Feasible model-based principal component analysis: Joint estimation of rank and error covariance matrix

Real-world inputs to principal component analysis are often corrupted by temporally or spatially correlated errors. There are several methods to mitigate this, e.g., generalized least-square matrix decomposition and maximum likelihood approaches; however, they all require that the number of components or the error covariances to be known in advance, rendering the methods infeasible. To address this issue, a novel method is developed which estimates the number of components and the error covariances at the same time. The method is based on working covariance models, an idea adapted from generalized estimating equations, where the user only specifies the structural form of the error covariances. If the structural form is also unknown, working covariance selection can be used to search for the best structure from a user-defined library. Experiments on synthetic and real data confirm the efficacy of the proposed approach.