  Principal components analysis (PCA) is a widely used dimension reduction
technique with an extensive range of applications. In this paper, an online
distributed algorithm is proposed for recovering the principal eigenspaces. We
further establish its rate of convergence and show how it relates to the number
of nodes employed in the distributed computation, the effective rank of the
data matrix under consideration, and the gap in the spectrum of the underlying
population covariance matrix. The proposed algorithm is illustrated on low-rank
approximation and $\boldsymbol{k}$-means clustering tasks. The numerical
results show a substantial computational speed-up vis-a-vis standard
distributed PCA algorithms, without compromising learning accuracy.
