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題名 階層式分群方法的同質性與穩固性
Homogeneity and Stability of Hierarchical Clustering作者 林韋志
Lin, Wei-Chih貢獻者 周珮婷
Chou, Pei-Ting
林韋志
Lin, Wei-Chih關鍵詞 非監督機器學習
階層式分群
分群驗證
Unsupervised Machine Learning
Hierarchical Clustering
Cluster Validation日期 2021 上傳時間 1-Jul-2021 17:34:21 (UTC+8) 摘要 現今，驗證分群結果較主流的方法是透過計算各種cluster validation index來檢驗，但是這些指數在類別變數很多的資料時卻不一定能得到合理的答案，因此，本研究利用階層式分群對目標變數建立分群樹，對另一變數則利用歐式距離建立分群樹，再根據兩分群樹繪製熱力圖，從熱力圖的顏色區塊找出資料幾何較相關的群體；接著，利用ANOVA的概念模擬原始資料，並以模擬資料的分群編碼繪製信度直方圖，以呈現群體相似度，進一步驗證階層式分群結果的正確性及穩固性；若信度直方圖所呈現的趨勢與原始分群結果符合，則可判斷分群的結果正確；本研究方法與cluster validation index的差異是我們可以依據熱力圖所呈現的資料幾何結構，在分群樹上的不同高度做切割，找出相關性高的群組，提出檢驗階層式分群結果的信度指標。
Nowadays, the most popular method of validating clustering results is to verify through various cluster validation indexes. However, these indexes may not get reasonable answers whenever data with a lot of categorical variables. This study aims to provide a stable method to detect the homogeneity and stability of Hierarchical Clustering (HC). Multiple HC trees based on simulated data are built, and the path to each category in a tree is recorded. Histogram based on the coding path of simulated data is built to validate the reliability and stability of the clustering results from HC. The difference between the proposed method and the common cluster validation indexes is that we can rely on the clustering results presented by the heatmap, cut at different heights on the dendrogram to find reasonable and highly relevant groups, and increase the flexibility of the clustering.參考文獻 一、 中文參考文獻[1] 張順全 (1999) 類別資料結構的訊息視覺化二、 英文參考文獻[1] Balcan, M. F., Liang, Y., & Gupta, P. (2014). Robust hierarchical clustering. The Journal of Machine Learning Research, 15(1), 3831-3871.[2] Ben-Hur, A., Elisseeff, A., & Guyon, I. (2001). A stability based method for discovering structure in clustered data. In Biocomputing 2002 (pp. 6-17).[3] Brock, G., Pihur, V., Datta, S., & Datta, S. (2011). clValid, an R package for cluster validation. Journal of Statistical Software (Brock et al., March 2008).[4] Caliński, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics-theory and Methods, 3(1), 1-27.[5] Carlsson, G. E., & Mémoli, F. (2010). Characterization, stability and convergence of hierarchical clustering methods. J. Mach. Learn. Res., 11(Apr), 1425-1470.[6] Chou, E., McVey, C., Hsieh, Y. C., Enriquez, S., & Hsieh, F. (2020). Extreme-K categorical samples problem. arXiv preprint arXiv:2007.15039.[7] Dunn, J. C. (1974). A graph theoretic analysis of pattern classification via Tamura`s fuzzy relation. IEEE Transactions on Systems, Man, and Cybernetics, (3), 310-313.[8] Dunn, J. C. (1974). Well-separated clusters and optimal fuzzy partitions. Journal of cybernetics, 4(1), 95-104.[9] Fushing, H., & Roy, T. (2018). Complexity of possibly gapped histogram and analysis of histogram. Royal Society open science, 5(2), 171026.[10] Goodman, L. A., & Kruskal, W. H. (1979). Measures of association for cross classifications. Measures of association for cross classifications, 2-34.