本篇論文提出了兩種基於機率模型的分群方法: Multivariate Beta Mixture Model (MBMM)和Flexible Bivariate Beta Mixture Model (FBBMM)。兩個模型的差異包含輸入的變量數(多變量和雙變量)和貝他分布的定義。我們基於期望最大化(Expectation-Maximization, EM)演算法、最大似然估計(maximum likelihood estimation, MLE)和最佳化方法sequential least squares programming optimizer (SLSQP)來估計模型參數。我們對人工合成和真實世界的資料集進行實驗，來確認MBMM和FBBMM的有效性。

This thesis presents two probability model-based clustering methods: the Multivariate Beta Mixture Model (MBMM) and the Flexible Bivariate Beta Mixture Model (FBBMM). Differences between the two models include the number of input variates (multivariate or bivariate) and the definition of the beta distributions. We estimate model parameters based on the Expectation-Maximization (EM) algorithm, the maximum likelihood estimation (MLE), and the sequential least squares programming optimizer (SLSQP). We conduct experiments on the synthetic and the real datasets to confirm the effectiveness of the MBMM and FBBMM.

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