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Статті в журналах з теми "Possibilistic clustering"

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Автор: Grafiati

Опубліковано: 28 вересня 2022

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1

Miyamoto, Sadaaki, Youhei Kuroda, and Kenta Arai. "Algorithms for Sequential Extraction of Clusters by Possibilistic Method and Comparison with Mountain Clustering." Journal of Advanced Computational Intelligence and Intelligent Informatics 12, no. 5 (September 20, 2008): 448–53. http://dx.doi.org/10.20965/jaciii.2008.p0448.

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In addition to fuzzy c-means, possibilistic clustering is useful because it is robust against noise in data. The generated clusters are, however, strongly dependent on an initial value. We propose a family of algorithms for sequentially generating clusters “one cluster at a time,” which includes possibilistic medoid clustering. These algorithms automatically determine the number of clusters. Due to possibilistic clustering's similarity to the mountain clustering by Yager and Filev, we compare their formulation and performance in numerical examples.

2

Yang, Miin-Shen, and Kuo-Lung Wu. "Unsupervised possibilistic clustering." Pattern Recognition 39, no. 1 (January 2006): 5–21. http://dx.doi.org/10.1016/j.patcog.2005.07.005.

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3

Ubukata, Seiki, Katsuya Koike, Akira Notsu, and Katsuhiro Honda. "MMMs-Induced Possibilistic Fuzzy Co-Clustering and its Characteristics." Journal of Advanced Computational Intelligence and Intelligent Informatics 22, no. 5 (September 20, 2018): 747–58. http://dx.doi.org/10.20965/jaciii.2018.p0747.

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In the field of cluster analysis, fuzzy theory including the concept of fuzzy sets has been actively utilized to realize flexible and robust clustering methods. FuzzyC-means (FCM), which is the most representative fuzzy clustering method, has been extended to achieve more robust clustering. For example, noise FCM (NFCM) performs noise rejection by introducing a noise cluster that absorbs noise objects and possibilisticC-means (PCM) performs the independent extraction of possibilistic clusters by introducing cluster-wise noise clusters. Similarly, in the field of co-clustering, fuzzy co-clustering induced by multinomial mixture models (FCCMM) was proposed and extended to noise FCCMM (NFCCMM) in an analogous fashion to the NFCM. Ubukata et al. have proposed noise clustering-based possibilistic co-clustering induced by multinomial mixture models (NPCCMM) in an analogous fashion to the PCM. In this study, we develop an NPCCMM scheme considering variable cluster volumes and the fuzziness degree of item memberships to investigate the specific aspects of fuzzy nature rather than probabilistic nature in co-clustering tasks. We investigated the characteristics of the proposed NPCCMM by applying it to an artificial data set and conducted document clustering experiments using real-life data sets. As a result, we found that the proposed method can derive more flexible possibilistic partitions than the probabilistic model by adjusting the fuzziness degrees of object and item memberships. The document clustering experiments also indicated the effectiveness of tuning the fuzziness degree of object and item memberships, and the optimization of cluster volumes to improve classification performance.

4

ZHOU, JIAN, and CHIH-CHENG HUNG. "A GENERALIZED APPROACH TO POSSIBILISTIC CLUSTERING ALGORITHMS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 15, supp02 (April 2007): 117–38. http://dx.doi.org/10.1142/s0218488507004650.

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Fuzzy clustering is an approach using the fuzzy set theory as a tool for data grouping, which has advantages over traditional clustering in many applications. Many fuzzy clustering algorithms have been developed in the literature including fuzzy c-means and possibilistic clustering algorithms, which are all objective-function based methods. Different from the existing fuzzy clustering approaches, in this paper, a general approach of fuzzy clustering is initiated from a new point of view, in which the memberships are estimated directly according to the data information using the fuzzy set theory, and the cluster centers are updated via a performance index. This new method is then used to develop a generalized approach of possibilistic clustering to obtain an infinite family of generalized possibilistic clustering algorithms. We also point out that the existing possibilistic clustering algorithms are members of this family. Following that, some specific possibilistic clustering algorithms in the new family are demonstrated by real data experiments, and the results show that these new proposed algorithms are efficient for clustering and easy for computer implementation.

5

De Cáceres, Miquel, Francesc Oliva, and Xavier Font. "On relational possibilistic clustering." Pattern Recognition 39, no. 11 (November 2006): 2010–24. http://dx.doi.org/10.1016/j.patcog.2006.04.008.

