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研究生:郭獻駿
研究生(外文):Hsien-Chun Kuo
論文名稱:區間資料的聚類演算法
論文名稱(外文):A clustering method for interval data
指導教授:楊敏生楊敏生引用關係
指導教授(外文):Miin-Shen Yang
學位類別:碩士
校院名稱:中原大學
系所名稱:應用數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:33
中文關鍵詞:最佳群集個數SCM區間資料
外文關鍵詞:the best number of clustersinterval dataSCM
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在模糊聚類方法的領域中,根據資料型態的不同有不同的聚類方法。聚類演算法主要目的是能將給定資料做分群,因此我們提出的聚類演算法是利用Yang and Wu 在2004提出的聚類演算法(SCM)上作延伸,針對區間型資料透過目標函數來求得最佳群組區間代表及最佳群集個數,為了確立此法為好的聚類演算法,我們執行了一些抽樣模擬的資料跟驗證過的實例,結果顯示出區間資料能透過此演算法有好的分類效果。


In fuzzy clustering for different data types, there are many different clustering methods. The main purpose of clustering algorithms is for clustering a given data set. In this thesis, we propose a clustering algorithm by extending Yang and Wu’s clustering algorithm, called SCM, such that it can handle interval data sets with the best representative of the group range and also the best number of clusters. In order to demonstrate this method as a good clustering algorithm, we perform some simulations with sampling data and also some real data sets. The results show that a range of information through this algorithm has good clustering results.


Chapter1.Introduction---------------------------------------------1
Chapter2.A clustering method for interval data--------------------3
2-1.Clustering Method and Its Objective Function------------------3
2-2.Correlation comparison algorithm for interval data------------5
2-3.The Clustering Algorithm for Interval Data--------------------6
Chapter3.Simulation data------------------------------------------8
Chapter4.Real data applications----------------------------------16
4-1. Experiment 1 Fat and Oils-----------------------------------16
4-2. Experiment 2 Cities Temperature-----------------------------18
Chapter5.Conclusions---------------------------------------------22
REFERENCES-------------------------------------------------------27

Fig.1 The flowchart for the proposed clustering method ISCM for interval Data -------7
Fig.2 Seed data sets show respectively equivalent size-----------------9
Fig.3 Interval data set span by γ_1 and γ_2 from Uniform(1,8)----------9
Fig.4 Clustering results-----------------------------------------------9
Fig.5 The Hierarchical Clustering tree--------------------------------10
Fig.6 Seed data sets, overlapping case -------------------------------10
Fig.7 Interval data set, overlapping case-----------------------------11
Fig.8 The result for overlapping case --------------------------------11
Fig.9 The Hierarchical Clustering tree--------------------------------11
Fig.10 Seed data sets, compare method---------------------------------12
Fig.11 Interval data set, compare method -----------------------------12
Fig.12 The result for ISCM interval data algorithm--------------------13
Fig.13 The Hierarchical Clustering tree-------------------------------13
Fig.14 IFCM for interval data: # of cluster = 2,3,4,5-----------------14
Fig.15 Add 50 data points and extend to interval data----------------15
Fig.16 The classification results IFCM with # of cluster center 3,,4,5-----15
Fig.17 The clusters results ISCM and the Hierarchical Clustering tree -----17
Fig.18 The Hierarchical Clustering tree on Fat and Oil data set------------18
Fig.19 The Hierarchical Clustering tree on the cities temperature ---------20
Fig.20 Location map 37 cities----------------------------------------------25

Table 1 Fat and Oils-------------------------------------------------------17
Table 2 Results------------------------------------------------------------18
Table 3-1 Results from ISCM for i.v, # of cluster=3----------------------- 18
Table 3-2 Results from ISCM for i.v,# of cluster=4-------------------------18
Table 4 Latitude and Longitude For Each Cities-----------------------------22
Table.5-1 cities temperature-----------------------------------------------23
Table.5-2 cities temperature-----------------------------------------------24

[1]L.A. Zadeh, “Fuzzy sets,” Information and Control, Vol. 8, pp. 338-353, 1965.
[2]R.M.C.R. de Souza, F.D.A.T. de Carvalho, “Clustering of interval data based on city–block distances,” Pattern Recognition Letters, Vol. 25, pp.353-365, 2004.
[3]D.S. Guru, B.B. Kiranagi, P. Nagabhushan, ”Multivalued type proximity measure and concept of mutual similarity value useful for clustering symbolic patterns," Pattern Recognition Letters, Vol. 25, pp.1203-1213, 2004.
[4]F.D.A.T. de Carvalho, P. Brito and H.H. Bock, ”Dynamic Clustering for Interval Data Based on L2 Distance,” Computational Statistics, Vol. 21, pp. 231-250, 2006.
[5]P. D'Urso and P. Giordani, ”A robust fuzzy k-means clustering model for interval valued data,” Computational Statistics, Vol. 21, pp.251-269, 2006.
[6]M. Chavent, F.D.A.T. de Carvalho, Y. Lechevallier, R. Verde, ”New clustering methods for interval data,” Computational Statistics, Vol. 21, pp.211-229, 2006.
[7]F.D. A.T. de Carvalho, ”Fuzzy c-means clustering methods for symbolic interval,” Pattern Recognition Letters, Vol. 28, pp. 423–437, 2007.
[8]F.D. A.T. de Carvalho, Y. Lechevallier, ”Dynamic clustering of interval-valued data based on adaptive quadratic distances,” IEEE Trans. on Systems, Man, Cyber.–Part A, Vol. 39, pp.1295-1305, 2009.
[9]F.D. A.T. de Carvalho, C.P. Tenório, ”Fuzzy k-means clustering algorithms for interval-valued data based on adaptive quadratic distances,” Fuzzy Sets and Systems, Vol. 161, pp.2978 –2999, 2010.
[10]M.S. Yang, K.L. Wu, ”A similarity-based robust clustering method,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 26, pp434-448, 2004.
[11]Fig. 20 Location map for 37 cities from http://texina.net/world_map_dzb.gif

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