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研究生： 方茜
Fang, Qian
論文名稱： 有初始值篩選的核函數K中心聚類法
Kernel K Medoids Algorithm with Selected Initial Values
指導教授： 溫敏杰
Wen, Miin-Jye
學位類別： 碩士
Master
系所名稱： 管理學院 - 統計學系
Department of Statistics
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 36
中文關鍵詞： 核函數 、K-中心點 、初始值
外文關鍵詞： Kernel function, K medoids, Initialization
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    • 本研究所提出的聚類方法將高斯核函數與 k-中心聚類法結合起來,與此同時,還 加入了利用變量 Vj (Park and Jun, 2009) 來對資料進行排序並篩選出 r 個中間值作為 我們的初始中心點。初始值的篩選讓聚類分析過程更加高效,而高斯核函數的加 入可以讓我們的聚類方法比較不容易受異常值和干擾數據的影響。為了評估我們 所提出來的方法,我們分析了一些真實數據,合成數據以及關聯數據,並用 ARI (Adjusted Rand Index), F1 score 和 MSE (Mean Squared Error) 這些指標進行結果評估, 將其與 k-平均值 (k means) 聚類法,k 中心點 (k medoids) 聚類法的分群評估結果進行 比較。評估結果顯示,本文所提出的分群方法與 k 平均值 (k means) 聚類法,k-中心 點 (kmedoids) 聚類法相比,有更好的分群效果。

    This study proposes a clustering algorithm that combine gaussian kernel function with k medoids clustering algorithm. In the meanwhile, we use a variable called Vj (Park and Jun, 2009) to rank objects and select the r middle values as our initial centers. The selection of initial values makes the clustering process more efficient, and the combination of gaussian kernel function makes the clustering outcome more resistant to outliers or noises. To evaluate the proposed algorithm, we analyze some real, synthetic and relational datasets and compar- ing with the results of other algorithms in terms of the Adjusted Rand Index, F1 score and Mean Squared Error. The outcomes show that our proposed algorithm having better cluster- ing performance over the other mentioned algorithms (k means, k medoids) in this study.

    摘要 i Abstract ii 致謝 iii Table of Contents iv List of Tables vi List of Figures vii Chapter 1. Introduction 1 Chapter 2. Background 3 K Means Algorithm and KMedoidsAlgorithm . . . . . . . . . . . . . . . . . 3 . K means .................................. 3 . K medoids................................. 5 Kernel Function.................................. 6 Initialization.................................... 8 RelationalData .................................. 9 Different Dissimilarity Measures......................... 9 . Distance-based dissimilarity measures................... 9 . Correlation-based dissimilarity measures . . . . . . . . . . . . . . . . . 11 Chapter 3. Kernel k medoids algorithm with selected initial values 13 TheProposedMethod............................... 13 SensitivityCurve ................................. 15 Chapter 4. Numerical Experiments 18 Measures of Results................................ 18 . Adjusted rand index ............................ 18 . F1 score................................... 18 . Mean squared error............................. 19 Conventional Data ................................ 19 . Data description .............................. 19 . Clustering outcomes ............................ 19 Synthetic Data................................... 20 . Synthetic data formed by skewed distributions . . . . . . . . . . . . . . 20 . Synthetic data with outlier or noise .................... 22 RelationalData .................................. 24 Chapter 5. Conclusion 26 Bibliography 27

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