本篇論文提出五組新的聚類演算法，第一個方法是適應性Ｃ群集(Adaptive C-Populations, ACP)聚類法。這個方法能夠正確的從未標注類別的資料集中偵測出樣本群聚的地方，以及具關鍵性的小樣本群．第二個方法稱為可能性潛藏變數(Possibilitic Latent Variable, PLV)聚類法。這個方法利用模糊潛藏變數來取代二元潛藏變數，並不採用高斯機率密度函數的假設，而假設一個可能性函數來度量一個樣本和群組之間的關係。這個新的方法可以適應許多不同的分佈，並不會限制在只能處理集中型的高斯分佈。第三個所提出的方法被命名為累加式模糊潛藏變數(Aggregative Fuzzy Latent Variable, AFLV)聚類法。這個方法是使用可能性潛藏變數聚類法相同的假設，但是設計來分析順序型資料。它首先根據各屬性上每一個參考值的出現頻率，估算出不同分佈的機率密度函數；然後再根據不同維度上分佈的相依關係，計算出每一個樣本的最後模糊歸屬度。第四個方法是模糊覆蓋聚類(Fuzzy Cover Clustering, FCC)法。這個方法利用模糊覆蓋來尋找資料集中的支持點。因為這些支持點總會落在資料密集的區域中，它們可以被連接起來構成類別的骨幹。而最終的類別數量可以反應出實際的資料群集狀況。最後一個方法是用來分析隨時間變化的基因表現資料集，找出共同表現樣板，這個方法被稱為變異量為基準的共同表現樣板偵測(Variation-based Co-expression Detection, VCD)法。這個方法一方面延續先前的模糊覆蓋理論，另外再提出一套可以量測基因表現趨勢的度量法．這個方法也不需要事先指定聚類數量，它可以根據基因表現的相似程度，自動找出共同表現的樣板個數。本論文根據各演算法的特性，設計不同的實驗資料集，驗證所提出方法的效能。

The dissertation presents five novel clustering algorithms. The first one is the Adaptive C-Populations (ACP) clustering algorithm. The algorithm is capable of identifying dense regions, as well as influential minor prototypes, in an unlabeled dataset. The second is referred to as the Possibilitic Latent Variable (PLV) clustering algorithm. The algorithm replaces the binary latent variable with the fuzzy latent variable and rejects the use of the Gaussain probability density function in favor of a possibilitic function to measure the cost for associating point with clusters. The algorithm is suitable for many different kinds of populations, not solely for compact Gaussian distribution. The third is entitled as the Aggregative Fuzzy Latent Variable (AFLV) clustering algorithm. It extends the method of the PLV algorithm, and is designed to analyze the ordinal data. The algorithm evaluates membership degrees of objects to mixtures in each attribute according to accumulative occurrences of reference values, and aggregates the degrees of dependent mixtures from different attributes to construct final clusters. The fourth is the Fuzzy Cover Clustering (FCC) algorithm. The fuzzy cover in the algorithm is used to identify the holding points in the dataset. Since these holding points are always located in dense regions, they can service as the backbones of final clusters. The results evolve naturally to reflect actual groups in the data. The last algorithm, designated as the Variation-based Co-expression Detection (VCD) algorithm, is proposed to detect co-expression patterns from time-vary gene expression data. The algorithm adopts the cover and features a new measurement criterion for calculating the degree of change of the expressions between adjacent time points and evaluating their trend similarities. It is also unnecessary to determine the number of clusters in advance since the algorithm automatically detects those genes whose profiles are grouped together. The performances of the proposed algorithms are carefully verified by conducting clustering tasks on the contents of datasets with different characteristics.

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