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6

Treerattanapitak, Kiatichai, and Chuleerat Jaruskulchai. "Possibilistic Exponential Fuzzy Clustering." Journal of Computer Science and Technology 28, no. 2 (March 2013): 311–21. http://dx.doi.org/10.1007/s11390-013-1331-7.

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7

Pimentel, Bruno Almeida, and Renata M. C. R. de Souza. "A Generalized Multivariate Approach for Possibilistic Fuzzy C-Means Clustering." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, no. 06 (November 27, 2018): 893–916. http://dx.doi.org/10.1142/s021848851850040x.

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Fuzzy c-Means (FCM) and Possibilistic c-Means (PCM) are the most popular algorithms of the fuzzy and possibilistic clustering approaches, respectively. A hybridization of these methods, called Possibilistic Fuzzy c-Means (PFCM), solves noise sensitivity defect of FCM and overcomes the coincident clusters problem of PCM. Although PFCM have shown good performance in cluster detection, it does not consider that different variables can produce different membership and possibility degrees and this can improve the clustering quality as it has been performed with the Multivariate Fuzzy c-Means (MFCM). Here, this work presents a generalized multivariate approach for possibilistic fuzzy c-means clustering. This approach gives a general form for the clustering criterion of the possibilistic fuzzy clustering with membership and possibility degrees different by cluster and variable and a weighted squared Euclidean distance in order to take into account the shape of clusters. Six multivariate clustering models (special cases) can be derivative from this general form and their properties are presented. Experiments with real and synthetic data sets validate the usefulness of the approach introduced in this paper using the special cases.

8

Krishnapuram, R., and J. M. Keller. "A possibilistic approach to clustering." IEEE Transactions on Fuzzy Systems 1, no. 2 (May 1993): 98–110. http://dx.doi.org/10.1109/91.227387.

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9

Xenaki, Spyridoula D., Konstantinos D. Koutroumbas, and Athanasios A. Rontogiannis. "Sparsity-Aware Possibilistic Clustering Algorithms." IEEE Transactions on Fuzzy Systems 24, no. 6 (December 2016): 1611–26. http://dx.doi.org/10.1109/tfuzz.2016.2543752.

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10

Chowdhary, Chiranji Lal, and D. P. Acharjya. "Clustering Algorithm in Possibilistic Exponential Fuzzy C-Mean Segmenting Medical Images." Journal of Biomimetics, Biomaterials and Biomedical Engineering 30 (January 2017): 12–23. http://dx.doi.org/10.4028/www.scientific.net/jbbbe.30.12.

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Different fuzzy segmentation methods were used in medical imaging from last two decades for obtaining better accuracy in various approaches like detecting tumours etc. Well-known fuzzy segmentations like fuzzy c-means (FCM) assign data to every cluster but that is not realistic in few circumstances. Our paper proposes a novel possibilistic exponential fuzzy c-means (PEFCM) clustering algorithm for segmenting medical images. This new clustering algorithm technology can maintain the advantages of a possibilistic fuzzy c-means (PFCM) and exponential fuzzy c-mean (EFCM) clustering algorithms to maximize benefits and reduce noise/outlier influences. In our proposed hybrid possibilistic exponential fuzzy c-mean segmentation approach, exponential FCM intention functions are recalculated and that select data into the clusters. Traditional FCM clustering process cannot handle noise and outliers so we require being added in clusters due to the reasons of common probabilistic constraints which give the total of membership’s degree in every cluster to be 1. We revise possibilistic exponential fuzzy clustering (PEFCM) which hybridize possibilistic method over exponential fuzzy c-mean segmentation and this proposed idea partition the data filters noisy data or detects them as outliers. Our result analysis by PEFCM segmentation attains an average accuracy of 97.4% compared with existing algorithms. It was concluded that the possibilistic exponential fuzzy c-means segmentation algorithm endorsed for additional efficient for accurate detection of breast tumours to assist for the early detection.

11

Esaki, Tomohito, Tomonori Hashiyama, and Yahachiro Tsukamoto. "Fuzzy Clustering Based on Total Uncertainty Degree." Journal of Advanced Computational Intelligence and Intelligent Informatics 11, no. 8 (October 20, 2007): 897–904. http://dx.doi.org/10.20965/jaciii.2007.p0897.

