改良式懲罰性模糊集群分析法之研究

劉湘川 ； 黃孝雲

《測驗統計年刊》 6期 (1998/12) Pp. 184-218

https://doi.org/10.6773/JRMS.199812.0184

摘要

本研究旨在探討並改進PFCM法，並以改進後之演算法，即IPFCM法，與PFCM法、FCM法及FCM-EM法針對呈二維混合常態分配的資料以電腦語言MATLAB撰寫程式來進行電腦模擬試驗，以比較各方法在多種情況下參數估計精確度及分群正確率上的優劣，希望藉由本研究能對PFCM法及IPFCM法有更深入的了解，並提供研究者在處理有限混合分配問題時，選擇適當集群分析法的依據。結果發現：1.IPFCM法確實改進了PFCM法；2.當資料確實符合混合常態分配且樣本數夠大時，FCM-EM不論在參數的估計度還是分群正確率上，都將是最佳的集群分析法；但如果樣本數不足或是無法確定分配是否完全符合混合常態分配時，IPFCM法都將是四種集群分析法中最佳的一種。所以本研究的建議為：1.若能確知資料的機率分佈且樣本數夠大時，可採用FCM-EM法；2.若無法確知資料的機率分佈或子分配樣本數皆小於30時，則可採用IPFCM法以獲得較佳的參數估計值及分群正確率。

並列摘要

The main purpose of this study is to examine and improve the PFCM method, and compare the improved PFCM method (IPFCM method) with PFCM method, FCM method, as well as FCM-EM method when data density is two-dimensional mixture normal distribution.The major findings are summarized as follows:(Ⅰ)The IPFCM method can indeed improve the PFCM method.(Ⅱ)When the data density fits the two-dimensional mixture normal distribution well and the sample size is large enough, the FCM-EM method is the best method. But if data density doesn't fit the mixture normal distribution well or the sample size is not large enough, the IPFCM method becomes the best choice of all methods.Based on the above conclusion, two suggestions are recommended:(Ⅰ)If the data density is known and the sample size is large enough, FCM-EM method should be adopted.(Ⅱ)If the data density is not certain or the sample size is less than 30, IPFCM method will be a better choice.