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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/103903


    Title: 數學規劃在叢聚分析上的應用研究
    Authors: 江振東
    Contributors: 李子壩
    江振東
    Date: 1984
    Issue Date: 2016-11-14 14:56:37 (UTC+8)
    Abstract: 第一章 緒論1
    1 . 1 引言1
    1 . 2 叢聚分析要素3
    1 . 3 問題描述5
    1 . 4 ( C-WGSS ) 模式述由7
    1 . 5 ( C-CM ) 模式初探14
    1 . 6 符號定義15
    第二章 數學規劃與叢聚分析的關係17
    2 . 1 叢聚完全列舉法17
    2 . 2 一般叢聚分析方法舉例：m-中位數演算法則17
    2 . 3 數學規劃與叢聚分析模式間的關聯性20
    第三章 分支定限法與叢聚分析22
    3 . 1 分支定限法概述22
    3 . 2 ( C-WGSS ) 模式問題24
    3 . 2 . 1 問題描述24
    3 . 2 . 2 預備理論25
    3 . 2 . 3 下界設定36
    3 . 2 . 4 分支演算法則49
    3 . 2 . 5 簡例分析53
    3 . 3 ( C-CM ) 模式問題60
    3 . 3 . 1 問題描述60
    3 . 3 . 2 演算法則60
    3 . 3 . 3 簡例分析65
    第四章 次梯度最佳化法與叢聚分析71
    4 . 1 次梯度最佳化法概述71
    4 . 2 ( C-CM) 模式問題 - 一般化情形76
    4 . 2 . 1 模式設定76
    4 . 2 . 2 演算法則84
    4 . 3 ( C-WG SS ) 模式問題 - 一度空間情形93
    4 . 3 . 1 問題描述 93
    4 . 3 . 2 應用模式推演95
    第五章 動態規劃法與叢聚分析103
    5 . 1 動態規劃法概述103
    5 . 2 ( C-WG SS ) 模式問題 - 一度空間情形105
    5 . 3 ( C-WG SS ) 模式問題 - 一般化情形111
    5 . 3 . 1 分配型式定義111
    5 . 3 . 2 模型描述115
    5 . 3 . 3 TFA 推導116
    5 . 3 . 4 NAT 推導121
    5 . 3 . 5 簡例分析130
    第六章 次梯度最佳化法模擬分析134
    6 . 1 分析目的134
    6 . 2 分析方法134
    6 . 3 結果分析137
    結語153
    參考書目155
    Reference: 1.林邦傑著，「集群分析及其應用」，教育與心理研究4期，台北：國立政治大學出版，民國七十年：頁31-57。
    2. Anderberg, M. R. ( 1973 ). Cluster Analysis for Applications. Academic Press, New York.
    3. Arthanari, T. S. and Dodge Y. ( 1981 ). Mathematical Programming in Statistics. Wiley, New York.
    4. Chatfield, C. and Collins, A. J. ( 1980 ) Introduction to Multivariate Analysis. Chapman and Hall, London“”
    5. Cox, D. R. ( 1957 ). “ Note on Grouping ”. J. Am. Stat. Assoc. 52, 543.
    6. Duran, B. S. and Odell, P. L. ( 1974 ).“Cluster Analysis : A Survey. ” In Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, New York.
    7. Everitt, B. S. ( 1974 ). Cluster Analysis. Halstead Press, London.
    8. Fisher, W. D. ( 1958 ). “ On Grouping for Maximum Homogenity. ” J. Am. Stat. Assoc. 53, 789.
    9. Geoffrion, A. M. ( 1974 ). “ Lagrangian Relaxation in Integer Programming. ” Math. Program. Stud. 2, 82.
    10. Hartigan, J. A. (1975). Clustering Algorithm. Wiley, New York.
    11. Held, M. and Karp, R. M. (1970 ) “ The Traveling Salesman Problem and Minimum Spanning Trees.” Operations Res. 18, 1138.
    12. Held, M., Wolfe, P. , and Crowder, H. ( 1974 ). “Validation of Subgradient Optimization. ” Math. Program. 6, 62.
    13. Hillier, F. S. and Lieberman G. J. ( 1980 ). Introduction to Operations Research. Holden-Day, Inc., San Francisco.
    14. Jarvinen, P., Rajala, J. and Sinervo, H. (1972) “A Branch and Bound Algorithm for Seeking the p-Median. ” Operations Res. 20, 173.
    15. Jensen, R. E. ( 1969 ). “ A Dynamic Programming Algorithm for Cluster Analysis. ” Operations Res. 17, 1034.
    16. Johnson, R. A. and Wichern D. W. ( 1982 ). Applied Multivariate Statistical Analysis. Prentice-Hall, Inc., Englewood Cliffs.
    17. Mulvey, J. M. and Crowder, H. P. ( 1979 ). “Cluster Analysis : An Application of Lagrangian Relaxation. ” Manage. Sci 25, 329
    18. Rao, M. R. (1971 ). “ Cluster Analysis and Mathematical Programming. ” J. Am. Stat. Assoc. 66, 622.
    19. Shapiro J. F. ( 1979 ). Mathematical Programming : Structure and Algorithms. Wiley, New York.
    20. Spath, H. (1980 ). Cluster Analysis Algorithm. Halsted Press, Chichester.
    21. Vinod, H. D.( 1969 ). “ Integer Programming and Theory of Grouping. ” J. Am. Stat. Assoc. 64, 506.
    22. Ward, J. H. Jr. ( 1963 ). “ Hierarchical Grouping to Optimize an Objective Function. ” J. Am. Stat. Assoc. 58, 236.
    Relation: 國立政治大學
    統計研究所
    碩士
    72
    Data Type: thesis
    Appears in Collections:[Department of Statistics] Theses

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