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博碩士論文 etd-0725106-184751 詳細資訊
Title page for etd-0725106-184751
論文名稱
Title
核心式的模糊群聚演算法及其在分類的應用
A kernel-based fuzzy clustering algorithm and its application in classification
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
61
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2006-07-10
繳交日期
Date of Submission
2006-07-25
關鍵字
Keywords
分類、核心函數、模糊群聚
kernel function, fuzzy clustering, classification
統計
Statistics
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中文摘要
在本篇論文中,我們提出核心式的模糊群聚演算法在特徵空間來解決分群問題。我們使用核心函數將資料從原來的資料空間投射到一個高維度的特徵空間,然後在特徵空間上用漸進式模糊群聚演算法將資料依相似度做分群。我們的方法能將原本資料空間中不歸則形狀的群聚轉換到特徵空間中的球體,在結束時能夠在原本的資料空間中將不規則的群聚表現出來。更進一步,我們將它運用在分類問題上,除了相似度計算還加入警戒測試和容錯功能,警戒測試是比對新資料和該群聚的類別是否相同。容錯功能在使用者允許下,可以將相似度夠高卻非同類的資料和群聚加以合併。在高維度的特徵空間中,資料之間的同異性會增強,可以在資料分佈中找到複雜的內部結構。在預測未知資料點的類別上,會有較佳的能力。
在群聚實驗中除了和在原本資料空間運作的自建構式法則比較,還有多球體的支援向量群聚比較,而分類實驗中會和決策樹做比較,來驗證我們方法的效能。
Abstract
In this paper, we purpose a kernel-based fuzzy clustering algorithm to cluster data patterns in the feature space. Our method uses kernel functions to project data from the original space into a high dimensional feature space, and data are divided into groups though their similarities in the feature space with an incremental clustering approach. After clustering, data patterns of the same cluster in the feature space are then grouped with an arbitrarily shaped boundary in the original space. As a result, clusters with arbitrary shapes are discovered in the original space. Clustering, which can be taken as unsupervised classification, has also been utilized in resolving classification problems. So, we extend our method to process the classification problems. By working in the high dimensional feature space where the data are expected to more separable, we can discover the inner structure of the data distribution. Therefore, our method has the advantage of dealing with new incoming data pattern efficiently. The effectiveness of our method is demonstrated in the experiment.
目次 Table of Contents
摘要 i
Abstract ii
圖目錄 v
表目錄 vii

第一章 簡介 1
1.1 研究動機 2
1.2 我們方法 3
1.3 論文架構 4

第二章 相關研究 5
2.1 自建構式法則 5
2.2 核心方法 9
2.3 支援向量群聚 11
2.4 多球體的支援向量群聚 17

第三章 研究方法 24
3.1 核心式的模糊群聚 24
3.2 應用於分類上的核心式群聚演算法 29

第四章 實驗 34
4.1 實驗一 和SCRG在效果上的比較 34
4.2 實驗二 和多球體支援向量群聚演算法的比較 39
4.3 實驗三 和決策樹的比較 41
4.3.1 人工資料集 42
4.3.2 鳶尾花資料集 43
4.3.3 葡萄酒資料集 45

第五章 結論 48

參考文獻 49

附錄1 — 公式推導 51
參考文獻 References
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[6] V. Vapnik, The Nature of Statistical Learning Theory, New York: Springer Verlag, 1995.
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[8] K.-R. Muller, S. Mika, G. Ratsch, K. Tsuda, and B. Scholkopf, “An introduction to kernel-based learning algorithms,” IEEE Transactions on Neural Networks, vol. 12, no. 2, pp. 181-201, March 2001.
[9] R. T. Ng and J. Han, “CLARANS: A Method for Clustering Objects for Spatial Data Mining,” IEEE Transactions on Knowledge and Data Engineering, vol. 14, no. 5, pp. 1003-1015, 2002.
[10] J. Sander, M. Ester, H. P. Kriegel, and X. Xu, “Density Based Clustering in Spatial Database: The Algorithm GDBSCAN and its Application,” Data Mining and Knowledge Discovery, vol. 3, no. 3, pp. 169-194, 1998.
[11] A. Ben-Hur, H. T. Siegelmann, and V. N. Vapnik, “A Support Vector Clustering Method,” Proceeding of International Conference on Pattern Recognition, vol. 2, pp. 728-732, Barcelona, Spain, 2000.
[12] A. Ben-Hur, H. T. Siegelmann, and V. N. Vapnik, “Support Vector Clustering, ” Journal of Machine Learning Research, vol. 2, pp. 125-137, 2001.
[13] F. Camastra and A. Verri, “A Novel Kernel Method for Clustering,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 5, pp. 801-805, 2005.
[14] J. H. Chiang and P. Y. Hao, “A New Kernel-Based Fuzzy Clustering Approach: Support Vector Clustering With Cell Growing,” IEEE Transactions on Fuzzy System, vol. 11, no. 4, pp. 518-527, 2003.
[15] C. L. Blake and C. J. Merz, “UCI repository of machine learning database,” http://www.ics.uci.edu/~mlearn/MLRepository.html, 1998.
[16] C. C. Chang and C. J. Lin, “A library for support vector machines,” http://www.csie.ntu.edu.tw/~cjlin/libsvm/, 2001.
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