群組加權之模糊聚類演算法

Cluster-Weighted Fuzzy Clustering Algorithms

田益誠(Yi-Cheng Tian)

指導教授 ： 楊敏生

中原大學/理學院/應用數學研究所/博士(2015年)

https://doi.org/10.6840/CYCU.2015.00101

摘要

一般來說,模糊聚類是由硬式聚類所擴展而來,在模糊聚類中,FCM是最聞名的模糊聚類方法,到目前為止,有各種FCM衍生的方法,然而,FCM和其衍生的演算法都會受到初始值的影響。在本文中,我們考慮加上一個群組加權項來修正初始值對模糊聚類演算法的影響,首先我們提出所謂群組加權的GFCM,然後我們建構群組加權的FCM, GK和ICS等演算法,最後我們以一些數值的例子和實際資料來比較群組加權的模糊聚類演算法和其它模糊聚類演算法,結果都驗證群組加權的模糊聚類演算法較其它模糊聚類演算法更具有優越性及有效性。

關鍵字

群聚分析 ； 模糊聚類 ； 模糊 c 均值 ； 初始值 ； 群組權重 ； 機率權重

並列摘要

Fuzzy clustering is generally extended from hard clustering based on fuzzy membership partitions. In fuzzy clustering, the fuzzy c-means (FCM) algorithm is the most well-known clustering method. Up to now, there are various generalizations of FCM. However, the FCM algorithm and its generalizations are always affected by initializations. In this paper, we consider a cluster-weighted term with an updating equation to adjust the effects of initializations to fuzzy clustering algorithms. We first propose the so-called cluster-weighted fuzzy clustering of the generalized FCM (GFCM). We then construct the cluster-weighted FCM, cluster-weighted Gustafson and Kessel (GK) and cluster-weighted inter-cluster separation (ICS) algorithms. Some numerical examples are used to compare our cluster-weighted fuzzy clustering with the fuzzy clustering algorithms. We also apply the cluster-weighted fuzzy clustering algorithms to real data sets. The results demonstrate the superiority and usefulness of our proposed cluster-weighted fuzzy clustering methods.

並列關鍵字

Cluster analysis ； Fuzzy clustering ； Fuzzy c-means (FCM) ； Initialization ； Cluster weight ； Probability weight

參考文獻

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