish normal and abnormal curves. Second, an improved fuzzy c-means algorithm is employed to cluster curves automatically. To be more specific, it can double-confirm the normal curves recognized in the first step as well as divide the abnormal curves into different types. Furthermore, possible causes for each fault type are inferred according to their curves. Our approach integrates fault detection and fault classification into one model and would better help the diagnosis of turnouts. The analysis results based on the similarity function and fuzzy c-means based two-stage algorithm algorithm indicate that the analyzed turnout fault types can be diagnosed automatically with high accuracy. Furthermore, since the proposed similarity function and fuzzy c-means algorithm does not need to know fault types in advance, it is applicable in identifying new fault types.

关键词： Turnout fault diagnosis Frechet distance fuzzy c-means algorithm similarity function and fuzzy c-means based two-stage algorithm

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Application of clustering Analysis in Brain Gene Data Based on Deep Learning

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IEEE AccESS 2019年 7卷 2947-2956页

作者： Suo, Yina Liu, Tingwei Jia, Xueyong Yu, Fuxing North China Univ Sci & Technol Informat Engn Inst Tangshan 063000 Peoples R China Shandong Univ Sch Math Jinan 250100 Shandong Peoples R China North China Univ Sci & Technol Coll Elect Engn Tangshan 063000 Peoples R China

In the current research, cluster analysis has become a very good way to obtain biological information by analyzing the brain gene expression data. In recent years, many experts have used improved traditional clustering algorithm and a new clustering algorithm to mine brain gene expression data. First, the random Forest method is used to preprocess high-dimensional and high-complexity brain gene expression data. Then, a clustering model based on deep learning is proposed, and a clustering algorithm is implemented by using deep belief network (DBN) and fuzzy c-means algorithm (FcM). This model makes full use of the generality of unsupervised learning of deep learning and clustering technology, combines the advantages of deep learning with clustering, and makes clustering effect better and more convenient for clustering high-dimensional data.

关键词： Deep belief network fuzzy c-means algorithm unsupervised learning brain gene data clustering

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Study of traffic-emitted lead pollution of soil and plants using different fuzzy clustering algorithms

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ANALYTIcAL AND BIOANALYTIcAL cHEMISTRY 2008年第5期390卷 1293-1301页

作者： Sarbu, costel Einax, Juergen W. Univ Babes Bolyai Fac Chem & Chem Engn Dept Analyt Chem Cluj Napoca 400028 Romania Univ Jena Inst Inorgan & Analyt Chem Dept Environm Anal D-07743 Jena Germany

We discuss the clustering of 234 environmental samples resulting from an extensive monitoring program concerning soil lead content, plant lead content, traffic density, and distance from the road at different sampling locations in former East Germany. considering the structure of data and the unsatisfactory results obtained applying classical clustering and principal component analysis, it appeared evident that fuzzy clustering could be one of the best solutions. In the following order we used different fuzzy clustering algorithms, namely, the fuzzy c-means (FcM) algorithm, the Gustafson-Kessel (GK) algorithm, which may detect clusters of ellipsoidal shapes in data by introducing an adaptive distance norm for each cluster, and the fuzzy c-varieties (FcV) algorithm, which was developed for recognition of r-dimensional linear varieties in high-dimensional data (lines, planes or hyperplanes). fuzzy clustering with convex combination of point prototypes and different multidimensional linear prototypes is also discussed and applied for the first time in analytical chemistry (environmetrics). The results obtained in this study show the advantages of the FcV and GK algorithms over the FcM algorithm. The performance of each algorithm is illustrated by graphs and evaluated by the values of some conventional cluster validity indices. The values of the validity indices are in very good agreement with the quality of the clustering results.

关键词： fuzzy c-means algorithm Gustafson-Kessel algorithm fuzzy c-varieties algorithm clustering validity soil and plant samples traffic-emitted lead pollution

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An improved FcM clustering algorithm with adaptive weights based on PSO-TVAc algorithm

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APPLIED INTELLIGENcE 2022年第8期52卷 9521-9536页