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Traditional Fuzzy c-Means (FCM) methods have probabilistic and additive restrictions that ∑ μ (x) = 1; the sum of membership values on the identified membership function is one. Possibilistic clustering methods identify membership functions without such constraints, but some parameters used in objective functions are difficult to understand and membership function shapes are independent of clusters estimated through possibilistic methods. We propose novel fuzzy clustering using a total uncertainty degree based on evidential theory with which we obtain nonadditive membership functions whose their shapes depend on data distribution, i.e., they mutually differ. Cluster meanings thus become easier to understand than in possibilistic methods and our proposal requires only one parameter “fuzzifier.” Numerical experiments demonstrated the feasibility of our proposal conducted.

12

Hamasuna, Yukihiro, and Yasunori Endo. "On Sequential Cluster Extraction Based onL1-Regularized Possibilisticc-Means." Journal of Advanced Computational Intelligence and Intelligent Informatics 19, no. 5 (September 20, 2015): 655–61. http://dx.doi.org/10.20965/jaciii.2015.p0655.

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Sequential cluster extraction algorithms are useful clustering methods that extract clusters one by one without the number of clusters having to be determined in advance. Typical examples of these algorithms are sequential hardc-means (SHCM) and possibilistic clustering (PCM) based algorithms. Two types ofL1-regularized possibilistic clustering are proposed to induce crisp and possibilistic allocation rules and to construct a novel sequential cluster extraction algorithm. The relationship between the proposed method and SHCM is also discussed. The effectiveness of the proposed method is verified through numerical examples. Results show that the entropy-based method yields better results for the Rand Index and the number of extracted clusters.

13

Wu, Xiao Hong, Tong Xiang Cai, Bin Wu, and Jun Sun. "Research on the Variety Discrimination of Apple Using a Hybrid Possibilistic Clustering." Advanced Materials Research 710 (June 2013): 768–71. http://dx.doi.org/10.4028/www.scientific.net/amr.710.768.

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Near infrared reflectance (NIR) spectroscopy has been used to obtain NIR spectra of two varieties of apple samples. The dimensionality of NIR spectra was reduced by principal component analysis (PCA), and discriminant information was extracted by linear discriminant analysis (LDA). Last, a hybrid possibilistic clustering algorithm (HPCA) was utilized as classifier to discriminate the apple samples of different varieties. HPCA integrates possibilistic clustering algorithm (PCA) and improved possibilistic c-means (IPCM) clustering algorithm, and produces not only the membership values but also typicality values by simple computation of the sample co-variance. Experimental results showed that HPCA, as an unsupervised learning algorithm, could quickly and easily discriminate the apple varieties.

14

Wan, Renxia, Yuelin Gao, and Caixia Li. "Weighted Fuzzy-Possibilistic C-Means Over Large Data Sets." International Journal of Data Warehousing and Mining 8, no. 4 (October 2012): 82–107. http://dx.doi.org/10.4018/jdwm.2012100104.

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Up to now, several algorithms for clustering large data sets have been presented. Most clustering approaches for data sets are the crisp ones, which cannot be well suitable to the fuzzy case. In this paper, the authors explore a single pass approach to fuzzy possibilistic clustering over large data set. The basic idea of the proposed approach (weighted fuzzy-possibilistic c-means, WFPCM) is to use a modified possibilistic c-means (PCM) algorithm to cluster the weighted data points and centroids with one data segment as a unit. Experimental results on both synthetic and real data sets show that WFPCM can save significant memory usage when comparing with the fuzzy c-means (FCM) algorithm and the possibilistic c-means (PCM) algorithm. Furthermore, the proposed algorithm is of an excellent immunity to noise and can avoid splitting or merging the exact clusters into some inaccurate clusters, and ensures the integrity and purity of the natural classes.

15

Hai-Jun, Fu, Wu Xiao-Hong, Mao Han-Ping, and Wu Bin. "Fuzzy Entropy Clustering Using Possibilistic Approach." Procedia Engineering 15 (2011): 1993–97. http://dx.doi.org/10.1016/j.proeng.2011.08.372.

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16

Zhang, J. S., and Y. W. Leung. "Improved Possibilistic C-Means Clustering Algorithms." IEEE Transactions on Fuzzy Systems 12, no. 2 (April 2004): 209–17. http://dx.doi.org/10.1109/tfuzz.2004.825079.

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17

Xenaki, Spyridoula D., Konstantinos D. Koutroumbas, and Athanasios A. Rontogiannis. "A Novel Adaptive Possibilistic Clustering Algorithm." IEEE Transactions on Fuzzy Systems 24, no. 4 (August 1, 2016): 791–810. http://dx.doi.org/10.1109/tfuzz.2015.2486806.