[11] Rendón, E., Abundez, I., Arizmendi, A., & Quiroz, E. M. (2011). Internal versus external cluster validation indexes. International Journal of computers and communications, 5(1), 27-34.[12] Shannon, C. E. (1948). A mathematical theory of communication. The Bell system technical journal, 27(3), 379-423.[13] Smith, S. P., & Dubes, R. (1980). Stability of a hierarchical clustering. Pattern Recognition, 12(3), 177-187. 描述 碩士
國立政治大學
統計學系
108354027資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108354027 資料類型 thesis dc.contributor.advisor 周珮婷 zh_TW dc.contributor.advisor Chou, Pei-Ting en_US dc.contributor.author (Authors) 林韋志 zh_TW dc.contributor.author (Authors) Lin, Wei-Chih en_US dc.creator (作者) 林韋志 zh_TW dc.creator (作者) Lin, Wei-Chih en_US dc.date (日期) 2021 en_US dc.date.accessioned 1-Jul-2021 17:34:21 (UTC+8) - dc.date.available 1-Jul-2021 17:34:21 (UTC+8) - dc.date.issued (上傳時間) 1-Jul-2021 17:34:21 (UTC+8) - dc.identifier (Other Identifiers) G0108354027 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/135931 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 108354027 zh_TW dc.description.abstract (摘要) 現今，驗證分群結果較主流的方法是透過計算各種cluster validation index來檢驗，但是這些指數在類別變數很多的資料時卻不一定能得到合理的答案，因此，本研究利用階層式分群對目標變數建立分群樹，對另一變數則利用歐式距離建立分群樹，再根據兩分群樹繪製熱力圖，從熱力圖的顏色區塊找出資料幾何較相關的群體；接著，利用ANOVA的概念模擬原始資料，並以模擬資料的分群編碼繪製信度直方圖，以呈現群體相似度，進一步驗證階層式分群結果的正確性及穩固性；若信度直方圖所呈現的趨勢與原始分群結果符合，則可判斷分群的結果正確；本研究方法與cluster validation index的差異是我們可以依據熱力圖所呈現的資料幾何結構，在分群樹上的不同高度做切割，找出相關性高的群組，提出檢驗階層式分群結果的信度指標。 zh_TW dc.description.abstract (摘要) Nowadays, the most popular method of validating clustering results is to verify through various cluster validation indexes. However, these indexes may not get reasonable answers whenever data with a lot of categorical variables. This study aims to provide a stable method to detect the homogeneity and stability of Hierarchical Clustering (HC). Multiple HC trees based on simulated data are built, and the path to each category in a tree is recorded. Histogram based on the coding path of simulated data is built to validate the reliability and stability of the clustering results from HC. The difference between the proposed method and the common cluster validation indexes is that we can rely on the clustering results presented by the heatmap, cut at different heights on the dendrogram to find reasonable and highly relevant groups, and increase the flexibility of the clustering. en_US dc.description.tableofcontents 目次第一章 緒論 1第二章 文獻探討 3第三章 研究方法 6第一節 極端T類別型資料問題之資料結構 6第二節 資料訊息內容及分群距離計算 7第三節 進階分群距離計算及HC樹 9第四節 分群結果評估 10第四章 研究過程與結果 13一、交通部觀光局觀光市場調查各國來台入境旅客目的統計資料集 13二、NBA 2019-2020 players shooting dataset 18三、政大各系外籍生資料集 25四、Kaggle電商女裝部統計資料集 29第五章 結論與建議 33第六章 參考文獻 34表次表3-1 資料結構範例 17表4-1 世界各國來台階層式分群 Cluster validation index 17表4-2 NBA球員階層式分群 Cluster validation index 23表4-3 政大各系階層式分群 Cluster validation index 28表4-4 電商各部門階層式分群 Cluster validation index 32圖次圖3-1 國家編碼範例 10圖3-2 分群驗證方法示意圖 12圖4-1 世界各國來台階層式分群圖 13圖4-2 世界各國來台目的歐式距離分群圖 14圖4-3 各國來台目的比例熱力圖 14圖4-4 A組模擬分群結果 