Trendafilov Nickolay T
University of the West of England, Bristol, UK.
Br J Math Stat Psychol. 2005 May;58(Pt 1):19-31. doi: 10.1111/j.2044-8317.2005.tb00313.x.
The well-known problem of fitting the exploratory factor analysis model is reconsidered where the usual least squares goodness-of-fit function is replaced by a more resistant discrepancy measure, based on a smooth approximation of the lI norm. Fitting the factor analysis model to the sample correlation matrix is a complex matrix optimization problem which requires the structure preservation of the unknown parameters (e.g. positive definiteness). The projected gradient approach is a natural way of solving such data matching problems as especially designed to follow the geometry of the model parameters. Two reparameterizations of the factor analysis model are considered. The approach leads to globally convergent procedures for simultaneous estimation of the factor analysis matrix parameters. Numerical examples illustrate the algorithms and factor analysis solutions.
重新考虑了拟合探索性因子分析模型这一著名问题，其中基于 l1 范数的平滑近似，将常用的最小二乘拟合优度函数替换为更具稳健性的差异度量。将因子分析模型拟合到样本相关矩阵是一个复杂的矩阵优化问题，它要求未知参数保持结构（例如正定）。投影梯度法是解决此类数据匹配问题的自然方法，特别设计用于遵循模型参数的几何结构。考虑了因子分析模型的两种重新参数化。该方法导致了用于同时估计因子分析矩阵参数的全局收敛程序。数值示例说明了算法和因子分析解决方案。