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18

Yu, Haiyan, Jiulun Fan, and Rong Lan. "Suppressed possibilistic c-means clustering algorithm." Applied Soft Computing 80 (July 2019): 845–72. http://dx.doi.org/10.1016/j.asoc.2019.02.027.

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19

El Harchaoui, Nour-Eddine, Mounir Ait Kerroum, Ahmed Hammouch, Mohamed Ouadou, and Driss Aboutajdine. "Unsupervised Approach Data Analysis Based on Fuzzy Possibilistic Clustering: Application to Medical Image MRI." Computational Intelligence and Neuroscience 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/435497.

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The analysis and processing of large data are a challenge for researchers. Several approaches have been used to model these complex data, and they are based on some mathematical theories: fuzzy, probabilistic, possibilistic, and evidence theories. In this work, we propose a new unsupervised classification approach that combines the fuzzy and possibilistic theories; our purpose is to overcome the problems of uncertain data in complex systems. We used the membership function of fuzzy c-means (FCM) to initialize the parameters of possibilistic c-means (PCM), in order to solve the problem of coinciding clusters that are generated by PCM and also overcome the weakness of FCM to noise. To validate our approach, we used several validity indexes and we compared them with other conventional classification algorithms: fuzzy c-means, possibilistic c-means, and possibilistic fuzzy c-means. The experiments were realized on different synthetics data sets and real brain MR images.

20

Szilágyi, László, Szidónia Lefkovits, and Sándor M. Szilágyi. "Self-Tuning Possibilistic c-Means Clustering Models." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 27, Supp01 (November 5, 2019): 143–59. http://dx.doi.org/10.1142/s0218488519400075.

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The relaxation of the probabilistic constraint of the fuzzy c-means clustering model was proposed to provide robust algorithms that are insensitive to strong noise and outlier data. These goals were achieved by the possibilistic c-means (PCM) algorithm, but these advantages came together with a sensitivity to cluster prototype initialization. According to the original recommendations, the probabilistic fuzzy c-means (FCM) algorithm should be applied to establish the cluster initialization and possibilistic penalty terms for PCM. However, when FCM fails to provide valid cluster prototypes due to the presence of noise, PCM has no chance to recover and produce a fine partition. This paper proposes a two-stage c-means clustering algorithm to tackle with most problems enumerated above. In the first stage called initialization, FCM with two modifications is performed: (1) extra cluster added for noisy data; (2) extra variable and constraint added to handle clusters of various diameters. In the second stage, a modified PCM algorithm is carried out, which also contains the cluster width tuning mechanism based on which it adaptively updates the possibilistic penalty terms. The proposed algorithm has less parameters than PCM when the number of clusters is [Formula: see text]. Numerical evaluation involving synthetic and standard test data sets proved the advantages of the proposed clustering model.

21

Putri, Ghina Nabila Saputro, Dwi Ispriyanti, and Tatik Widiharih. "IMPLEMENTASI ALGORITMA FUZZY C-MEANS DAN FUZZY POSSIBILISTICS C-MEANS UNTUK KLASTERISASI DATA TWEETS PADA AKUN TWITTER TOKOPEDIA." Jurnal Gaussian 11, no. 1 (May 13, 2022): 86–98. http://dx.doi.org/10.14710/j.gauss.v11i1.33996.

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Social media has become the most popular media, which can be accessed by young to old age. Twitter became one of the effective media and the familiar one used by the public, thus making the company make Twitter one of the promotional tools, one of which is Tokopedia. The research aims to group tweets uploaded by @tokopedia Twitter accounts based on the type of tweets content that gets a lot of retweets and likes by followers of @tokopedia. Application of text mining to cluster tweets on the @tokopedia Twitter account using Fuzzy C-Means and Fuzzy Possibilistic C-Means algorithms that viewed the accuracy comparison of both methods used the Modified Partition Coefficient (MPC) cluster validity. The clustering process was carried out five times by the number of clusters ranging from 3 to 7 clusters. The results of the study showed the Fuzzy C-Means method is a better method compared to the Fuzzy Possibilistic C-Means method in clustering data tweets, with the number of clusters formed is 4. The content type formed is related to promo, discount, cashback, prize quizzes, and event promotions organized by Tokopedia. Content with the highest average number of retweets and likes is about automotive deals, sports tools, and merchandise offerings. So, that PT Tokopedia can use this content type as a tool for advertising on Twitter because it gets more likes by followers of @tokopedia.Keywords: Data Tweets, Clustering, Fuzzy C-Means, Fuzzy Possibilistics C-Means, Modified Partition Coefficient.

