使用壓縮的模糊C-均數演算法估計混合型常態分配之參數
中文摘要
模糊c-均數演算法（fuzzy c-means, FCM）於模糊聚類分析中
是為人所熟知且被廣泛使用的群集方法。於Wu and Yang（2002）中，
提出新的距離測度，並在c-均數聚類演算法中取代歐幾里得距離度
量，發展出AFCM演算法。本篇亦提及另一新距離度量，應用於c-均
數聚類演算法中，稱為CFCM演算法。兩者皆為FCM演算法的推廣。
此外，為了改善FCM演算法收斂之速度，Fan et al.（2003）亦發表
了壓縮的模糊c-均數演算法（suppressed fuzzy c-means, S-FCM）。
本篇論文，將提出新的壓縮參數於S-FCM演算法，稱為修正的壓
縮模糊c-均數演算法（modify S-FCM, MS-FCM），此想法是基於群與
群之間的分離強度。把S-FCM演算法及MS-FCM演算法分別應用於AFCM
演算法與CFCM演算法中，並結合12種資料型態，對混合型常態分配
作參數之估計。其結果將列表比較，並以參數估計結果之均方差（mean
squared error, MSE）及平均迭代次數（average number of iteration, NI）作比較的依據。
由結果發現，於三種不同的演算法中（S-FCM演算法、S-AFCM演
算法與S-CFCM演算法），加入提出的新壓縮參數後，由於更適用於不
同的資料型態，因此，對參數估計之精確性與效率性兩方面均有良好
表現的趨勢。

Using Suppressed FCM Algorithm to Estimate
Parameters of Normal Distribution
Abstract
The fuzzy c-means clustering algorithm（FCM algorithm）
is the well known and most powerful method used in cluster
analysis. Wu and Yan （2002）proposed a new metric to replace
the Euclidean metric in the c-means clustering algorithm, and
developed an alternative fuzzy c-means algorithm called AFCM
algorithm. In this paper, we also propose another new metric
and apply in the c-means clustering algorithm, which is called
the Cauchy fuzzy c-means algorithm（CFCM algorithm）.Both
algorithms are the extension of fuzzy c-means algorithm.
Additionally, intent to improve the convergent speed of the FCM
algorithm, Fan et al（2003）also proposed the suppressed fuzzy
c-means（S-FCM）.
In this paper, we also propose a new suppressed parameter
in S-FCM algorithm, which is called modified S-FCM（MS-FCM）,
the idea is based on the strength given by . We apply
S-FCM algorithm and MS-FCM algorithm in AFCM algorithm and CFCM
algorithm individually, and combine these algorithms with
twelve data types, then estimate parameters of mixed normal
distribution. To compare with results, we list them in the
tables, and use the comparisons criterion of mean squared error
and average number of iteration.
By the result, we find that the accuracy and efficiency of
parameter of estimation have good performance in the S-FCM
algorithm, S-AFCM algorithm and S-CFCM algorithm because the
proposed new parameter is suitable for different data types.

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