Mixtures of probabilistic principal component analysis (MPPCA) is a well-known mixture model extension of principal component analysis (PCA). Similar to PCA, MPPCA assumes the data samples in each mixture contain homoscedastic noise. However, datasets with heterogeneous noise across samples are becoming increasingly common, as larger datasets are generated by collecting samples from several sources with varying noise profiles. The performance of MPPCA is suboptimal for data with heteroscedastic noise across samples. This paper proposes a heteroscedastic mixtures of probabilistic PCA technique (HeMPPCAT) that uses a generalized expectation-maximization (GEM) algorithm to jointly estimate the unknown underlying factors, means, and noise variances under a heteroscedastic noise setting. Simulation results illustrate the improved factor estimates and clustering accuracies of HeMPPCAT compared to MPPCA.

翻译：混合概率主成分分析（MPPCA）是主成分分析（PCA）的一种经典混合模型扩展。与PCA类似，MPPCA假设每个混合成分中的数据样本包含同方差噪声。然而，随着通过收集来自多个具有不同噪声特征的来源的样本生成更大规模的数据集，样本间存在异方差噪声的数据集正变得日益普遍。对于跨样本存在异方差噪声的数据，MPPCA的性能并非最优。本文提出了一种异方差混合概率PCA技术（HeMPPCAT），该技术采用广义期望最大化（GEM）算法，在异方差噪声设定下联合估计未知潜在因子、均值及噪声方差。仿真结果表明，与MPPCA相比，HeMPPCAT在因子估计精度和聚类准确度方面均有显著提升。