22

Pimentel, Bruno Almeida, and Renata M. C. R. De Souza. "Possibilistic Clustering Methods for Interval-Valued Data." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 22, no. 02 (April 2014): 263–91. http://dx.doi.org/10.1142/s0218488514500135.

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Outliers may have many anomalous causes, for example, credit card fraud, cyberintrusion or breakdown of a system. Several research areas and application domains have investigated this problem. The popular fuzzy c-means algorithm is sensitive to noise and outlying data. In contrast, the possibilistic partitioning methods are used to solve these problems and other ones. The goal of this paper is to introduce cluster algorithms for partitioning a set of symbolic interval-type data using the possibilistic approach. In addition, a new way of measuring the membership value, according to each feature, is proposed. Experiments with artificial and real symbolic interval-type data sets are used to evaluate the methods. The results of the proposed methods are better than the traditional soft clustering ones.

23

Gupta, Saroj Kumar, M. V. Jagannatha Reddy, and A. Nanda Kumar. "Possibilistic Clustering Adaptive Smoothing Bilateral Filter Using Artificial Neural Network." International Journal of Engineering and Technology 2, no. 6 (2010): 499–503. http://dx.doi.org/10.7763/ijet.2010.v2.171.

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24

Azzouzi, Souad, Amal Hjouji, Jaouad EL- Mekkaoui, and Ahmed EL Khalfi. "A Generalization of Possibilistic Fuzzy C-Means Method for Statistical Clustering of Data." International Journal of Circuits, Systems and Signal Processing 15 (December 17, 2021): 1766–80. http://dx.doi.org/10.46300/9106.2021.15.191.

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The Fuzzy C-means (FCM) algorithm has been widely used in the field of clustering and classification but has encountered difficulties with noisy data and outliers. Other versions of algorithms related to possibilistic theory have given good results, such as Fuzzy C- Means(FCM), possibilistic C-means (PCM), Fuzzy possibilistic C-means (FPCM) and possibilistic fuzzy C- Means algorithm (PFCM).This last algorithm works effectively in some environments but encountered more shortcomings with noisy databases. To solve this problem, we propose in this manuscript, a new algorithm named Improved Possibilistic Fuzzy C-Means (ImPFCM) by combining the PFCM algorithm with a very powerful statistical method. The properties of this new ImPFCM algorithm show that it is not only applicable on clusters of spherical shapes, but also on clusters of different sizes and densities. The results of the comparative study with very recent algorithms indicate the performance and the superiority of the proposed approach to easily group the datasets in a large-dimensional space and to use not only the Euclidean distance but more sophisticated standards norms, capable to deal with much more complicated problems. On the other hand, we have demonstrated that the ImPFCM algorithm is also capable of detecting the cluster center with high accuracy and performing satisfactorily in multiple environments with noisy data and outliers.

25

Bouzbida, Mohamed, Lassad Hassine, and Abdelkader Chaari. "Robust Kernel Clustering Algorithm for Nonlinear System Identification." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/2427309.

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In engineering field, it is necessary to know the model of the real nonlinear systems to ensure its control and supervision; in this context, fuzzy modeling and especially the Takagi-Sugeno fuzzy model has drawn the attention of several researchers in recent decades owing to their potential to approximate nonlinear behavior. To identify the parameters of Takagi-Sugeno fuzzy model several clustering algorithms are developed such as the Fuzzy C-Means (FCM) algorithm, Possibilistic C-Means (PCM) algorithm, and Possibilistic Fuzzy C-Means (PFCM) algorithm. This paper presents a new clustering algorithm for Takagi-Sugeno fuzzy model identification. Our proposed algorithm called Robust Kernel Possibilistic Fuzzy C-Means (RKPFCM) algorithm is an extension of the PFCM algorithm based on kernel method, where the Euclidean distance used the robust hyper tangent kernel function. The proposed algorithm can solve the nonlinear separable problems found by FCM, PCM, and PFCM algorithms. Then an optimization method using the Particle Swarm Optimization (PSO) method combined with the RKPFCM algorithm is presented to overcome the convergence to a local minimum of the objective function. Finally, validation results of examples are given to demonstrate the effectiveness, practicality, and robustness of our proposed algorithm in stochastic environment.