15圖4-5 B組模擬分群結果 15圖4-6 C組模擬分群結果 16圖4-7 D組模擬分群結果 16圖4-8 E組模擬分群結果 16圖4-9 19-20賽季NBA球員階層式分群圖 – 左半邊 18圖4-10 19-20賽季NBA球員階層式分群圖 - 右半邊 19圖4-11 19-20賽季NBA球員出手型態歐式距離分群圖 19圖4-12 NBA球員出手比例熱力圖 20圖4-13 A組模擬分群結果 21圖4-14 B組模擬分群結果 21圖4-15 C組模擬分群結果 21圖4-16 D組模擬分群結果 22圖4-17 E組模擬分群結果 22圖4-18 F組模擬分群結果 22圖4-19 G組模擬分群結果 23圖4-20 H組模擬分群結果 23圖4-21 政大各系所階層式分群圖 25圖4-22 政大外籍生國籍歐式距離分群圖 25圖4-23 國立政治大學各系外籍生比例熱力圖 26圖4-24 A組模擬分群結果 27圖4-25 B組模擬分群結果 27圖4-26 C組模擬分群結果 28圖4-27 D組模擬分群結果 28圖4-28 各部門階層式分群圖 29圖4-29 顧客評分歐式距離分群圖 30圖4-30 電商女裝部評分比例熱力圖 30圖4-31 A組模擬分群結果 31圖4-32 B組模擬分群結果 31 zh_TW dc.format.extent 1947826 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108354027 en_US dc.subject (關鍵詞) 非監督機器學習 zh_TW dc.subject (關鍵詞) 階層式分群 zh_TW dc.subject (關鍵詞) 分群驗證 zh_TW dc.subject (關鍵詞) Unsupervised Machine Learning en_US dc.subject (關鍵詞) Hierarchical Clustering en_US dc.subject (關鍵詞) Cluster Validation en_US dc.title (題名) 階層式分群方法的同質性與穩固性 zh_TW dc.title (題名) Homogeneity and Stability of Hierarchical Clustering en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) 一、 中文參考文獻[1] 張順全 (1999) 類別資料結構的訊息視覺化二、 英文參考文獻[1] Balcan, M. F., Liang, Y., & Gupta, P. (2014). Robust hierarchical clustering. The Journal of Machine Learning Research, 15(1), 3831-3871.[2] Ben-Hur, A., Elisseeff, A., & Guyon, I. (2001). A stability based method for discovering structure in clustered data. In Biocomputing 2002 (pp. 6-17).[3] Brock, G., Pihur, V., Datta, S., & Datta, S. (2011). clValid, an R package for cluster validation. Journal of Statistical Software (Brock et al., March 2008).[4] Caliński, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics-theory and Methods, 3(1), 1-27.[5] Carlsson, G. E., & Mémoli, F. (2010). Characterization, stability and convergence of hierarchical clustering methods. J. Mach. Learn. Res., 11(Apr), 1425-1470.[6] Chou, E., McVey, C., Hsieh, Y. C., Enriquez, S., & Hsieh, F. (2020). Extreme-K categorical samples problem. arXiv preprint arXiv:2007.15039.[7] Dunn, J. C. (1974). A graph theoretic analysis of pattern classification via Tamura`s fuzzy relation. IEEE Transactions on Systems, Man, and Cybernetics, (3), 310-313.[8] Dunn, J. C. (1974). Well-separated clusters and optimal fuzzy partitions. Journal of cybernetics, 4(1), 95-104.[9] Fushing, H., & Roy, T. (2018). Complexity of possibly gapped histogram and analysis of histogram. Royal Society open science, 5(2), 171026.[10] Goodman, L. A., & Kruskal, W. H. (1979). Measures of association for cross classifications. Measures of association for cross classifications, 2-34.[11] Rendón, E., Abundez, I., Arizmendi, A., & Quiroz, E. M. (2011). Internal versus external cluster validation indexes. International Journal of computers and communications, 5(1), 27-34.[12] Shannon, C. E. (1948). A mathematical theory of communication. The Bell system technical journal, 27(3), 379-423.[13] Smith, S. P., & Dubes, R. (1980). Stability of a hierarchical clustering. Pattern Recognition, 12(3), 177-187. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202100611 en_US
