ファジィクラスタリングとファジィクラスタリングモデル
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| Published in | 知能と情報 Vol. 31; no. 3; pp. 75 - 81 |
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| Main Author | |
| Format | Journal Article |
| Language | Japanese |
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日本知能情報ファジィ学会
15.06.2019
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| Online Access | Get full text |
| ISSN | 1347-7986 1881-7203 |
| DOI | 10.3156/jsoft.31.3_75 |
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| Author | 佐藤, 美佳 |
|---|---|
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| Copyright | 2019 日本知能情報ファジィ学会 |
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| DOI | 10.3156/jsoft.31.3_75 |
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| Discipline | Engineering Mathematics |
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| EndPage | 81 |
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| PublicationTitle | 知能と情報 |
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| References | [12] M. J. Sabin: “Convergence and Consistency of Fuzzy c-means/ISODATA Algorithms,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-9, No.5, pp. 661-668, 1987. [27] M. Sato, Y. Sato, and L. C. Jain: Fuzzy Clustering Models and Applications, Springer, 1997. [32] M. Sato-Ilic, S. Ito and S. Takahashi: “Nonlinear Kernel-Based Fuzzy Clustering Model,” Developments in Fuzzy Clustering, VEVER, pp. 56-73, 2009. [21] I. Gath and A. B. Geva: “Unsupervised Optimal Fuzzy Clustering,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-11, No.7, pp. 773-781, 1989. [24] P. Arabie and J. D. Carroll: “MAPCLUS: A Mathematical Programming Approach to Fitting the ADCLUS Model,” Psychometrica, Vol.45, pp. 211-235, 1980. [31] B. Schweizer and A. Sklar: Probabilistic Metric Spaces, Dover Publications, 2005. [38] L. Ai-Ping, J. Yan, and W. Quan-Yuan: “Harmonic Triangular Norm Aggregation Operators in Multicriteria Decision Systems,” J. of Convergence Information Technology, Vol.2, No.1, pp. 83-92, 2007. [35] R. M. Tardiff: “Topologies for Probabilistic Metric Spaces,” Pacific J. of Mathematics, Vol.65, No.1, pp. 233-251, 1976. [23] R. N. Shepard and P. Arabie: “Additive Clustering: Representation of Similarities as Combinations of Discrete Overlapping Properties,” Psychological Review, Vol.86, No.2, pp. 87-123, 1979. [13] L. A. Zadeh: “Similarity Relations and Fuzzy Orderings,” Inform. Sci., Vol.3, pp. 177-200, 1971. [17] A. Kandel and L. Yelowitz: “Fuzzy Chains,” IEEE Trans. Syst., Man, Cybern., SMC-4, No.5, pp. 472-475, 1974. [6] J. C. Dunn: “A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Comppact Well-Separated Clusters,” J. Cybernetics, Vol.3, No.3, pp. 32-57, 1973. [41] F. Klawonn, R. Kruse and R. Winkler: “Fuzzy Clustering: More than just Fuzzification,” Fuzzy Sets and Systems, Vol.281, pp. 272-279, 2015. [29] K. Menger: “Statistical Metrics,” Proc. Nat. Acad. of Sci., Vol.28, pp. 535-537, 1942. [4] I. Gitman and M. D. Levine: “An Algorithm for Detecting Unimodal Fuzzy Sets and Its Application as a Clustering Technique,” IEEE Trans. Comput., C-19, No.7, pp. 583-593, 1965. [11] J. C. Bezdek, R. J. Hathaway, M. J. Sabin, and W. T. Tucker: “Convergence Theory for Fuzzy c-Means: Counterexamples and Repairs,” IEEE Trans. Syst., Man, Cybern., SMC-17, No.5, pp. 873-877, 1987. [16] S. Warshall: “A Theorem on Boolean Matrices,” J. Ass. Comput. Math., Vol.9, pp. 11-12, 1962. [5] D. Wishart: “An Algorithm for Hierarchical Classifications,” Biometrics, Vol.25, No.1, pp. 165-170, 1969. [33] J. Shawe-Taylor