Finite mixture modelling is a popular method in the field of clustering and is beneficial largely due to its soft cluster membership probabilities. A common method for fitting finite mixture models is to employ spectral clustering, which can utilize the expectation-maximization (EM) algorithm. However, the EM algorithm falls victim to a number of issues, including convergence to sub-optimal solutions. We address this issue by developing two novel algorithms that incorporate the spectral decomposition of the data matrix and a non-parametric bootstrap sampling scheme. Simulations display the validity of our algorithms and demonstrate not only their flexibility, but also their computational efficiency and ability to avoid poor solutions when compared to other clustering algorithms for estimating finite mixture models. Our techniques are more consistent in their convergence when compared to other bootstrapped algorithms that fit finite mixture models.

翻译：有限混合模型是聚类领域中一种流行的方法，其优势主要源于其软聚类成员概率。拟合有限混合模型的常用方法是采用谱聚类，该方法可利用期望最大化（EM）算法。然而，EM算法存在若干问题，包括收敛到次优解。针对这一问题，我们开发了两种新型算法，该算法融合了数据矩阵的谱分解与非参数自助抽样方案。模拟实验验证了我们算法的有效性，并展示了其灵活性、计算效率，以及在估计有限混合模型时相较于其他聚类算法避免次优解的能力。与其他拟合有限混合模型的自助算法相比，我们的方法在收敛一致性上表现更优。