最大熵聚類概似方法

Maximum entropy-type classification likelihood methods

莊景棠(Jing-Tang Juang)

指導教授 ： 楊敏生

中原大學/理學院/應用數學系/碩士(2007年)

https://doi.org/10.6840/cycu200700512

摘要

模糊聚類分析中，模糊C-均值(Fuzzy c-means ; FCM) [5]聚類演算法是最著名且最為廣泛被運用的方法。而在大多的文章中，都是針對模糊C-均值演算法做進一步的推廣；例如：Yang [6] (1993)所提出的一組由模糊類別最大概似程序(FCML)推導出來的刑罰形FCM，稱為PFCM演算法；Wei 和 Fahn [7]提出最大熵(MEC)演算法；以及Wu 和 Yang [8]所提的一組新的指數距離來替換歐式距離，推導出的相對式FCM，稱之AFCM演算法；其皆是利用FCM的概念，去改變距離或擴展加入隸屬度等，來分出更完善的結果。
此篇論文中，我們將探討模糊c-均值(FCM)演算法的推廣。在模糊c-均值(FCM) 之目標函數中，該如何作變化，才能得到較好與較快速的聚類方法，因
此，我們將在模糊c-均值之目標函數中加入了調整項(Regularization)，其調整項是由隸屬度的調整變化得之，根據此項調整原則，我們把模糊c-均值演算法推廣為最大熵演算法。
我們再將所提之最大熵演算法與模糊c-均值及刑罰型模糊c-均值等演算法，針對混合常態分配作參數估計之比數，由數值的模擬比較後，判別此三種演算法的精確性與效率性之優劣情況。

關鍵字

聚類概似方法

並列摘要

In fuzzy cluster analysis , the fuzzy c-means (FCM) clustering algorithm is the best known and most used method. There are many generalized types of FCM. Some of them such as fuzzy classification maximum likelihood (FCML) induce to penalized fuzzy c-means (PFCM) , Maximum entropy classification (MEC) and alternative fuzzy c-means (AFCM) , will be studied in this thesis, then we can get better results.
In this paper , we make the extension of the FCM , based on this class of fuzzy c-means clustering algorithm , we extend them by adding a regularization , the regularization is change by membership , we can derive a generalized type of fuzzy c-means clustering algorithms , called the maximum entropy clustering algorithm (MEC). By doing some numerical examples , for estimating the parameters of the normal mixtures , we find that MEC is more accuracy and effective then PFCM and
FCM.

並列關鍵字

classification likelihood methods

參考文獻

[1] Zadeh, L.A. (1965), Fuzzy sets, Information and Control, 8, 338-353

[2] Bezdek, J.C. (1981), Pattern Recognition with Fuzzy objective Function Algorithms, Plenum press, New York, 1981.

[3] Hoppner, F., Klawonn, R., Kruse R. and Runkler T. (1999), Fuzzy Cluster Analysis Methods for classification Data Analysis and Image Recognition Wiley, New York, 1999.

[4] Yang M.S. (1993), A survey of fuzzy clustering, Mathematical and computer Modeling, vol.18, pp.1-16.

[5] Dunn, J.C. (1974), A fuzzy relative of the ISODADA process and its use in detecting compact, well-separated clusters, Journal of Cybrnetics, 3, 32-57