Abstract: In this paper, we study the leading eigenvector problem in a statistically distributed setting and propose a communication-efficient algorithm based on Riemannian optimization, which trades local computation for global communication. Theoretical analysis shows that the proposed algorithm linearly converges to the centralized empirical risk minimization solution regarding the number of communication rounds. When the number of data points in local machines is sufficiently large, the proposed algorithm achieves a significant reduction of communication cost over existing distributed PCA algorithms. Superior performance in terms of communication cost of the proposed algorithm is verified on real-world and synthetic datasets.