One-bit principal subspace estimation

This paper proposes a simple sensing and estimation framework, called one-bit sketching, to faithfully recover the principal subspace of a data stream or dataset from a set of one-bit measurements collected at distributed sensors. Each bit indicates the comparison outcome between energy projections of the local sample covariance matrix over a pair of random directions. By leveraging low-dimensional structures, the top eigenvectors of a properly designed surrogate matrix is shown to recover the principal subspace as soon as the number of bit measurements exceeds certain threshold. The sample complexity to obtain reliable comparison outcomes is also obtained. We further develop a low-complexity algorithm to estimate the principal subspace in an online fashion when the bits arrive sequentially at the fusion center. Numerical examples on line spectrum estimation are provided to validate the proposed approach.