本文主要目的為延續以資料間距為基礎的非監督式聚類演算法，並提出一個全新的聚類方式，避免在圓形的切割方式下，將非當前聚類的資料點給切割進來。以適當的假設方法，決定初始聚類中心後，由近至遠地抓取參考點，並計算每次新增線段的最短距離，若新增線段的最短距離與上次最短距離超過一定倍率，則完成參考資料集。並使用此參考資料集，計算參考資料集內所有成員間的距離，並利用標準差的概念，挑選合適的參考資料間距，並計算出擴散半徑。最後，從初始參考點開始以兩倍擴散半徑慢慢擴散，在此擴散半徑中的資料點則為下次擴散點，並歸納為同一聚類，並從原資料集移除已分類資料點。如此週而復始，直至原資料集內沒有任何資料點，所有資料點皆分類完畢後，演算法就此結束。此演算法利用小圓形能組成各種圖形的概念，透過擴散的方式，抓取鄰近的資料點，能更利於延展型聚類的分類結果。最後，為了試驗本文提出的方法，總共模擬了六組不同特性的資料樣本，每個樣本對於資料個數多寡、聚類數量、資料分佈的疏密程度及聚類延展性皆有不同的變化。模擬的結果將以資料分佈為基礎的分監督式聚類分割法的結果做比較，列出實驗結果予以對照。

In this thesis, we proposed a new way of clustering expandable clusters by basing on “An unsupervised clustering approach based on its data distribution” to avoid any resultant cluster to include any data point belong to other clusters. After using an appropriate way to decide the initial clustering center, the algorithm we proposed extracts data points to the referenced subset from the near to far and calculates the minimum length of newly added lines in this time. If the ratio of minimum length this time to the minimum length of previous time is over a certain threshold, the algorithm will stop extracting any more data point and complete the referenced subset. Then the algorithm calculates all the distances among data points located in the referenced subset, and picks an appropriate length by using the concept of standard deviation as the “spreading radius” of the cluster. The algorithm then spreads the cluster area from initial clustering center by using a larger clustering radius that is twice long of the current spreading radius. Any data points within the longer clustering radius will be included in the new but larger cluster. This scenarios will repeat until all the data points have been classified in clusters. Finally, the proposed approach is tested against six sets of sample data with various data distributions, number of clusters and levels of expansions. The experimental result has shown that the proposed approach in this thesis works pretty well on not only simple and grouped data distribution, but also the ones that have high degrees of expansions.

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