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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/108118
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dc.contributor.advisor蔡炎龍zh_TW
dc.contributor.advisorTsai, Yen Lungen_US
dc.contributor.author陳名秀zh_TW
dc.contributor.authorChen, Ming Hsiuen_US
dc.creator陳名秀zh_TW
dc.creatorChen, Ming Hsiuen_US
dc.date2016en_US
dc.date.accessioned2017-04-05T07:36:35Z-
dc.date.available2017-04-05T07:36:35Z-
dc.date.issued2017-04-05T07:36:35Z-
dc.identifierG0103751005en_US
dc.identifier.urihttp://nccur.lib.nccu.edu.tw/handle/140.119/108118-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學系zh_TW
dc.description103751005zh_TW
dc.description.abstract霍奇排名是在近幾年才運用在排名的一種方法。在大多數現在的資料庫 中,資料庫很龐大,有些甚至會需要網路連結,而且很多會有資料不完整或 是資料不平衡的狀況。我們選擇用霍奇排名這種排名方法來處理可能會遇到 的這些困擾。\n這篇論文主要目的是想用運用基本的線性代數來研究霍奇排名和推導組合霍奇理論。zh_TW
dc.description.abstractHodgeRank is a method of ranking that is new in recent years. In most of modern datasets, the amount of data is very large, some also need the internet connection, and plenty of them have the feature that incomplete or imbalanced. We use the method of HodgeRank to deal with these difficulties.\nThis thesis is primary using elementary linear algebra to survey HodgeRank and deduce the combinatorial Hodge Theorem.en_US
dc.description.tableofcontents1 Introduction......................................... 1\n2 Pairwise Ranking .................................... 4\n2.1 PairwiseRankingProblems............................ 4\n2.2 IntroductiontoHodgeRank............................ 4\n2.3 PossibleApplicationsofPairwiseRankings ............ 6\n2.3.1 RankingStudentsinaClass ......................... 6\n2.3.2 MovieRecommendationSystems ...................... 7 \n2.3.3 RankingSportsTeam................................ 7\n2.4 PairwiseRankingfromVoting ......................... 8\n2.5 ProblemsofPairwiseRanking ......................... 8\n3 Background .......................................... 9\n3.1 SomeSimpleFactsinLinearAlgebra .................... 9 \n3.2 TheFirstIsomorphismTheorem ....................... 13\n4 Combinatorial Hodge Theory ......................... 16\n4.1 CochainComplex.................................... 16 \n4.2 CombinatorialHodgeTheory.......................... 17 \n4.3 Application ...................................... 20\n5 Combinatorial Hodge Theory on Graphs ............... 22\n5.1 GraphsandFunctionsonGraphs........................ 22 \n5.2 Matrices.......................................... 32 \n5.3 InnerProduct ..................................... 33 \n5.4 FindtheGlobalRanking ............................. 35 \n5.5 ApplyingCombinatorialHodgeTheory ................. 35 \n5.6 PracticalExample.................................. 36\n6 Conclusion ......................................... 40\nBibliography.......................................... 41zh_TW
dc.format.extent384611 bytes-
dc.format.mimetypeapplication/pdf-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G0103751005en_US
dc.subject霍奇理論zh_TW
dc.subject霍奇排名zh_TW
dc.subject組合霍奇理論zh_TW
dc.subjectHodgeRanken_US
dc.subjectCombinatorial Hodge theoremen_US
dc.subjectOmbinatorial Hodge decompositionen_US
dc.title霍奇排名之理論分析zh_TW
dc.titleTheoretic Aspect of HodgeRanken_US
dc.typethesisen_US
dc.relation.reference[1] Kenneth J. Arrow. A difficulty in the concept of social welfare. Journal of Political Economy, 58(4):328–346, 1950.\n[2] Ralph Allan Bradley and Milton E. Terry. Rank analysis of incomplete block designs. I. The method of paired comparisons. Biometrika, 39:324–345, 1952.\n[3] Corinna Cortes, Mehryar Mohri, and Ashish Rastogi. Magnitude-preserving ranking algo- rithms. In Proceedings of the 24th International Conference on Machine Learning, ICML ’07, pages 169–176, New York, NY, USA, 2007. ACM.\n[4] H. A. David. The method of paired comparisons, volume 41 of Griffin’s Statistical Mono- graphs & Courses. Charles Griffin & Co., Ltd., London; The Clarendon Press, Oxford University Press, New York, second edition, 1988.\n[5] Dorit S. Hochbaum and Asaf Levin. Methodologies and algorithms for group-rankings decision. Manage. Sci., 52(9):1394–1408, September 2006.\n[6] Xiaoye Jiang, Lek-Heng Lim, Yuan Yao, and Yinyu Ye. Statistical ranking and combina- torial Hodge theory. Math. Program., 127(1, Ser. B):203–244, 2011.\n[7]M.G.KendallandB.BabingtonSmith.Onthemethodofpairedcomparisons.Biometrika, 31:324–345, 1940.\n[8] George Miller. The magical number seven, plus or minus two: Some limits on our capacity for processing information, 1956. One of the 100 most influential papers in cognitive science: http://cogsci.umn.edu/millennium/final.html\n[9] Frederick Mosteller. Remarks on the method of paired comparisons: I. the least squares solution assuming equal standard deviations and equal correlations. Psychometrika, 16(1): 3–9, 1951.\n[10] Frederick Mosteller. Remarks on the method of paired comparisons: Ii. the effect of an aberrant standard deviation when equal standard deviations and equal correlations are as- sumed. Psychometrika, 16(2):203–206, 1951.\n[11] Frederick Mosteller. Remarks on the method of paired comparisons: Iii. a test of signif- icance for paired comparisons when equal standard deviations and equal correlations are assumed. Psychometrika, 16(2):207–218, 1951.\n[12] Gottfried E. Noether. Remarks about a paired comparison model. Psychometrika, 25:357– 367, 1960.\n[13] Donald G. Saari and Vincent R. Merlin. A geometric examination of Kemeny’s rule. Soc. Choice Welf., 17(3):403–438, 2000.\n[14] Thomas L. Saaty. A scaling method for priorities in hierarchical structures. J. Mathemat- ical Psychology, 15(3):234–281, 1977.\n[15] Claire Voisin. Hodge theory and complex algebraic geometry. I, volume 76 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, english edi- tion, 2007. Translated from the French by Leila Schneps.\n[16]ClaireVoisin.Hodgetheoryandcomplexalgebraicgeometry.II,volume77ofCambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, english edi- tion, 2007. Translated from the French by Leila Schneps.\n[17] Douglas B. West. Introduction to graph theory. Prentice Hall, Inc., Upper Saddle River, NJ, 1996.zh_TW
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