The mixture of factor analyzers (MFA) model has emerged as a useful tool to perform dimensionality reduction and model-based clustering for heterogeneous data. In seeking the most appropriate number of factors (q) of a MFA model with the number of components (g) fixed a priori, a two-stage procedure is commonly implemented by firstly carrying out parameter estimation over a set of prespecified numbers of factors, and then selecting the best q according to certain penalized likelihood criteria. When the dimensionality of data grows higher, such a procedure can be computationally prohibitive. To overcome this obstacle, we develop an automated learning scheme, called the automated MFA (AMFA) algorithm, to effectively merge parameter estimation and selection of q into a one-stage algorithm. The proposed AMFA procedure that allows for much lower computational cost is also extended to accommodate missing values. Moreover, we explicitly derive the score vector and the empirical information matrix for calculating standard errors associated with the estimated parameters. The potential and applicability of the proposed method are demonstrated through a number of real datasets with genuine and synthetic missing values.

因子分析器（MFA）模型的混合已成为一种有用的工具，可以对异类数据执行降维和基于模型的聚类。在寻求先验地固定了组件数量（g）的MFA模型中最合适的因子数量（q）时，通常通过首先对一组预定数量的因子进行参数估计来实施两阶段过程，然后根据某些惩罚可能性标准选择最佳q。当数据的维数越来越高时，此过程可能会在计算上受到限制。为了克服这一障碍，我们开发了一种称为自动MFA（AMFA）算法的自动学习方案，以有效地合并参数估计和选择q变成一个一级算法。所提议的允许计算成本低得多的AMFA过程也得到了扩展，以适应缺失值。此外，我们显式导出得分向量和经验信息矩阵，以计算与估计参数相关的标准误差。通过大量具有真实和综合缺失值的真实数据集，证明了该方法的潜力和适用性。