張少同Chang, Shao-Tung蔡宗穎Cai, Zong-Ying2023-12-089999-12-312023-12-082022https://etds.lib.ntnu.edu.tw/thesis/detail/9ae568ef804aecf622d7e99c8a595cea/http://rportal.lib.ntnu.edu.tw/handle/20.500.12235/121087在聚類的問題中圖形的邊緣識別是我們感興趣的議題，我們回顧了以往的文獻並注意到模糊c殼(Fuzzy C-Shells/FCS)聚類可以用於該領域，FCS是模糊c均值(Fuzzy C-means/FCM)的一種變體，與FCM不同的是FCS考慮的是資料與殼的距離而不是簇中心，這樣的改變可以使得FCS有邊緣辨識的能力，而FCS依據一開始所選的不同形狀的殼而有許多衍生的演算法，但這些演算法都是基於一開始給定的殼形進行聚類，這使得在實際運用上有它的侷限性。因此，我們提出了一種即使在不給定殼形的情況下也能運行的殼聚類演算法，我們通過調整半徑參數來構建FCS中目標函數與非線性回歸(Non-linear Regression)之間的關係，這種方式令我們可以在迭代過程中逐漸確定殼的形狀，這樣的方法比其他殼形聚類演算法更加靈活，且不需要隨著一開始給定的殼形而改變演算法，最後我們用模擬和實際數據證明了該方法的有效性。The edge recognition of graphs in the problem of clustering is of interest to us. From our reviewed literature, we noticed that fuzzy c-shells (FCS) clustering can be used for this problem. FCS is a variant of fuzzy c-means (FCM). Unlike FCM, FCS considers the distance between the data and the ‘shell’ rather than the cluster center. This change allows FCS to have edge recognition capabilities. There are many derivations of the FCS algorithm depending on the chosen shells. These algorithms are clustered based on a given specific shell shape. However, sub-clusters may have different shapes in the real problems of clustering. Subsequently, these algorithms are limited in reality.Therefore, we propose a method for shell clustering requiring no knowledge of the shell. We construct a relationship between the objective function of the FCS and the non-linear regression by adjusting the radius parameter. Such an approach allows the shape of the shell to be determined gradually during the process of iterations. This method is more flexible than other existing shell clustering methods. We demonstrate the effectiveness of the method with simulated and real datasets.聚類分析模糊C殼聚類非線性回歸邊緣辨識ClusteringFuzzy C-ShellsNon-linear Regressionedge recognitionetd