Dynamic evidential clustering algorithm

Abstract In this paper, a dynamic evidential clustering algorithm (DEC) is introduced to address the computational burden of existing methods. To derive such a solution, an FCM-like objective function is first employed and minimized to obtain the support levels of the real singletons (specific) clusters to which the query objects belong, and then the query objects isinitially adaptively assigned to outlier, precise or imprecise one via a new rule-based on the conflicts between the different support levels. For each imprecise object, it is finally reassigned to the singleton clusters or related meta-cluster by partial credal redistribution with the corresponding dynamic edited framework to reduce the computational burden. The proposed method can reduce the complexity to the level similar to that of the fuzzy and possibilistic clustering, which can effectively extend the application of evidential clustering, especially in big data. The effectiveness of the DEC method is tested by four experiments with artificial and real datasets.

[1]  Anil K. Jain Data clustering: 50 years beyond K-means , 2010, Pattern Recognit. Lett..

[2]  Thierry Denoeux,et al.  Decision-Making with Belief Functions: a Review , 2018, Int. J. Approx. Reason..

[3]  Bibhas C. Giri,et al.  Developing a closed-loop supply chain model with price and quality dependent demand and learning in production in a stochastic environment , 2018, International Journal of Systems Science: Operations & Logistics.

[4]  Quan Pan,et al.  ECMdd: Evidential c-medoids clustering with multiple prototypes , 2016, Pattern Recognit..

[5]  Seyed Ashkan Hoseini Shekarabi,et al.  An integrated stochastic EPQ model under quality and green policies: generalised cross decomposition under the separability approach , 2019, International Journal of Systems Science: Operations & Logistics.

[6]  Xinyang Deng,et al.  Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory , 2017, Int. J. Intell. Syst..

[7]  Xiangzhi Bai,et al.  Similarity Measure-Based Possibilistic FCM With Label Information for Brain MRI Segmentation , 2019, IEEE Transactions on Cybernetics.

[8]  Yi Yang,et al.  Belief Interval-Based Distance Measures in the Theory of Belief Functions , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[9]  Yu Liu,et al.  Evidence Combination Based on Credal Belief Redistribution for Pattern Classification , 2020, IEEE Transactions on Fuzzy Systems.

[10]  Bay Vo,et al.  F-Mapper: A Fuzzy Mapper clustering algorithm , 2020, Knowl. Based Syst..

[11]  Quan Pan,et al.  Median evidential c-means algorithm and its application to community detection , 2015, Knowl. Based Syst..

[12]  Jiye Liang,et al.  The $K$-Means-Type Algorithms Versus Imbalanced Data Distributions , 2012, IEEE Transactions on Fuzzy Systems.

[13]  Chunfeng Lian,et al.  Joint Tumor Segmentation in PET-CT Images Using Co-Clustering and Fusion Based on Belief Functions , 2019, IEEE Transactions on Image Processing.

[14]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[15]  Jian-Bo Yang,et al.  Data classification using evidence reasoning rule , 2017, Knowl. Based Syst..

[16]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[17]  Jean Dezert,et al.  Combination of Classifiers With Different Frames of Discernment Based on Belief Functions , 2021, IEEE Transactions on Fuzzy Systems.

[18]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[19]  Rajesh N. Davé,et al.  Characterization and detection of noise in clustering , 1991, Pattern Recognit. Lett..

[20]  B. Giri,et al.  Coordinating a supply chain with backup supplier through buyback contract under supply disruption and uncertain demand , 2014 .

[21]  Thierry Denoeux,et al.  BPEC: Belief-Peaks Evidential Clustering , 2019, IEEE Transactions on Fuzzy Systems.

[22]  James C. Bezdek,et al.  A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  Philippe Smets,et al.  The Combination of Evidence in the Transferable Belief Model , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[24]  Thierry Denoeux,et al.  Evidential clustering of large dissimilarity data , 2016, Knowl. Based Syst..

[25]  S. Sen,et al.  Clustering of relational data containing noise and outliers , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[26]  Thierry Denoeux A k -Nearest Neighbor Classification Rule Based on Dempster-Shafer Theory , 2008, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[27]  Yong Deng,et al.  A Matrix Method of Basic Belief Assignment's Negation in Dempster–Shafer Theory , 2020, IEEE Transactions on Fuzzy Systems.

[28]  Thierry Denoeux,et al.  ECM: An evidential version of the fuzzy c , 2008, Pattern Recognit..

[29]  Jean Dezert,et al.  Credal c-means clustering method based on belief functions , 2015, Knowl. Based Syst..

[30]  Thierry Denoeux,et al.  A k-nearest neighbor classification rule based on Dempster-Shafer theory , 1995, IEEE Trans. Syst. Man Cybern..

[31]  Anjali Awasthi,et al.  A goal-oriented approach based on fuzzy axiomatic design for sustainable mobility project selection , 2019 .

[32]  Philippe Smets,et al.  Decision making in the TBM: the necessity of the pignistic transformation , 2005, Int. J. Approx. Reason..

[33]  Seyed Taghi Akhavan Niaki,et al.  Optimization of a multiproduct economic production quantity problem with stochastic constraints using sequential quadratic programming , 2015, Knowl. Based Syst..

[34]  Seyed Ashkan Hoseini Shekarabi,et al.  Modelling And optimal lot-sizing of the replenishments in constrained, multi-product and bi-objective EPQ models with defective products: Generalised Cross Decomposition , 2020, International Journal of Systems Science: Operations & Logistics.

[35]  Thierry Denoeux,et al.  Combination of Transferable Classification With Multisource Domain Adaptation Based on Evidential Reasoning , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[36]  Masoud Rabbani,et al.  A hybrid robust possibilistic approach for a sustainable supply chain location-allocation network design , 2018, International Journal of Systems Science: Operations & Logistics.

[37]  Songsak Sriboonchitta,et al.  Evaluating and Comparing Soft Partitions: An Approach Based on Dempster–Shafer Theory , 2018, IEEE Transactions on Fuzzy Systems.

[38]  James M. Keller,et al.  A possibilistic fuzzy c-means clustering algorithm , 2005, IEEE Transactions on Fuzzy Systems.

[39]  Mauro Barni,et al.  Comments on "A possibilistic approach to clustering" , 1996, IEEE Trans. Fuzzy Syst..

[40]  Miin-Shen Yang,et al.  A Feature-Reduction Fuzzy Clustering Algorithm Based on Feature-Weighted Entropy , 2018, IEEE Transactions on Fuzzy Systems.

[41]  Thierry Denoeux,et al.  k-CEVCLUS: Constrained evidential clustering of large dissimilarity data , 2017, Knowl. Based Syst..

[42]  Thierry Denoeux,et al.  Clustering interval-valued proximity data using belief functions , 2004, Pattern Recognit. Lett..

[43]  Thierry Denoeux,et al.  EVCLUS: evidential clustering of proximity data , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[44]  Yi Yang,et al.  A new distance-based total uncertainty measure in the theory of belief functions , 2016, Knowl. Based Syst..