Factor Analysis from Quadratic Sampling

Factor analysis decomposition, i.e., decomposition of a covariance matrix as a sum of a low-rank positive semidefinite matrix and a diagonal matrix is an important problem in a variety of areas, such as signal processing, machine learning, system identification, and statistical inference. In this letter, the focus is on computing the factor analysis decomposition from a set of quadratic (or symmetric rank-one) measurements of a covariance matrix. Commonly used minimum trace factor analysis heuristic can be adapted to solve this problem when all the measurements are available. However, the resulting convex program is not suitable for processing large-scale or streaming data. Therefore, this letter presents a low-complexity iterative algorithm, which recovers the unknowns through a series of rank-one updates. The iterative algorithm performs better than the convex program when only a finite number of data snapshots are available.