姓名 |
范文翔(Wen-Hsiang Fan)
查詢紙本館藏 |
畢業系所 |
統計研究所 |
論文名稱 |
一個估計資料群數的新方法 (A new method for estimating the number of clusters)
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相關論文 | |
檔案 |
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摘要(中) |
估計資料群數是群集分析(cluster analysis)中一個重要的問題。在本篇論文中,我們嘗試模型選取中最被普遍使用的貝氏訊息準則(Bayesian information criterion)做為群集問題中選取群數的標準。然而,在資料變數為一維的情況下,我們發現使用BIC會高估資料的真實群數;即使嘗試各種不同的懲罰項,並沒有找到一個有效的一致性訊息準則(consistent information criterion)。因此,本篇論文提出了一個群數估計的新方法,並經由程式模擬說明其估計資料群數的準確性。 |
摘要(英) |
A major problem in cluster analysis is to find the number of clusters. In this paper, we try to use Bayesian information criterion(BIC), a wide-used criterion in model selection problem, as a criterion to estimate the number of clusters. However, we found that the ture number of clusters would be overestimated when using BIC as a criterion in one dimension case. We can not find a consistent information criterion in the problem of number estimation. We propose a new method for estimating the number of clusters and show the currency of the method via simulation study. |
關鍵字(中) |
★ K平均值分群演算法 ★ 訊息準則 |
關鍵字(英) |
★ Information criterion ★ K-means clustering algorithm |
論文目次 |
一、緒論..................................1
1.1 研究背景..............................1
1.2 研究動機..............................2
二、文獻回顧..............................3
2.1 Gap統計量.............................3
2.2 Calinski-Harabasz index...............4
2.3 Krzanowski-Lai index..................5
2.4 Hartigan統計量........................5
三、一致性訊息準則在集群分析上的探討......7
3.1 高估分群群數現象的發生................9
3.2 低估分群群數現象的發生................11
3.3 使用一致性訊息準則估計群數的模擬結果..12
四、估計群數的新方法......................16
4.1 最小變量法............................18
4.2 模擬研究..............................19
五、結論與未來方向........................22
參考文獻..................................23 |
參考文獻 |
[1] Calinski, R. B. and Harabasz, J. A.(1974). A denrite method for cluster analysis. Communications in Statistics 3, 1-27.
[2] Hartigan, J. A.(1975). Clustering Algorithms. Wiley.
[3] Kaufman, L. and Rousseeuw, P.(1990). Finding Groups in Data: An Introduction to Cluster Analysis. New York: Wiley.
[4] Krzanowski, W. J. and Lai, Y. T.(1985). A criterion for determining the number of clusters in a data set. Biometrics 44, 23-34.
[5] Milligan, G. W. and Cooper, M. C.(1985). An examination of procedures for determining the number of clusters in a data set. Psychometrika 50, 159-179
[6] Sugar, Catherine A. and James, Gareth M.(2003). Finding the number of clusters in a data set: An information theoretic approach. Journal of the American Statistical Association 98, 750-763.
[7] Tibshirani, R., Walther, G., and Hastie, T.(2001). Estimating the number of clusters in a data set via the gap statistics. Journal of the Royal Statistical Society, Series B 63, 411-423. |
指導教授 |
銀慶剛(Ching-Kang Ing)
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審核日期 |
2008-7-17 |
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