26

Hamasuna, Yukihiro, Yasunori Endo, and Sadaaki Miyamoto. "On tolerant fuzzy c-means clustering and tolerant possibilistic clustering." Soft Computing 14, no. 5 (June 3, 2009): 487–94. http://dx.doi.org/10.1007/s00500-009-0451-z.

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27

Chen, Jiashun, Hao Zhang, Dechang Pi, Mehmed Kantardzic, Qi Yin, and Xin Liu. "A Weight Possibilistic Fuzzy C-Means Clustering Algorithm." Scientific Programming 2021 (June 10, 2021): 1–10. http://dx.doi.org/10.1155/2021/9965813.

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Fuzzy C-means (FCM) is an important clustering algorithm with broad applications such as retail market data analysis, network monitoring, web usage mining, and stock market prediction. Especially, parameters in FCM have influence on clustering results. However, a lot of FCM algorithm did not solve the problem, that is, how to set parameters. In this study, we present a kind of method for computing parameters values according to role of parameters in the clustering process. New parameters are assigned to membership and typicality so as to modify objective function, on the basis of which Lagrange equation is constructed and iterative equation of membership is acquired, so does the typicality and center equation. At last, a new possibilistic fuzzy C-means based on the weight parameter algorithm (WPFCM) was proposed. In order to test the efficiency of the algorithm, some experiments on different datasets are conducted to compare WPFCM with FCM, possibilistic C-means (PCM), and possibilistic fuzzy C-means (PFCM). Experimental results show that iterative times of WPFCM are less than FCM about 25% and PFCM about 65% on dataset X12. Resubstitution errors of WPFCM are less than FCM about 19% and PCM about 74% and PFCM about 10% on the IRIS dataset.

28

Ismail, Mohamed Maher Ben, Sara N. Alfaraj, and Ouiem Bchir. "Automatic Image Annotation using Possibilistic Clustering Algorithm." INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGENT SYSTEMS 19, no. 4 (December 31, 2019): 250–62. http://dx.doi.org/10.5391/ijfis.2019.19.4.250.

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29

Yu, Hong, and Hu Luo. "A novel possibilistic fuzzy leader clustering algorithm." International Journal of Hybrid Intelligent Systems 8, no. 1 (March 18, 2011): 31–40. http://dx.doi.org/10.3233/his-2011-0129.

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30

Škrjanc, Igor, and Dejan Dovžan. "Evolving Gustafson-kessel Possibilistic c-Means Clustering." Procedia Computer Science 53 (2015): 191–98. http://dx.doi.org/10.1016/j.procs.2015.07.294.

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31

Tang, Yiming, Xianghui Hu, Witold Pedrycz, and Xiaocheng Song. "Possibilistic fuzzy clustering with high-density viewpoint." Neurocomputing 329 (February 2019): 407–23. http://dx.doi.org/10.1016/j.neucom.2018.11.007.

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32

Hu, Yating, Chuncheng Zuo, Fuheng Qu, and Weili Shi. "Unsupervised Possibilistic Clustering Based on Kernel Methods." Physics Procedia 25 (2012): 1084–90. http://dx.doi.org/10.1016/j.phpro.2012.03.203.

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33

Barni, M., V. Cappellini, and A. Mecocci. "Comments on "A possibilistic approach to clustering"." IEEE Transactions on Fuzzy Systems 4, no. 3 (August 1996): 393–96. http://dx.doi.org/10.1109/91.531780.

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34

Chaudhuri, Arindam. "Intuitionistic Fuzzy Possibilistic C Means Clustering Algorithms." Advances in Fuzzy Systems 2015 (2015): 1–17. http://dx.doi.org/10.1155/2015/238237.

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Анотація:

Intuitionistic fuzzy sets (IFSs) provide mathematical framework based on fuzzy sets to describe vagueness in data. It finds interesting and promising applications in different domains. Here, we develop an intuitionistic fuzzy possibilistic C means (IFPCM) algorithm to cluster IFSs by hybridizing concepts of FPCM, IFSs, and distance measures. IFPCM resolves inherent problems encountered with information regarding membership values of objects to each cluster by generalizing membership and nonmembership with hesitancy degree. The algorithm is extended for clustering interval valued intuitionistic fuzzy sets (IVIFSs) leading to interval valued intuitionistic fuzzy possibilistic C means (IVIFPCM). The clustering algorithm has membership and nonmembership degrees as intervals. Information regarding membership and typicality degrees of samples to all clusters is given by algorithm. The experiments are performed on both real and simulated datasets. It generates valuable information and produces overlapped clusters with different membership degrees. It takes into account inherent uncertainty in information captured by IFSs. Some advantages of algorithms are simplicity, flexibility, and low computational complexity. The algorithm is evaluated through cluster validity measures. The clustering accuracy of algorithm is investigated by classification datasets with labeled patterns. The algorithm maintains appreciable performance compared to other methods in terms of pureness ratio.

