Factor analysis parameter estimation from incomplete data

An expectation–maximization (EM) algorithm for factor analysis parameter estimation when observations are missing is developed. In contrast to existing EM algorithms for this problem, the algorithm here is developed assuming the missing observations are not part of the complete data in the EM formulation. The resulting algorithm provides increased computational efficiency through sparse matrix operations. The algorithm is demonstrated on two sparse, high-dimensional data sets that are prohibitively large for existing algorithms: the Netflix movie recommendation data set and the Yahoo! musical item data set. The resulting factor models are applied to predict missing values using conditional mean estimation, achieving root mean square errors of 0.9001 and 24.08 on the Netflix and Yahoo! data sets, respectively.