and N. Cristianini: Kernel Methods for Pattern Analysis, Cambridge University Press, 2004. [42] G. Peters: “Is There Any Need for Rough Clustering?,” Pattern Recognition Letters, Vol.53, pp. 31-37, 2015. [8] M. Roubens: “Pattern Classification Problems and Fuzzy Sets,” Fuzzy Sets and Systems, Vol.1, pp. 239-253, 1978. [15] J. C. Dunn and A Graph: “Theoretic Anallysis of Pattern Classification via Tamura’s Fuzzy Relation,” IEEE Trans. Syst., Man, Cybern., SMC-4, No.3, pp. 310-313, 1974. [19] M. P. Windham: “Cluster Validity for the Fuzzy c-Means Clustering Algorithm,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-4, No.4, pp. 357-363, 1982. [20] E. Backer and A. K. Jain: “A Clustering Performance Measure Based on Fuzzy Set Decomposition,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-3, No.1, pp. 66-75, 1981. [28] M. Sato and Y. Sato: “On a General Fuzzy Additive Clustering Model,” Int. J. of Intelligent Automation and Soft Computing, Vol.1, No.4, pp. 439-448, 1995. [44] A. Babaeian and M. Babaee: “A. Bayestehtashk, M. Bandarabadi,” Nonlinear Subspace Clustering using Curvature Constrained Distances, Pattern Recogn. Lett., Vol.68, No.1, pp. 118-125, 2015. [18] J. C. Bezdek and J. D. Harris: “Fuzzy Partitions and Relations; An Axiomatic Basis for Clustering,” Fuzzy Sets and Systems, Vol.1, pp. 111-127, 1978. [45] A. Király, Á, Vathy-Fogarassy, and J. Abonyi: “Geodesic Distance based Fuzzy c-Medoid Clustering – Searching for Central Points in Graphs and High Dimensional Data,” Fuzzy Sets Syst., Vol.286, pp. 157-172, 2016. [39] J. M. Merigo and M. Casanovas: “Fuzzy Generalized Hybrid Aggregation Operators and its Application in Fuzzy Decision Making,” Int. J. of Fuzzy Systems, Vol.12, No.1, pp. 15-24, 2010. [22] X. L. Xie and G. Beni: “A Validity Measure for Fuzzy Clustering,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-13, No.8, pp. 841-847, 1991. [25] W. S. Desarbo: “GENNCLUS: New Models for General Nonhierarchical Clustering Analysis,” Psychometrica, Vol.47, pp. 449-475, 1982. [30] E. P. Klement, R. Mesiar and E. Pap: Triangular Norms, Kluwer Academic Publications, 2000. [37] G. Beliakov: “How to Build Aggregation Operators from Data,” Int. J. of Intelligent Systems, Vol.18, pp. 903-923, 2003. [40] F. Klawonn: “Exploring Data Sets for Clusters and Validating Single Clusters,” Procedia Computer Science, Vol.96, pp. 1381-1390, 2016. [3] E. H. Ruspini: “A New Approach to Clustering,” Inform. Control., Vol.15, No.1, pp. 22-32, 1969. [26] 佐藤美佳, 佐藤義治: “加法的ファジィクラスタリングモデル,” 日本ファジィ学会誌, Vol.6, No.2, pp. 319-332, 1994. [10] J. C. Bezdek: “A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-2, No.1, pp. 1-8, 1980. [1] L. A. Zadeh: “Fuzzy Sets,” Inform. Control., Vol.8, pp. 338-353, 1965. [9] D. E. Gustafson and W. C. Kessel: “Fuzzy Clustering with a Fuzzy Covariance Matrix,” Proc. IEEE CDC, pp. 761-766, 1979. [36] R. M. Tardiff: “On a Functional Inequality Arising in the Construction of the Product of Several Metric Spaces,” Aequationes Mathematicae, Vol.20, pp. 51-58, 1980. [14] S. Tamura, S. Higuchi, and K. Tanaka: “Pattern Classification Based on Fuzzy Relations,” IEEE Trans. Syst., Man, Cybern., SMC-1, No.1, pp. 61-66, 1971. [7] J. C. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, 1981. [2] L. A. Zadeh: “Outline of a New Approach to the Analysis of Complex Systems and Decision Processes,” IEEE Trans. Syst., Man, Cybern., SMC-3, No.1, pp. 28-44, 1973. [34] M. Sato-Ilic: “Generalized Aggregation Operator based Nonlinear Fuzzy Clustering Model,” Intelligent Engineering Systems through Artificial Neural Networks, Vol.20, pp. 493-500, 2010. [43] D. Ienco and G. Bordogna: “Fuzzy Extensions of the DBScan Clustering Algorithm,” Soft Comput., Vol.22, pp. 1719-1730, 2018. |