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Pal, N. R., K. Pal, J. M. Keller, and J. C. Bezdek. "A possibilistic fuzzy c-means clustering algorithm." IEEE Transactions on Fuzzy Systems 13, no. 4 (August 2005): 517–30. http://dx.doi.org/10.1109/tfuzz.2004.840099.

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36

Tsaipei Wang. "Possibilistic Shell Clustering of Template-Based Shapes." IEEE Transactions on Fuzzy Systems 17, no. 4 (August 2009): 777–93. http://dx.doi.org/10.1109/tfuzz.2008.924360.

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37

Yang, Miin-Shen, and Chien-Yo Lai. "A Robust Automatic Merging Possibilistic Clustering Method." IEEE Transactions on Fuzzy Systems 19, no. 1 (February 2011): 26–41. http://dx.doi.org/10.1109/tfuzz.2010.2077640.

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38

Yu, Haiyan, and Jiulun Fan. "Cutset-type possibilistic c-means clustering algorithm." Applied Soft Computing 64 (March 2018): 401–22. http://dx.doi.org/10.1016/j.asoc.2017.12.024.

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39

Coppi, Renato, Pierpaolo D’Urso, and Paolo Giordani. "Fuzzy and possibilistic clustering for fuzzy data." Computational Statistics & Data Analysis 56, no. 4 (April 2012): 915–27. http://dx.doi.org/10.1016/j.csda.2010.09.013.

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40

Hu, Ya Ting, Fu Heng Qu, Yao Hong Xue, and Yong Yang. "An Efficient and Robust Kernelized Possibilistic C-Means Clustering Algorithm." Advanced Materials Research 962-965 (June 2014): 2881–85. http://dx.doi.org/10.4028/www.scientific.net/amr.962-965.2881.

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To avoid the initialization sensitivity and low computational efficiency problems of the kernelized possibilistic c-means clustering algorithm (KPCM), a new clustering algorithm called efficient and robust kernelized possibilistic c-means clustering algorithm (ERKPCM) was proposed in this paper. ERKPCM improved KPCM by two ways. First, the data are refined by the data reduction technique, which makes it keep the data structure of the original data and have higher efficiency. Secondly, weighted clustering algorithm is executed several times to estimate cluster centers accurately, which makes it more robust to initializations and get more reasonable partitions. As a by-product, ERKPCM overcomes the problem of generating coincident clusters of KPCM. The contrast experimental results with conventional algorithms show that ERKPCM is more robust to initializations, and has a relatively high precision and efficiency.

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Hamasuna, Yukihiro, and Yasunori Endo. "On Cluster Extraction from Relational Data UsingL1-Regularized Possibilistic Assignment Prototype Algorithm." Journal of Advanced Computational Intelligence and Intelligent Informatics 19, no. 1 (January 20, 2015): 23–28. http://dx.doi.org/10.20965/jaciii.2015.p0023.

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This paper proposes entropy-basedL1-regularized possibilistic clustering and a method of sequential cluster extraction from relational data.Sequential cluster extractionmeans that the algorithm extracts cluster one by one. The assignment prototype algorithmis a typical clustering method for relational data. The membership degree of each object to each cluster is calculated directly from dissimilarities between objects. An entropy-basedL1-regularized possibilistic assignment prototype algorithm is proposed first to induce belongingness for a membership grade. An algorithm of sequential cluster extraction based on the proposed method is constructed and the effectiveness of the proposed methods is shown through numerical examples.

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Miyamoto, Sadaaki. "Formulation of Fuzzyc-Means Clustering Using Calculus of Variations and Twofold Membership Clusters." Journal of Advanced Computational Intelligence and Intelligent Informatics 12, no. 5 (September 20, 2008): 454–60. http://dx.doi.org/10.20965/jaciii.2008.p0454.