作者： Hu, Jianhua Yin, Huilin Wei, Guoliang Song, Yan Univ Shanghai Sci & Technol Coll Sci Shanghai 200093 Peoples R China Univ Shanghai Sci & Technol Dept Control Sci & Engn Shanghai 200093 Peoples R China

fuzzy c-means clustering algorithm (FcM), as the most widely used clustering algorithm, works by iteratively updating the membership degree and the cluster centers to improve the effectiveness of clustering. The performance of FcM algorithm is chiefly evaluated by intra-cluster compactness and inter-cluster separation. However, it has some defects such as high dependency on the initial cluster centers, sensitivity to the noise samples and outliers, difficulties in obtaining the optimization of hyperparameters, a fairly poor performance on datasets with the nonuniform distribution. The main purpose of this paper is to tackle these issues. The novelty of this paper is three-fold: 1) a new FcM clustering algorithm (i.e., cWAFcM) has been proposed, which has a good capability of performing the clustering on datasets with nonuniform distribution and reducing the high dependency on the initial cluster centers;2) considering the merits of AFcM-SP in removing noise samples and cWAFcM in performing clustering on datasets with nonuniform distribution, a combination of the objective functions of these two clustering algorithms is developed to construct the hybrid AFcM algorithm;and 3) during the parameter setting by means of the PSO algorithm with time-varying acceleration coefficients (PSO-TVAc), a new index, namely adaptive clustering validity index (AcVI), is presented to describe the intra-cluster compactness and the inter-cluster separation in a proper manner. Experiments on six data sets in UcI and one artificial data set have been carried out with a comparison of five well-known FcM algorithms. Experimental results have demonstrated that the proposed hybrid AFcM with adaptive weights can more effectively enhance the performance of FcM to increase the clustering effectiveness than the contrastive algorithms. The ranks for seven algorithms on seven datasets in terms of cVIXB, accuracy, and normalized mutual information(NMI), further verifying the superiority of the new al

关键词： fuzzy c-means algorithm Particle swarm optimization clustering validity index Adaptive weight

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A stratified sampling based clustering algorithm for large-scale data

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KNOWLEDGE-BASED SYSTEMS 2019年 163卷 416-428页

作者： Zhao, Xingwang Liang, Jiye Dang, chuangyin Shanxi Univ Sch Comp & Informat Technol Key Lab Computat Intelligence & Chinese Informat Minist Educ Taiyuan 030006 Shanxi Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China

Large-scale data analysis is a challenging and relevant task for present-day research and industry. As a promising data analysis tool, clustering is becoming more important in the era of big data. In large-scale data clustering, sampling is an efficient and most widely used approximation technique. Recently, several sampling-based clustering algorithms have attracted considerable attention in large-scale data analysis owing to their efficiency. However, some of these existing algorithms have low clustering accuracy, whereas others have high computational complexity. To overcome these deficiencies, a stratified sampling based clustering algorithm for large-scale data is proposed in this paper. Its basic steps include: (1) obtaining a number of representative samples from different strata with a stratified sampling scheme, which are formed by locality sensitive hashing technique, (2) partitioning the chosen samples into different clusters using the fuzzy c-means clustering algorithm, (3) assigning the out-of-sample objects into their closest clusters via data labeling technique. The performance of the proposed algorithm is compared with the state-of-the-art sampling-based fuzzy c-means clustering algorithms on several large-scale data sets including synthetic and real ones. The experimental results show that the proposed algorithm outperforms the related algorithms in terms of clustering quality and computational efficiency for large-scale data sets. (c) 2018 Published by Elsevier B.V.

关键词： Large-scale data fuzzy c-means algorithm Stratified sampling Data labeling

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Methods for robust clustering of epileptic EEG spikes

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IEEE TRANSAcTIONS ON BIOMEDIcAL ENGINEERING 2000年第7期47卷 857-868页

作者： Wahlberg, P Lantz, G Univ Lund Dept Elect Engn & Comp Sci Signal Proc Grp S-22100 Lund Sweden Univ Hosp HUG Dept Neurol Human Brain Mapping Lab CH-1211 Geneva 14 Switzerland

We investigate algorithms for clustering of epileptic electroencephalogram (EEG) spikes. Such a method is useful prior to averaging and inverse computations since the spikes of a patient often belong to a few distinct classes. Data sets often contain outliers, which makes algorithms with robust performance desirable. We compare the fuzzy c-means (FcM) algorithm and a graph-theoretic algorithm. We give criteria for determination of the correct level of outlier contamination. The performance is then studied by aid of simulations, which show good results for a range of circumstances, for both algorithms. The graph-theoretic method gave better results than FcM for simulated signals. Also, when evaluating the methods on seven real-life data sets, the graph-theoretic method was the better method, in terms of closeness to the manual assessment by a neurophysiologist. However, there was some discrepancy between manual and automatic clustering and we suggest as an alternative method a human choice among a limited set of automatically obtained clusterings. Furthermore, we evaluate geometrically weighted feature extraction and conclude that it is useful as a supplementary dimension for clustering.

关键词： clustering electrode geometry epileptic EEG spikes fuzzy c-means algorithm graph theory k-components localization of foci outlier contamination robustness

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