| References_xml | – reference: [7] J. C. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, 1981. – reference: [3] E. H. Ruspini: “A New Approach to Clustering,” Inform. Control., Vol.15, No.1, pp. 22-32, 1969. – reference: [8] M. Roubens: “Pattern Classification Problems and Fuzzy Sets,” Fuzzy Sets and Systems, Vol.1, pp. 239-253, 1978. – reference: [10] J. C. Bezdek: “A Convergence Theorem for the Fuzzy ISODATA Clustering Algorithms,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-2, No.1, pp. 1-8, 1980. – reference: [32] M. Sato-Ilic, S. Ito and S. Takahashi: “Nonlinear Kernel-Based Fuzzy Clustering Model,” Developments in Fuzzy Clustering, VEVER, pp. 56-73, 2009. – reference: [15] J. C. Dunn and A Graph: “Theoretic Anallysis of Pattern Classification via Tamura’s Fuzzy Relation,” IEEE Trans. Syst., Man, Cybern., SMC-4, No.3, pp. 310-313, 1974. – reference: [4] I. Gitman and M. D. Levine: “An Algorithm for Detecting Unimodal Fuzzy Sets and Its Application as a Clustering Technique,” IEEE Trans. Comput., C-19, No.7, pp. 583-593, 1965. – reference: [40] F. Klawonn: “Exploring Data Sets for Clusters and Validating Single Clusters,” Procedia Computer Science, Vol.96, pp. 1381-1390, 2016. – reference: [44] A. Babaeian and M. Babaee: “A. Bayestehtashk, M. Bandarabadi,” Nonlinear Subspace Clustering using Curvature Constrained Distances, Pattern Recogn. Lett., Vol.68, No.1, pp. 118-125, 2015. – reference: [12] M. J. Sabin: “Convergence and Consistency of Fuzzy c-means/ISODATA Algorithms,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-9, No.5, pp. 661-668, 1987. – reference: [34] M. Sato-Ilic: “Generalized Aggregation Operator based Nonlinear Fuzzy Clustering Model,” Intelligent Engineering Systems through Artificial Neural Networks, Vol.20, pp. 493-500, 2010. – reference: [41] F. Klawonn, R. Kruse and R. Winkler: “Fuzzy Clustering: More than just Fuzzification,” Fuzzy Sets and Systems, Vol.281, pp. 272-279, 2015. – reference: [43] D. Ienco and G. Bordogna: “Fuzzy Extensions of the DBScan Clustering Algorithm,” Soft Comput., Vol.22, pp. 1719-1730, 2018. – reference: [22] X. L. Xie and G. Beni: “A Validity Measure for Fuzzy Clustering,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-13, No.8, pp. 841-847, 1991. – reference: [24] P. Arabie and J. D. Carroll: “MAPCLUS: A Mathematical Programming Approach to Fitting the ADCLUS Model,” Psychometrica, Vol.45, pp. 211-235, 1980. – reference: [39] J. M. Merigo and M. Casanovas: “Fuzzy Generalized Hybrid Aggregation Operators and its Application in Fuzzy Decision Making,” Int. J. of Fuzzy Systems, Vol.12, No.1, pp. 15-24, 2010. – reference: [5] D. Wishart: “An Algorithm for Hierarchical Classifications,” Biometrics, Vol.25, No.1, pp. 165-170, 1969. – reference: [16] S. Warshall: “A Theorem on Boolean Matrices,” J. Ass. Comput. Math., Vol.9, pp. 11-12, 1962. – reference: [29] K. Menger: “Statistical Metrics,” Proc. Nat. Acad. of Sci., Vol.28, pp. 535-537, 1942. – reference: [1] L. A. Zadeh: “Fuzzy Sets,” Inform. Control., Vol.8, pp. 338-353, 1965. – reference: [17] A. Kandel and L. Yelowitz: “Fuzzy Chains,” IEEE Trans. Syst., Man, Cybern., SMC-4, No.5, pp. 472-475, 1974. – reference: [42] G. Peters: “Is There Any Need for Rough Clustering?,” Pattern Recognition Letters, Vol.53, pp. 31-37, 2015. – reference: [11] J. C. Bezdek, R. J. Hathaway, M. J. Sabin, and W. T. Tucker: “Convergence Theory for Fuzzy