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A membership matrix of fuzzyc-means clustering is associated with corresponding fuzzy classification rules as membership functions defined on the whole data space. We directly derive such functions in fuzzyc-means and possibilistic clustering using the calculus of variations, generalizing ordinary fuzzyc-means and deriving new twofold membership clustering using this framework.

43

Gu, Yuxin, Tongguang Ni, and Yizhang Jiang. "Deep Possibilistic C -means Clustering Algorithm on Medical Datasets." Computational and Mathematical Methods in Medicine 2022 (April 16, 2022): 1–10. http://dx.doi.org/10.1155/2022/3469979.

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In the past, the possibilistic C -means clustering algorithm (PCM) has proven its superiority on various medical datasets by overcoming the unstable clustering effect caused by both the hard division of traditional hard clustering models and the susceptibility of fuzzy C -means clustering algorithm (FCM) to noise. However, with the deep integration and development of the Internet of Things (IoT) as well as big data with the medical field, the width and height of medical datasets are growing bigger and bigger. In the face of high-dimensional and giant complex datasets, it is challenging for the PCM algorithm based on machine learning to extract valuable features from thousands of dimensions, which increases the computational complexity and useless time consumption and makes it difficult to avoid the quality problem of clustering. To this end, this paper proposes a deep possibilistic C -mean clustering algorithm (DPCM) that combines the traditional PCM algorithm with a special deep network called autoencoder. Taking advantage of the fact that the autoencoder can minimize the reconstruction loss and the PCM uses soft affiliation to facilitate gradient descent, DPCM allows deep neural networks and PCM’s clustering centers to be optimized at the same time, so that it effectively improves the clustering efficiency and accuracy. Experiments on medical datasets with various dimensions demonstrate that this method has a better effect than traditional clustering methods, besides being able to overcome the interference of noise better.

44

Wu, Xiao Hong, Bin Wu, and Jie Wen Zhao. "Improved Inter-Cluster Separation Algorithm." Key Engineering Materials 439-440 (June 2010): 361–66. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.361.

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The inter-cluster separation (ICS) algorithm adds the separation item into the objective function to minimize the fuzzy Euclidean distance and maximize the inter-cluster separation. However, ICS is sensitive to noisy data, so an improved inter-cluster separation (IICS) algorithm is proposed to deal with this problem. It is claimed that IICS is an incorporation of ICS and improved possibilistic c-means (IPCM) clustering. IICS can produce both possibilities and memberships simultaneously, and it overcomes the noise sensitivity problem of ICS and the coincident clusters problem of possibilistic c-means (PCM) clustering. Further, IICS does not depend on the parameters that exist in IPCM. The experimental results show that IICS compares favorably with ICS.

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Thiyagarajan, V. S., and Venkatachalapathy Venkatachalapathy. "Privacy Preserving Probabilistic Possibilistic Fuzzy C Means Clustering." Research Journal of Applied Sciences, Engineering and Technology 11, no. 1 (September 5, 2015): 27–39. http://dx.doi.org/10.19026/rjaset.11.1672.

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46

A.Viattchenin, Dmitri, and Stanislau Shyrai. "Intuitionistic Heuristic Prototype-based Algorithm of Possibilistic Clustering." Communications on Applied Electronics 1, no. 8 (May 26, 2015): 30–40. http://dx.doi.org/10.5120/cae-1629.

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47

Fadhel, Mohamed, and Adel M. "Selecting Parameters of the Fuzzy Possibilistic Clustering Algorithm." Communications on Applied Electronics 5, no. 10 (September 26, 2016): 42–52. http://dx.doi.org/10.5120/cae2016652389.

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48

Chatzis, Sotirios P., and Gavriil Tsechpenakis. "A possibilistic clustering approach toward generative mixture models." Pattern Recognition 45, no. 5 (May 2012): 1819–25. http://dx.doi.org/10.1016/j.patcog.2011.10.010.

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49

Yang, Miin-Shen, Shou-Jen Chang-Chien, and Yessica Nataliani. "A Fully-Unsupervised Possibilistic C-Means Clustering Algorithm." IEEE Access 6 (2018): 78308–20. http://dx.doi.org/10.1109/access.2018.2884956.

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50

Tjhi, William-Chandra, and Lihui Chen. "Possibilistic fuzzy co-clustering of large document collections." Pattern Recognition 40, no. 12 (December 2007): 3452–66. http://dx.doi.org/10.1016/j.patcog.2007.04.017.

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