c-Means: Counterexamples and Repairs,” IEEE Trans. Syst., Man, Cybern., SMC-17, No.5, pp. 873-877, 1987. – reference: [35] R. M. Tardiff: “Topologies for Probabilistic Metric Spaces,” Pacific J. of Mathematics, Vol.65, No.1, pp. 233-251, 1976. – reference: [20] E. Backer and A. K. Jain: “A Clustering Performance Measure Based on Fuzzy Set Decomposition,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-3, No.1, pp. 66-75, 1981. – reference: [31] B. Schweizer and A. Sklar: Probabilistic Metric Spaces, Dover Publications, 2005. – reference: [25] W. S. Desarbo: “GENNCLUS: New Models for General Nonhierarchical Clustering Analysis,” Psychometrica, Vol.47, pp. 449-475, 1982. – reference: [26] 佐藤美佳, 佐藤義治: “加法的ファジィクラスタリングモデル,” 日本ファジィ学会誌, Vol.6, No.2, pp. 319-332, 1994. – reference: [36] R. M. Tardiff: “On a Functional Inequality Arising in the Construction of the Product of Several Metric Spaces,” Aequationes Mathematicae, Vol.20, pp. 51-58, 1980. – reference: [37] G. Beliakov: “How to Build Aggregation Operators from Data,” Int. J. of Intelligent Systems, Vol.18, pp. 903-923, 2003. – reference: [23] R. N. Shepard and P. Arabie: “Additive Clustering: Representation of Similarities as Combinations of Discrete Overlapping Properties,” Psychological Review, Vol.86, No.2, pp. 87-123, 1979. – reference: [6] J. C. Dunn: “A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Comppact Well-Separated Clusters,” J. Cybernetics, Vol.3, No.3, pp. 32-57, 1973. – reference: [13] L. A. Zadeh: “Similarity Relations and Fuzzy Orderings,” Inform. Sci., Vol.3, pp. 177-200, 1971. – reference: [19] M. P. Windham: “Cluster Validity for the Fuzzy c-Means Clustering Algorithm,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-4, No.4, pp. 357-363, 1982. – reference: [21] I. Gath and A. B. Geva: “Unsupervised Optimal Fuzzy Clustering,” IEEE Trans. Pattern Anal. Machine Intell., PAMI-11, No.7, pp. 773-781, 1989. – reference: [33] J. Shawe-Taylor and N. Cristianini: Kernel Methods for Pattern Analysis, Cambridge University Press, 2004. – reference: [9] D. E. Gustafson and W. C. Kessel: “Fuzzy Clustering with a Fuzzy Covariance Matrix,” Proc. IEEE CDC, pp. 761-766, 1979. – reference: [18] J. C. Bezdek and J. D. Harris: “Fuzzy Partitions and Relations; An Axiomatic Basis for Clustering,” Fuzzy Sets and Systems, Vol.1, pp. 111-127, 1978. – reference: [30] E. P. Klement, R. Mesiar and E. Pap: Triangular Norms, Kluwer Academic Publications, 2000. – reference: [2] L. A. Zadeh: “Outline of a New Approach to the Analysis of Complex Systems and Decision Processes,” IEEE Trans. Syst., Man, Cybern., SMC-3, No.1, pp. 28-44, 1973. – reference: [27] M. Sato, Y. Sato, and L. C. Jain: Fuzzy Clustering Models and Applications, Springer, 1997. – reference: [28] M. Sato and Y. Sato: “On a General Fuzzy Additive Clustering Model,” Int. J. of Intelligent Automation and Soft Computing, Vol.1, No.4, pp. 439-448, 1995. – reference: [14] S. Tamura, S. Higuchi, and K. Tanaka: “Pattern Classification Based on Fuzzy Relations,” IEEE Trans. Syst., Man, Cybern., SMC-1, No.1, pp. 61-66, 1971. – reference: [45] A. Király, Á, Vathy-Fogarassy, and J. Abonyi: “Geodesic Distance based Fuzzy c-Medoid Clustering – Searching for Central Points in Graphs and High Dimensional Data,” Fuzzy Sets Syst., Vol.286, pp. 157-172, 2016. – reference: [38] L. Ai-Ping, J. Yan, and W. Quan-Yuan: “Harmonic Triangular Norm Aggregation Operators in Multicriteria Decision Systems,” J. of Convergence Information Technology, Vol.2, No.1, pp. 83-92, 2007. |
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